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@online{noauthor_elia_nodate,
title = {Elia: de electriciteitsmarkt en -systeem},
url = {https://www.elia.be/nl/elektriciteitsmarkt-en-systeem},
shorttitle = {Elia},
abstract = {Elia deelt de Europese ambitie om een geïntegreerde elektriciteitsmarkt tot stand te brengen en verschillende marktspelers aan te moedigen tot het aanbieden van systeemdiensten.},
urldate = {2023-06-23},
langid = {dutch},
file = {Snapshot:/Users/victormylle/Zotero/storage/7QY94WTW/elektriciteitsmarkt-en-systeem.html:text/html},
}
@article{toubeau_interpretable_2022,
title = {Interpretable Probabilistic Forecasting of Imbalances in Renewable-Dominated Electricity Systems},
volume = {13},
issn = {1949-3029, 1949-3037},
url = {https://ieeexplore.ieee.org/document/9464660/},
doi = {10.1109/TSTE.2021.3092137},
abstract = {High penetration of renewable energy such as wind power and photovoltaic ({PV}) requires large amounts of flexibility to balance their inherent variability. Making an accurate prediction of the future power system imbalance is an efficient approach to reduce these balancing costs. However, the imbalance is affected not only by renewables but also by complex market dynamics and technology constraints, for which the dependence structure is unknown. Therefore, this paper introduces a new architecture of sequence-to-sequence recurrent neural networks to efficiently process time-based information in an interpretable fashion. To that end, the selection of relevant variables is internalized into the model, which provides insights on the relative importance of individual inputs, while bypassing the cumbersome need for data preprocessing. Then, the model is further enriched with an attention mechanism that is tailored to focus on the relevant contextual information, which is useful to better understand the underlying dynamics such as seasonal patterns. Outcomes show that adding modules to generate explainable forecasts makes the model more efficient and robust, thus leading to enhanced performance.},
pages = {1267--1277},
number = {2},
journaltitle = {{IEEE} Transactions on Sustainable Energy},
shortjournal = {{IEEE} Trans. Sustain. Energy},
author = {Toubeau, Jean-Francois and Bottieau, Jeremie and Wang, Yi and Vallee, Francois},
urldate = {2023-09-28},
date = {2022-04},
langid = {english},
file = {Toubeau et al. - 2022 - Interpretable Probabilistic Forecasting of Imbalan.pdf:/Users/victormylle/Zotero/storage/WA7DZBXX/Toubeau et al. - 2022 - Interpretable Probabilistic Forecasting of Imbalan.pdf:application/pdf},
}
@article{bond-taylor_deep_2022,
title = {Deep Generative Modelling: A Comparative Review of {VAEs}, {GANs}, Normalizing Flows, Energy-Based and Autoregressive Models},
volume = {44},
issn = {0162-8828, 2160-9292, 1939-3539},
url = {https://ieeexplore.ieee.org/document/9555209/},
doi = {10.1109/TPAMI.2021.3116668},
shorttitle = {Deep Generative Modelling},
abstract = {Deep generative models are a class of techniques that train deep neural networks to model the distribution of training samples. Research has fragmented into various interconnected approaches, each of which make trade-offs including run-time, diversity, and architectural restrictions. In particular, this compendium covers energy-based models, variational autoencoders, generative adversarial networks, autoregressive models, normalizing flows, in addition to numerous hybrid approaches. These techniques are compared and contrasted, explaining the premises behind each and how they are interrelated, while reviewing current state-of-the-art advances and implementations.},
pages = {7327--7347},
number = {11},
journaltitle = {{IEEE} Transactions on Pattern Analysis and Machine Intelligence},
shortjournal = {{IEEE} Trans. Pattern Anal. Mach. Intell.},
author = {Bond-Taylor, Sam and Leach, Adam and Long, Yang and Willcocks, Chris G.},
urldate = {2023-10-11},
date = {2022-11-01},
langid = {english},
file = {Bond-Taylor et al. - 2022 - Deep Generative Modelling A Comparative Review of.pdf:/Users/victormylle/Zotero/storage/UNAST9UC/Bond-Taylor et al. - 2022 - Deep Generative Modelling A Comparative Review of.pdf:application/pdf},
}
@article{lecun_tutorial_nodate,
title = {A Tutorial on Energy-Based Learning},
abstract = {Energy-Based Models ({EBMs}) capture dependencies between variables by associating a scalar energy to each configuration of the variables. Inference consists in clamping the value of observed variables and finding configurations of the remaining variables that minimize the energy. Learning consists in finding an energy function in which observed configurations of the variables are given lower energies than unobserved ones. The {EBM} approach provides a common theoretical framework for many learning models, including traditional discriminative and generative approaches, as well as graph-transformer networks, conditional random fields, maximum margin Markov networks, and several manifold learning methods.},
author = {{LeCun}, Yann and Chopra, Sumit and Hadsell, Raia and Ranzato, Marc’Aurelio and Huang, Fu Jie},
langid = {english},
file = {LeCun et al. - A Tutorial on Energy-Based Learning.pdf:/Users/victormylle/Zotero/storage/8932975Z/LeCun et al. - A Tutorial on Energy-Based Learning.pdf:application/pdf},
}
@article{gatta_neural_2022,
title = {Neural networks generative models for time series},
volume = {34},
issn = {1319-1578},
url = {https://www.sciencedirect.com/science/article/pii/S1319157822002361},
doi = {10.1016/j.jksuci.2022.07.010},
abstract = {Nowadays, time series are a widely-exploited methodology to describe phenomena belonging to different fields. In fact, electrical consumption can be explained, from a data analysis perspective, with a time series, as for healthcare, financial index, air pollution or parking occupancy rate. Applying time series to different areas of interest has contributed to the exponential rise in interest by both practitioners and academics. On the other side, especially regarding static data, a new trend is acquiring even more relevance in the data analysis community, namely neural network generative approaches. Generative approaches aim to generate new, fake samples given a dataset of real data by implicitly learning the probability distribution underlining data. In this way, several tasks can be addressed, such as data augmentation, class imbalance, anomaly detection or privacy. However, even if this topic is relatively well-established in the literature related to static data regarding time series, the debate is still open. This paper contributes to this debate by comparing four neural network-based generative approaches for time series belonging to the state-of-the-art methodologies in literature. The comparison has been carried out on five public and private datasets and on different time granularities, with a total number of 13 experimental scenario. Our work aims to provide a wide overview of the performances of the compared methodologies when working in different conditions like seasonality, strong autoregressive components and long or short sequences.},
pages = {7920--7939},
number = {10},
journaltitle = {Journal of King Saud University - Computer and Information Sciences},
shortjournal = {Journal of King Saud University - Computer and Information Sciences},
author = {Gatta, Federico and Giampaolo, Fabio and Prezioso, Edoardo and Mei, Gang and Cuomo, Salvatore and Piccialli, Francesco},
urldate = {2023-10-11},
date = {2022-11-01},
keywords = {Deep learning, Generative adversarial networks, Healthcare, Industry 4.0, Time series},
file = {Full Text:/Users/victormylle/Zotero/storage/ZU6BCM28/Gatta et al. - 2022 - Neural networks generative models for time series.pdf:application/pdf;ScienceDirect Snapshot:/Users/victormylle/Zotero/storage/2HSHCJN7/S1319157822002361.html:text/html},
}
@article{dumas_deep_2022,
title = {A deep generative model for probabilistic energy forecasting in power systems: normalizing flows},
volume = {305},
issn = {03062619},
url = {https://linkinghub.elsevier.com/retrieve/pii/S0306261921011909},
doi = {10.1016/j.apenergy.2021.117871},
shorttitle = {A deep generative model for probabilistic energy forecasting in power systems},
abstract = {Greater direct electrification of end-use sectors with a higher share of renewables is one of the pillars to power a carbon-neutral society by 2050. However, in contrast to conventional power plants, renewable energy is subject to uncertainty raising challenges for their interaction with power systems. Scenario-based probabilistic forecasting models have become a vital tool to equip decision-makers. This paper presents to the power systems forecasting practitioners a recent deep learning technique, the normalizing flows, to produce accurate scenario-based probabilistic forecasts that are crucial to face the new challenges in power systems applications. The strength of this technique is to directly learn the stochastic multivariate distribution of the underlying process by maximizing the likelihood. Through comprehensive empirical evaluations using the open data of the Global Energy Forecasting Competition 2014, we demonstrate that this methodology is competitive with other state-of-the-art deep learning generative models: generative adversarial networks and variational autoencoders. The models producing weather-based wind, solar power, and load scenarios are properly compared in terms of forecast value by considering the case study of an energy retailer and quality using several complementary metrics. The numerical experiments are simple and easily reproducible. Thus, we hope it will encourage other forecasting practitioners to test and use normalizing flows in power system applications such as bidding on electricity markets, scheduling power systems with high renewable energy sources penetration, energy management of virtual power plan or microgrids, and unit commitment.},
pages = {117871},
journaltitle = {Applied Energy},
shortjournal = {Applied Energy},
author = {Dumas, Jonathan and Wehenkel, Antoine and Lanaspeze, Damien and Cornélusse, Bertrand and Sutera, Antonio},
urldate = {2023-10-11},
date = {2022-01},
langid = {english},
file = {Dumas et al. - 2022 - A deep generative model for probabilistic energy f.pdf:/Users/victormylle/Zotero/storage/3CW249QI/Dumas et al. - 2022 - A deep generative model for probabilistic energy f.pdf:application/pdf},
}
@article{lu_scenarios_2022,
title = {Scenarios modelling for forecasting day-ahead electricity prices: Case studies in Australia},
volume = {308},
issn = {0306-2619},
url = {https://www.sciencedirect.com/science/article/pii/S0306261921015555},
doi = {10.1016/j.apenergy.2021.118296},
shorttitle = {Scenarios modelling for forecasting day-ahead electricity prices},
abstract = {Electricity prices in spot markets are volatile and can be affected by various factors, such as generation and demand, system contingencies, local weather patterns, bidding strategies of market participants, and uncertain renewable energy outputs. Because of these factors, electricity price forecasting is challenging. This paper proposes a scenario modeling approach to improve forecasting accuracy, conditioning time series generative adversarial networks on external factors. After data pre-processing and condition selection, a conditional {TSGAN} or {CTSGAN} is designed to forecast electricity prices. Wasserstein Distance, weights limitation, and {RMSProp} optimizer are used to ensure that the {CTGAN} training process is stable. By changing the dimensionality of random noise input, the point forecasting model can be transformed into a probabilistic forecasting model. For electricity price point forecasting, the proposed {CTSGAN} model has better accuracy and has better generalization ability than the {TSGAN} and other deep learning methods. For probabilistic forecasting, the proposed {CTSGAN} model can significantly improve the continuously ranked probability score and Winkler score. The effectiveness and superiority of the proposed {CTSGAN} forecasting model are verified by case studies.},
pages = {118296},
journaltitle = {Applied Energy},
shortjournal = {Applied Energy},
author = {Lu, Xin and Qiu, Jing and Lei, Gang and Zhu, Jianguo},
urldate = {2023-10-13},
date = {2022-02-15},
keywords = {Generative adversarial networks, Conditions, Electricity Price, Point forecasting, Probabilistic forecasting},
file = {Lu et al. - 2022 - Scenarios modelling for forecasting day-ahead elec.pdf:/Users/victormylle/Zotero/storage/3XL3T253/Lu et al. - 2022 - Scenarios modelling for forecasting day-ahead elec.pdf:application/pdf;ScienceDirect Snapshot:/Users/victormylle/Zotero/storage/9K2RFGGU/S0306261921015555.html:text/html},
}
@article{gabrielli_data-driven_2022,
title = {Data-driven modeling for long-term electricity price forecasting},
volume = {244},
issn = {03605442},
url = {https://linkinghub.elsevier.com/retrieve/pii/S036054422200010X},
doi = {10.1016/j.energy.2022.123107},
abstract = {Estimating the financial viability of renewable energy investments requires the availability of long-term, finely-resolved electricity prices over the investment lifespan. This entails, however, two major challenges: (i) the combination of extensive time horizons and fine time resolutions, and (ii) the prediction of out-of-sample electricity prices in future energy and market scenarios, or shifts in pricing regime, that were not observed in the past. This paper tackles such challenges by proposing a data-driven model for the long-term prediction of electricity market prices that is based on Fourier analysis. The electricity price is decomposed into components leading to its base evolution, which are described through the amplitudes of the main frequencies of the Fourier series, and components leading to high price volatility, which are described by the residual frequencies. The former are predicted via a regression model that uses as input annual values of relevant energy and market quantities, such as electricity generation, prices and demands. The proposed method shows capable of (i) predicting the most relevant dynamics of the electricity price; (ii) generalization by capturing the market mechanisms of previously unseen electricity markets. These findings support the relevance and validity of data-driven, finely-resolved, long-term predictions and highlight the potential for hybrid data-driven and market-based models.},
pages = {123107},
journaltitle = {Energy},
shortjournal = {Energy},
author = {Gabrielli, Paolo and Wüthrich, Moritz and Blume, Steffen and Sansavini, Giovanni},
urldate = {2023-10-15},
date = {2022-04},
langid = {english},
file = {Gabrielli et al. - 2022 - Data-driven modeling for long-term electricity pri.pdf:/Users/victormylle/Zotero/storage/YHDVP399/Gabrielli et al. - 2022 - Data-driven modeling for long-term electricity pri.pdf:application/pdf},
}
@misc{kollovieh_predict_2023,
title = {Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting},
url = {http://arxiv.org/abs/2307.11494},
shorttitle = {Predict, Refine, Synthesize},
abstract = {Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific forecasting or imputation tasks. In this work, we explore the potential of task-agnostic, unconditional diffusion models for several time series applications. We propose {TSDiff}, an unconditionally trained diffusion model for time series. Our proposed self-guidance mechanism enables conditioning {TSDiff} for downstream tasks during inference, without requiring auxiliary networks or altering the training procedure. We demonstrate the effectiveness of our method on three different time series tasks: forecasting, refinement, and synthetic data generation. First, we show that {TSDiff} is competitive with several task-specific conditional forecasting methods (predict). Second, we leverage the learned implicit probability density of {TSDiff} to iteratively refine the predictions of base forecasters with reduced computational overhead over reverse diffusion (refine). Notably, the generative performance of the model remains intact -- downstream forecasters trained on synthetic samples from {TSDiff} outperform forecasters that are trained on samples from other state-of-the-art generative time series models, occasionally even outperforming models trained on real data (synthesize).},
number = {{arXiv}:2307.11494},
publisher = {{arXiv}},
author = {Kollovieh, Marcel and Ansari, Abdul Fatir and Bohlke-Schneider, Michael and Zschiegner, Jasper and Wang, Hao and Wang, Yuyang},
urldate = {2023-10-15},
date = {2023-07-21},
eprinttype = {arxiv},
eprint = {2307.11494 [cs, stat]},
keywords = {Computer Science - Machine Learning, Computer Science - Artificial Intelligence, Statistics - Machine Learning, {TODO}},
file = {arXiv.org Snapshot:/Users/victormylle/Zotero/storage/PBVHEPD9/2307.html:text/html;Full Text PDF:/Users/victormylle/Zotero/storage/QIBWKG57/Kollovieh et al. - 2023 - Predict, Refine, Synthesize Self-Guiding Diffusio.pdf:application/pdf},
}
@misc{rasul_autoregressive_2021,
title = {Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting},
url = {http://arxiv.org/abs/2101.12072},
abstract = {In this work, we propose {\textbackslash}texttt\{{TimeGrad}\}, an autoregressive model for multivariate probabilistic time series forecasting which samples from the data distribution at each time step by estimating its gradient. To this end, we use diffusion probabilistic models, a class of latent variable models closely connected to score matching and energy-based methods. Our model learns gradients by optimizing a variational bound on the data likelihood and at inference time converts white noise into a sample of the distribution of interest through a Markov chain using Langevin sampling. We demonstrate experimentally that the proposed autoregressive denoising diffusion model is the new state-of-the-art multivariate probabilistic forecasting method on real-world data sets with thousands of correlated dimensions. We hope that this method is a useful tool for practitioners and lays the foundation for future research in this area.},
number = {{arXiv}:2101.12072},
publisher = {{arXiv}},
author = {Rasul, Kashif and Seward, Calvin and Schuster, Ingmar and Vollgraf, Roland},
urldate = {2023-10-15},
date = {2021-02-02},
eprinttype = {arxiv},
eprint = {2101.12072 [cs]},
keywords = {Computer Science - Machine Learning, Computer Science - Artificial Intelligence},
file = {arXiv.org Snapshot:/Users/victormylle/Zotero/storage/8LIRWZ4G/2101.html:text/html;Full Text PDF:/Users/victormylle/Zotero/storage/QPPFJVR5/Rasul et al. - 2021 - Autoregressive Denoising Diffusion Models for Mult.pdf:application/pdf},
}
@article{cramer_normalizing_2022,
title = {Normalizing flow-based day-ahead wind power scenario generation for profitable and reliable delivery commitments by wind farm operators},
volume = {166},
issn = {0098-1354},
url = {https://www.sciencedirect.com/science/article/pii/S0098135422002617},
doi = {10.1016/j.compchemeng.2022.107923},
abstract = {We present a specialized scenario generation method that utilizes forecast information to generate scenarios for day-ahead scheduling problems. In particular, we use normalizing flows to generate wind power scenarios by sampling from a conditional distribution that uses wind speed forecasts to tailor the scenarios to a specific day. We apply the generated scenarios in a stochastic day-ahead bidding problem of a wind electricity producer and analyze whether the scenarios yield profitable decisions. Compared to Gaussian copulas and Wasserstein-generative adversarial networks, the normalizing flow successfully narrows the range of scenarios around the daily trends while maintaining a diverse variety of possible realizations. In the stochastic day-ahead bidding problem, the conditional scenarios from all methods lead to significantly more stable profitable results compared to an unconditional selection of historical scenarios. The normalizing flow consistently obtains the highest profits, even for small sets scenarios.},
pages = {107923},
journaltitle = {Computers \& Chemical Engineering},
shortjournal = {Computers \& Chemical Engineering},
author = {Cramer, Eike and Paeleke, Leonard and Mitsos, Alexander and Dahmen, Manuel},
urldate = {2023-10-18},
date = {2022-10-01},
keywords = {Scenario generation, Stability, Stochastic programming, Wind power},
file = {ScienceDirect Snapshot:/Users/victormylle/Zotero/storage/PT76E9DL/S0098135422002617.html:text/html;Submitted Version:/Users/victormylle/Zotero/storage/M9KFSG3M/Cramer et al. - 2022 - Normalizing flow-based day-ahead wind power scenar.pdf:application/pdf},
}
@inproceedings{zhang_diffusion_2021,
title = {Diffusion Normalizing Flow},
volume = {34},
url = {https://proceedings.neurips.cc/paper/2021/hash/876f1f9954de0aa402d91bb988d12cd4-Abstract.html},
abstract = {We present a novel generative modeling method called diffusion normalizing flow based on stochastic differential equations ({SDEs}). The algorithm consists of two neural {SDEs}: a forward {SDE} that gradually adds noise to the data to transform the data into Gaussian random noise, and a backward {SDE} that gradually removes the noise to sample from the data distribution. By jointly training the two neural {SDEs} to minimize a common cost function that quantifies the difference between the two, the backward {SDE} converges to a diffusion process the starts with a Gaussian distribution and ends with the desired data distribution. Our method is closely related to normalizing flow and diffusion probabilistic models, and can be viewed as a combination of the two. Compared with normalizing flow, diffusion normalizing flow is able to learn distributions with sharp boundaries. Compared with diffusion probabilistic models, diffusion normalizing flow requires fewer discretization steps and thus has better sampling efficiency. Our algorithm demonstrates competitive performance in both high-dimension data density estimation and image generation tasks.},
pages = {16280--16291},
booktitle = {Advances in Neural Information Processing Systems},
publisher = {Curran Associates, Inc.},
author = {Zhang, Qinsheng and Chen, Yongxin},
urldate = {2023-10-18},
date = {2021},
keywords = {{TODO}},
file = {Full Text PDF:/Users/victormylle/Zotero/storage/U45EUFZU/Zhang and Chen - 2021 - Diffusion Normalizing Flow.pdf:application/pdf},
}
@misc{rezende_variational_2016,
title = {Variational Inference with Normalizing Flows},
url = {http://arxiv.org/abs/1505.05770},
abstract = {The choice of approximate posterior distribution is one of the core problems in variational inference. Most applications of variational inference employ simple families of posterior approximations in order to allow for efficient inference, focusing on mean-field or other simple structured approximations. This restriction has a significant impact on the quality of inferences made using variational methods. We introduce a new approach for specifying flexible, arbitrarily complex and scalable approximate posterior distributions. Our approximations are distributions constructed through a normalizing flow, whereby a simple initial density is transformed into a more complex one by applying a sequence of invertible transformations until a desired level of complexity is attained. We use this view of normalizing flows to develop categories of finite and infinitesimal flows and provide a unified view of approaches for constructing rich posterior approximations. We demonstrate that the theoretical advantages of having posteriors that better match the true posterior, combined with the scalability of amortized variational approaches, provides a clear improvement in performance and applicability of variational inference.},
number = {{arXiv}:1505.05770},
publisher = {{arXiv}},
author = {Rezende, Danilo Jimenez and Mohamed, Shakir},
urldate = {2023-10-18},
date = {2016-06-14},
eprinttype = {arxiv},
eprint = {1505.05770 [cs, stat]},
note = {version: 6},
keywords = {Computer Science - Machine Learning, Computer Science - Artificial Intelligence, Statistics - Machine Learning, Statistics - Computation, Statistics - Methodology},
file = {arXiv.org Snapshot:/Users/victormylle/Zotero/storage/2J7MPVV5/1505.html:text/html;Full Text PDF:/Users/victormylle/Zotero/storage/GQWIFAAN/Rezende and Mohamed - 2016 - Variational Inference with Normalizing Flows.pdf:application/pdf},
}
@article{sweidan_probabilistic_nodate,
title = {Probabilistic Prediction in scikit-learn},
abstract = {Adding confidence measures to predictive models should increase the trustworthiness, but only if the models are well-calibrated. Historically, some algorithms like logistic regression, but also neural networks, have been considered to produce well-calibrated probability estimates off-the-shelf. Other techniques, like decision trees and Naive Bayes, on the other hand, are infamous for being significantly overconfident in their probabilistic predictions. In this paper, a large experimental study is conducted to investigate how well-calibrated models produced by a number of algorithms in the scikit-learn library are out-of-the-box, but also if either the built-in calibration techniques Platt scaling and isotonic regression, or Venn-Abers, can be used to improve the calibration. The results show that of the seven algorithms evaluated, the only one obtaining well-calibrated models without the external calibration is logistic regression. All other algorithms, i.e., decision trees, adaboost, gradient boosting, {kNN}, naive Bayes and random forest benefit from using any of the calibration techniques. In particular, decision trees, Naive Bayes and the boosted models are substantially improved using external calibration. From a practitioner’s perspective, the obvious recommendation becomes to incorporate calibration when using probabilistic prediction. Comparing the different calibration techniques, Platt scaling and {VennAbers} generally outperform isotonic regression, on these rather small datasets. Finally, the unique ability of Venn-Abers to output not only well-calibrated probability estimates, but also the confidence in these estimates is demonstrated.},
author = {Sweidan, Dirar and Johansson, Ulf},
langid = {english},
file = {Sweidan and Johansson - Probabilistic Prediction in scikit-learn.pdf:/Users/victormylle/Zotero/storage/8LDMB83T/Sweidan and Johansson - Probabilistic Prediction in scikit-learn.pdf:application/pdf},
}
@article{baskan_scenario-based_2023,
title = {A Scenario-Based Model Comparison for Short-Term Day-Ahead Electricity Prices in Times of Economic and Political Tension},
volume = {16},
issn = {1999-4893},
url = {https://www.mdpi.com/1999-4893/16/4/177},
doi = {10.3390/a16040177},
abstract = {In recent years, energy prices have become increasingly volatile, making it more challenging to predict them accurately. This uncertain market trend behavior makes it harder for market participants, e.g., power plant dispatchers, to make reliable decisions. Machine learning ({ML}) has recently emerged as a powerful artificial intelligence ({AI}) technique to get reliable predictions in particularly volatile and unforeseeable situations. This development makes {ML} models an attractive complement to other approaches that require more extensive human modeling effort and assumptions about market mechanisms. This study investigates the application of machine and deep learning approaches to predict day-ahead electricity prices for a 7-day horizon on the German spot market to give power plants enough time to ramp up or down. A qualitative and quantitative analysis is conducted, assessing model performance concerning the forecast horizon and their robustness depending on the selected hyperparameters. For evaluation purposes, three test scenarios with different characteristics are manually chosen. Various models are trained, optimized, and compared with each other using common performance metrics. This study shows that deep learning models outperform tree-based and statistical models despite or because of the volatile energy prices.},
pages = {177},
number = {4},
journaltitle = {Algorithms},
shortjournal = {Algorithms},
author = {Baskan, Denis E. and Meyer, Daniel and Mieck, Sebastian and Faubel, Leonhard and Klöpper, Benjamin and Strem, Nika and Wagner, Johannes A. and Koltermann, Jan J.},
urldate = {2023-10-22},
date = {2023-03-24},
langid = {english},
file = {Baskan et al. - 2023 - A Scenario-Based Model Comparison for Short-Term D.pdf:/Users/victormylle/Zotero/storage/TU5JX5D4/Baskan et al. - 2023 - A Scenario-Based Model Comparison for Short-Term D.pdf:application/pdf},
}
@misc{narayan_regularization_2021,
title = {Regularization Strategies for Quantile Regression},
url = {http://arxiv.org/abs/2102.05135},
abstract = {We investigate different methods for regularizing quantile regression when predicting either a subset of quantiles or the full inverse {CDF}. We show that minimizing an expected pinball loss over a continuous distribution of quantiles is a good regularizer even when only predicting a specific quantile. For predicting multiple quantiles, we propose achieving the classic goal of non-crossing quantiles by using deep lattice networks that treat the quantile as a monotonic input feature, and we discuss why monotonicity on other features is an apt regularizer for quantile regression. We show that lattice models enable regularizing the predicted distribution to a location-scale family. Lastly, we propose applying rate constraints to improve the calibration of the quantile predictions on specific subsets of interest and improve fairness metrics. We demonstrate our contributions on simulations, benchmark datasets, and real quantile regression problems.},
number = {{arXiv}:2102.05135},
publisher = {{arXiv}},
author = {Narayan, Taman and Wang, Serena and Canini, Kevin and Gupta, Maya},
urldate = {2023-11-14},
date = {2021-02-09},
eprinttype = {arxiv},
eprint = {2102.05135 [cs, stat]},
note = {version: 1},
keywords = {Computer Science - Machine Learning, Statistics - Machine Learning, Statistics - Methodology},
file = {arXiv.org Snapshot:/Users/victormylle/Zotero/storage/DQZGHBIS/2102.html:text/html;Full Text PDF:/Users/victormylle/Zotero/storage/W6WTUZQ3/Narayan et al. - 2021 - Regularization Strategies for Quantile Regression.pdf:application/pdf},
}
@misc{chung_beyond_2021,
title = {Beyond Pinball Loss: Quantile Methods for Calibrated Uncertainty Quantification},
url = {http://arxiv.org/abs/2011.09588},
shorttitle = {Beyond Pinball Loss},
abstract = {Among the many ways of quantifying uncertainty in a regression setting, specifying the full quantile function is attractive, as quantiles are amenable to interpretation and evaluation. A model that predicts the true conditional quantiles for each input, at all quantile levels, presents a correct and efficient representation of the underlying uncertainty. To achieve this, many current quantile-based methods focus on optimizing the so-called pinball loss. However, this loss restricts the scope of applicable regression models, limits the ability to target many desirable properties (e.g. calibration, sharpness, centered intervals), and may produce poor conditional quantiles. In this work, we develop new quantile methods that address these shortcomings. In particular, we propose methods that can apply to any class of regression model, allow for selecting a trade-off between calibration and sharpness, optimize for calibration of centered intervals, and produce more accurate conditional quantiles. We provide a thorough experimental evaluation of our methods, which includes a high dimensional uncertainty quantification task in nuclear fusion.},
number = {{arXiv}:2011.09588},
publisher = {{arXiv}},
author = {Chung, Youngseog and Neiswanger, Willie and Char, Ian and Schneider, Jeff},
urldate = {2023-12-14},
date = {2021-12-09},
eprinttype = {arxiv},
eprint = {2011.09588 [cs, stat]},
keywords = {Computer Science - Machine Learning, Statistics - Machine Learning},
file = {arXiv.org Snapshot:/Users/victormylle/Zotero/storage/WWFHI3UN/2011.html:text/html;Full Text PDF:/Users/victormylle/Zotero/storage/SHMRZ3Q7/Chung et al. - 2021 - Beyond Pinball Loss Quantile Methods for Calibrat.pdf:application/pdf},
}
@online{noauthor_liberalised_nodate,
title = {The liberalised electricity market includes many parties who all have to work together and at the same time try to make a profit. An overview of the most...},
url = {https://www.next-kraftwerke.be/en/knowledge-hub/players-in-the-belgian-power-market/},
abstract = {The liberalised electricity market includes many parties who all have to work together and at the same time try to make a profit. An overview of the most...},
urldate = {2024-03-20},
file = {Snapshot:/Users/victormylle/Zotero/storage/M9XWVY6F/players-in-the-belgian-power-market.html:text/html},
}
@misc{ho_denoising_2020,
title = {Denoising Diffusion Probabilistic Models},
url = {http://arxiv.org/abs/2006.11239},
doi = {10.48550/arXiv.2006.11239},
abstract = {We present high quality image synthesis results using diffusion probabilistic models, a class of latent variable models inspired by considerations from nonequilibrium thermodynamics. Our best results are obtained by training on a weighted variational bound designed according to a novel connection between diffusion probabilistic models and denoising score matching with Langevin dynamics, and our models naturally admit a progressive lossy decompression scheme that can be interpreted as a generalization of autoregressive decoding. On the unconditional {CIFAR}10 dataset, we obtain an Inception score of 9.46 and a state-of-the-art {FID} score of 3.17. On 256x256 {LSUN}, we obtain sample quality similar to {ProgressiveGAN}. Our implementation is available at https://github.com/hojonathanho/diffusion},
number = {{arXiv}:2006.11239},
publisher = {{arXiv}},
author = {Ho, Jonathan and Jain, Ajay and Abbeel, Pieter},
urldate = {2024-04-02},
date = {2020-12-16},
eprinttype = {arxiv},
eprint = {2006.11239 [cs, stat]},
keywords = {Computer Science - Machine Learning, Statistics - Machine Learning},
file = {arXiv Fulltext PDF:/Users/victormylle/Zotero/storage/CYMHCMUT/Ho et al. - 2020 - Denoising Diffusion Probabilistic Models.pdf:application/pdf;arXiv.org Snapshot:/Users/victormylle/Zotero/storage/CE8R84V5/2006.html:text/html},
}
@inproceedings{dumas_probabilistic_2019,
title = {Probabilistic Forecasting of Imbalance Prices in the Belgian Context},
url = {http://arxiv.org/abs/2106.07361},
doi = {10.1109/EEM.2019.8916375},
abstract = {Forecasting imbalance prices is essential for strategic participation in the short-term energy markets. A novel two-step probabilistic approach is proposed, with a particular focus on the Belgian case. The first step consists of computing the net regulation volume state transition probabilities. It is modeled as a matrix computed using historical data. This matrix is then used to infer the imbalance prices since the net regulation volume can be related to the level of reserves activated and the corresponding marginal prices for each activation level are published by the Belgian Transmission System Operator one day before electricity delivery. This approach is compared to a deterministic model, a multi-layer perceptron, and a widely used probabilistic technique, Gaussian Processes.},
pages = {1--7},
booktitle = {2019 16th International Conference on the European Energy Market ({EEM})},
author = {Dumas, Jonathan and Boukas, Ioannis and de Villena, Miguel Manuel and Mathieu, Sébastien and Cornélusse, Bertrand},
urldate = {2024-04-17},
date = {2019-09},
eprinttype = {arxiv},
eprint = {2106.07361 [cs, eess, q-fin]},
keywords = {Computer Science - Machine Learning, Electrical Engineering and Systems Science - Signal Processing, Quantitative Finance - Statistical Finance},
file = {arXiv.org Snapshot:/Users/victormylle/Zotero/storage/3N56FPYP/2106.html:text/html;Full Text PDF:/Users/victormylle/Zotero/storage/958MBH5M/Dumas et al. - 2019 - Probabilistic Forecasting of Imbalance Prices in t.pdf:application/pdf},
}
@article{gunduz_transfer_2023,
title = {Transfer learning for electricity price forecasting},
volume = {34},
issn = {2352-4677},
url = {https://www.sciencedirect.com/science/article/pii/S2352467723000048},
doi = {10.1016/j.segan.2023.100996},
abstract = {Electricity price forecasting is an essential task in all the deregulated markets of the world. The accurate prediction of day-ahead electricity prices is an active research field and available data from various markets can be used as input for forecasting. A collection of models have been proposed for this task, but the fundamental question on how to use the available big data is often neglected. In this paper, we propose to use transfer learning as a tool for utilizing information from other electricity price markets for forecasting. We pre-train a neural network model on source markets and finally do a fine-tuning for the target market. Moreover, we test different ways to use the rich input data from various electricity price markets to forecast 24 steps ahead in hourly frequency. Our experiments on four different day-ahead markets indicate that transfer learning improves the electricity price forecasting performance in a statistically significant manner. Furthermore, we compare our results with state-of-the-art methods in a rolling window scheme to demonstrate the performance of the transfer learning approach. Our method improves the performance of the state-of-the-art algorithms by 7\% for the French market and 3\% for the German market.},
pages = {100996},
journaltitle = {Sustainable Energy, Grids and Networks},
shortjournal = {Sustainable Energy, Grids and Networks},
author = {Gunduz, Salih and Ugurlu, Umut and Oksuz, Ilkay},
urldate = {2024-04-17},
date = {2023-06-01},
keywords = {Artificial neural networks, Electricity price forecasting, Market integration, Transfer learning},
file = {ScienceDirect Snapshot:/Users/victormylle/Zotero/storage/BWI5FHS4/S2352467723000048.html:text/html;Submitted Version:/Users/victormylle/Zotero/storage/62FHBWJ8/Gunduz et al. - 2023 - Transfer learning for electricity price forecastin.pdf:application/pdf},
}
@article{lago_forecasting_2018,
title = {Forecasting spot electricity prices: Deep learning approaches and empirical comparison of traditional algorithms},
volume = {221},
issn = {0306-2619},
url = {https://www.sciencedirect.com/science/article/pii/S030626191830196X},
doi = {10.1016/j.apenergy.2018.02.069},
shorttitle = {Forecasting spot electricity prices},
abstract = {In this paper, a novel modeling framework for forecasting electricity prices is proposed. While many predictive models have been already proposed to perform this task, the area of deep learning algorithms remains yet unexplored. To fill this scientific gap, we propose four different deep learning models for predicting electricity prices and we show how they lead to improvements in predictive accuracy. In addition, we also consider that, despite the large number of proposed methods for predicting electricity prices, an extensive benchmark is still missing. To tackle that, we compare and analyze the accuracy of 27 common approaches for electricity price forecasting. Based on the benchmark results, we show how the proposed deep learning models outperform the state-of-the-art methods and obtain results that are statistically significant. Finally, using the same results, we also show that: (i) machine learning methods yield, in general, a better accuracy than statistical models; (ii) moving average terms do not improve the predictive accuracy; (iii) hybrid models do not outperform their simpler counterparts.},
pages = {386--405},
journaltitle = {Applied Energy},
shortjournal = {Applied Energy},
author = {Lago, Jesus and De Ridder, Fjo and De Schutter, Bart},
urldate = {2024-04-17},
date = {2018-07-01},
keywords = {Deep learning, Electricity price forecasting, Benchmark study},
file = {Full Text:/Users/victormylle/Zotero/storage/SZAAF5RK/Lago et al. - 2018 - Forecasting spot electricity prices Deep learning.pdf:application/pdf;ScienceDirect Snapshot:/Users/victormylle/Zotero/storage/5JH9JLSM/S030626191830196X.html:text/html},
}
@article{weron_electricity_2014,
title = {Electricity price forecasting: A review of the state-of-the-art with a look into the future},
volume = {30},
issn = {0169-2070},
url = {https://www.sciencedirect.com/science/article/pii/S0169207014001083},
doi = {10.1016/j.ijforecast.2014.08.008},
shorttitle = {Electricity price forecasting},
abstract = {A variety of methods and ideas have been tried for electricity price forecasting ({EPF}) over the last 15 years, with varying degrees of success. This review article aims to explain the complexity of available solutions, their strengths and weaknesses, and the opportunities and threats that the forecasting tools offer or that may be encountered. The paper also looks ahead and speculates on the directions {EPF} will or should take in the next decade or so. In particular, it postulates the need for objective comparative {EPF} studies involving (i) the same datasets, (ii) the same robust error evaluation procedures, and (iii) statistical testing of the significance of one model’s outperformance of another.},
pages = {1030--1081},
number = {4},
journaltitle = {International Journal of Forecasting},
shortjournal = {International Journal of Forecasting},
author = {Weron, Rafał},
urldate = {2024-05-02},
date = {2014-10-01},
keywords = {Electricity price forecasting, Autoregression, Day-ahead market, Factor model, Forecast combination, Neural network, Probabilistic forecast, Seasonality},
file = {ScienceDirect Snapshot:/Users/victormylle/Zotero/storage/DDGF263F/S0169207014001083.html:text/html},
}
@article{poggi_electricity_2023,
title = {Electricity Price Forecasting via Statistical and Deep Learning Approaches: The German Case},
volume = {3},
rights = {http://creativecommons.org/licenses/by/3.0/},
issn = {2673-9909},
url = {https://www.mdpi.com/2673-9909/3/2/18},
doi = {10.3390/appliedmath3020018},
shorttitle = {Electricity Price Forecasting via Statistical and Deep Learning Approaches},
abstract = {Our research involves analyzing the latest models used for electricity price forecasting, which include both traditional inferential statistical methods and newer deep learning techniques. Through our analysis of historical data and the use of multiple weekday dummies, we have proposed an innovative solution for forecasting electricity spot prices. This solution involves breaking down the spot price series into two components: a seasonal trend component and a stochastic component. By utilizing this approach, we are able to provide highly accurate predictions for all considered time frames.},
pages = {316--342},
number = {2},
journaltitle = {{AppliedMath}},
author = {Poggi, Aurora and Di Persio, Luca and Ehrhardt, Matthias},
urldate = {2024-05-02},
date = {2023-06},
langid = {english},
note = {Number: 2
Publisher: Multidisciplinary Digital Publishing Institute},
keywords = {deep learning, autoregressive, electricity price forecasting, machine learning, neural network, statistical method, univariate model},
file = {Full Text PDF:/Users/victormylle/Zotero/storage/3IR29RU3/Poggi et al. - 2023 - Electricity Price Forecasting via Statistical and .pdf:application/pdf},
}
@online{noauthor_welcome_nodate,
title = {Welcome — Elia Open Data Portal},
url = {https://opendata.elia.be/pages/home/},
urldate = {2024-05-18},
file = {Welcome — Elia Open Data Portal:/Users/victormylle/Zotero/storage/SYR9PM3Z/home.html:text/html},
}
@online{noauthor_imbalance_nodate,
title = {Imbalance prices per quarter-hour (Historical data)},
url = {https://opendata.elia.be/explore/dataset/ods047/information/?sort=datetime},
abstract = {System imbalance prices applied if an imbalance is found between injections and offtakes in a balance responsible parties ({BRPs}) balance area. When imbalance prices are published on a quarter-hourly basis, the published prices have not yet been validated and can therefore only be used as an indication of the imbalance price.Only after the published prices have been validated can they be used for invoicing purposes. The records for month M are validated after the 15th of month M+1. Contains the historical data and is refreshed daily.This dataset contains data until 21/05/2024 (before {MARI} local go-live).},
urldate = {2024-05-18},
langid = {british},
file = {Snapshot:/Users/victormylle/Zotero/storage/PZI6PTQ2/information.html:text/html},
}
@online{noauthor_measured_nodate,
title = {Measured and forecasted total load on the Belgian grid (Historical data)},
url = {https://opendata.elia.be/explore/dataset/ods001/table/?sort=datetime},
abstract = {Measured and upscaled, most recent, day-ahead and week-ahead forecasts for total load on the Belgian grid.},
urldate = {2024-05-18},
langid = {british},
file = {Snapshot:/Users/victormylle/Zotero/storage/8857IXIQ/table.html:text/html},
}
@online{noauthor_measured_nodate-1,
title = {Measured and forecasted total load on the Belgian grid (Historical data)},
url = {https://opendata.elia.be/explore/dataset/ods001/table/?sort=datetime},
abstract = {Measured and upscaled, most recent, day-ahead and week-ahead forecasts for total load on the Belgian grid.},
urldate = {2024-05-18},
langid = {british},
file = {Snapshot:/Users/victormylle/Zotero/storage/88FLT7BA/table.html:text/html},
}
@online{noauthor_photovoltaic_nodate,
title = {Photovoltaic power production estimation and forecast on Belgian grid (Historical)},
url = {https://opendata.elia.be/explore/dataset/ods032/table/?sort=datetime},
abstract = {Measured and upscaled photovoltaic power generation on the Belgian grid.Please note that the measured and forecast values are in {MW}, it is of the users responsibility to interpret the values as such.},
urldate = {2024-05-18},
langid = {british},
file = {Snapshot:/Users/victormylle/Zotero/storage/7VB5YHYE/table.html:text/html},
}
@online{noauthor_wind_nodate,
title = {Wind power production estimation and forecast on Belgian grid (Historical)},
url = {https://opendata.elia.be/explore/dataset/ods031/information/},
abstract = {Measured and upscaled wind power generation on the Belgian grid.Please note that the measured and forecast values are in {MW}, it is of the users responsibility to interpret the values as such.},
urldate = {2024-05-18},
langid = {british},
file = {Snapshot:/Users/victormylle/Zotero/storage/UTJUH5VQ/information.html:text/html},
}
@online{noauthor_intraday_nodate,
title = {Intraday implicit net position (Belgium's balance)},
url = {https://opendata.elia.be/explore/dataset/ods022/information/?sort=datetime},
abstract = {Net sum of intraday nominations of the implicit capacity allocated for energy exchanges for Belgium.},
urldate = {2024-05-18},
langid = {british},
file = {Snapshot:/Users/victormylle/Zotero/storage/XJ7KBDWG/information.html:text/html},
}

10
Reports/Thesis/acronyms.tex
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@@ -78,11 +78,10 @@
long = Pinball Loss Function
}
\DeclareAcronym{CDF}{
short = CDF,
long = Cumulative Distribution Function
}
@@ -165,3 +164,4 @@
short = MDP,
long = Marginal price of downward activation
}

32
Reports/Thesis/references.bib
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@@ -667,3 +667,35 @@ Publisher: Multidisciplinary Digital Publishing Institute},
langid = {english},
file = {Gneiting and Raftery - 2007 - Strictly Proper Scoring Rules, Prediction, and Est.pdf:/Users/victormylle/Zotero/storage/UTDSA82K/Gneiting and Raftery - 2007 - Strictly Proper Scoring Rules, Prediction, and Est.pdf:application/pdf},
}
@online{team_pinball_nodate,
title = {Pinball Loss Function Definition},
url = {https://www.lokad.com/pinball-loss-function-definition/},
abstract = {The pinball loss function is a metric used to assess the accuracy of a quantile forecast.},
author = {team, Lokad},
urldate = {2024-05-20},
langid = {english},
file = {Snapshot:/Users/victormylle/Zotero/storage/K5Q5MH2R/pinball-loss-function-definition.html:text/html},
}
@article{hochreiter_long_1997,
title = {Long Short-Term Memory},
volume = {9},
doi = {10.1162/neco.1997.9.8.1735},
pages = {1735--1780},
number = {8},
journaltitle = {Neural Computation},
author = {Hochreiter, Sepp and Schmidhuber, Jürgen},
date = {1997},
note = {Publisher: {MIT} Press},
}
@inproceedings{cho_learning_2014,
title = {Learning Phrase Representations using {RNN} Encoder-Decoder for Statistical Machine Translation},
doi = {10.3115/v1/D14-1179},
pages = {1724--1734},
booktitle = {Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing ({EMNLP})},
publisher = {Association for Computational Linguistics},
author = {Cho, Kyunghyun and van Merriënboer, Bart and Bahdanau, Dzmitry and Bengio, Yoshua},
date = {2014},
}

15
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20
Reports/Thesis/sections/background.tex
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@@ -34,7 +34,7 @@ The imbalance price is a crucial factor in the management of electricity grids,
Another key concept is the Area Control Error (ACE), which measures the discrepancy between planned (scheduled) and actual power exchanges in the control area. Specifically, ACE quantifies the difference between the scheduled values and actual values of power exchanges, accounting for frequency deviations. In the Belgian control area, this measurement indicates how much the actual conditions deviate from what was anticipated, providing a real-time assessment of grid balance.
The System Imbalance (SI) is derived by subtracting the NRV from the ACE. This calculation provides a measure of the overall grid imbalance, where SI = ACE - NRV. The value of the SI directly influences the calculation of the imbalance price. The TSO uses the magnitude of the System Imbalance to determine the appropriate imbalance price, ensuring that costs are allocated to market participants based on their contribution to the overall grid imbalance. \cite{elia_tariffs_2022 }
The System Imbalance (SI) is derived by subtracting the NRV from the ACE. This calculation provides a measure of the overall grid imbalance, where SI = ACE - NRV. The value of the SI directly influences the calculation of the imbalance price. The TSO uses the magnitude of the System Imbalance to determine the appropriate imbalance price, ensuring that costs are allocated to market participants based on their contribution to the overall grid imbalance. \cite{elia_tariffs_2022}
The Transmission System Operator (TSO) can activate reserves to maintain grid stability, and these reserves are supplied by entities known as Balancing Service Providers (BSPs). BSPs are crucial participants in the electricity market as they provide the necessary reserve capacity that the TSO can call upon in times of need. Each BSP submits bids to the TSO for the potential activation of these reserves. These bids are detailed and include several key components: the specific type of reserve being offered, the total volume of energy available for activation (measured in megawatt-hours, MWh), the price per MWh at which the BSP is willing to provide this reserve, and a start price which initiates the reserve's deployment. Through this bidding process, the TSO selects the most cost-effective and appropriate offers to ensure the grid's stability and balance.
@@ -118,20 +118,20 @@ There exist many different types of generative models. Some of the most popular
\end{itemize}
\subsection{Quantile Regression}
Any feedforward neural network can also be used to output distributions for the target values. For example, if the distribution is assumed to be normal, the model can output the mean and the variance of the target value. This way, the model can output a distribution for the target value instead of a single forecast value. The outputted distribution allows for multiple samples to be drawn from the distribution. This can be used to generate multiple full-day generations of the NRV.
Any feedforward neural network can also be used to output distributions for the target values. For example, if the distribution is assumed to be normal, the model can output the mean and the standard deviation of the target value. This way, the model can output a distribution for the target value instead of a single forecast value. The outputted distribution allows for multiple samples to be drawn from the distribution. This can be used to generate multiple full-day generations of the NRV.
This method requires that the distributions of the target values be known in advance, or at least assumed. However, it is common for these distributions to be unknown. Fortunately, there is an alternative approach that can estimate the distribution of the target values without prior knowledge of the distribution. This technique is known as quantile regression, introduced by Koenker and Bassett \cite{koenker_regression_1978}.
Quantile regression is a method that uses feedforward neural networks to estimate multiple quantiles of the target values. A quantile is a statistical value of a random variable below which a certain proportion of observations fall. For example, the 25th quantile is the value below which 25\% of the observations fall. By estimating multiple quantiles using quantile regression, the distribution of the target values can be reconstructed. For each quarter of the day, the quantiles of the NRV are estimated by the model and used to reconstruct the distributions of the NRV. For each quarter of the day, a distribution can be reconstructed and samples can be drawn from this distribution. This way, multiple full-day generations of the NRV can be generated.
Quantile regression is a method that uses feedforward neural networks to estimate multiple quantiles of the target value. A quantile is a statistical value of a random variable below which a certain proportion of observations fall. For example, the 25th quantile is the value below which 25\% of the observations fall. An example is shown in Figure \ref{fig:quantile_example}. By estimating multiple quantiles using quantile regression, the cumulative distribution of the target values can be reconstructed. For each quarter of the day, the quantiles of the NRV are estimated by the model and used to reconstruct the distribution of the NRV for that quarter. Samples can then be drawn from this reconstructed distribution. This way, multiple full-day generations of the NRV can be generated.
\begin{figure}[H]
\centering
\includegraphics[width=0.8\textwidth]{images/quantile_regression/cdf_quantiles_example.png}
\caption{Example of a cumulative distribution function and some quantiles. The quantiles are the values below which a certain proportion of observations fall.}
\caption{Example of a cumulative distribution function (CDF) and some quantiles. The quantiles are the values below which a certain proportion of observations fall.}
\label{fig:quantile_example}
\end{figure}
The model outputs quantiles that can be used to reconstruct the cumulative distribution function of a target NRV value. This distribution can then be used to sample the NRV value for a quarter. An example of the output of a quantile regression model is shown in figure \ref{fig:quantile_regression_example}. The output values of the different quantiles are plotted and interpolated to get the cumulative distribution function. In this thesis, the quantiles used are 1\%, 5\%, 10\%, 15\%, 30\%, 40\%, 50\%, 60\%, 70\%, 85\%, 90\%, 95\%, and 99\%. These are chosen to get a good approximation of the cumulative distribution function. More quantiles at the tails of the distribution are used because the edges of the distribution are important. They capture extreme outcomes, which are crucial for risk management, decision-making under uncertainty, and ensuring model robustness and accuracy.
The model outputs quantiles that can be used to reconstruct the cumulative distribution function (CDF) of a target NRV value. This distribution can then be used to sample the NRV value for a quarter. An example of the output of a quantile regression model is shown in figure \ref{fig:quantile_regression_example}. The output values of the different quantiles are plotted and interpolated to get the cumulative distribution function. In this thesis, the quantiles used are 1\%, 5\%, 10\%, 15\%, 30\%, 40\%, 50\%, 60\%, 70\%, 85\%, 90\%, 95\%, and 99\%. These are chosen to get a good approximation of the cumulative distribution function. More quantiles at the tails of the distribution are used because the edges of the distribution are important. They capture extreme outcomes, which are crucial for risk management, decision-making under uncertainty, and ensuring model robustness and accuracy.
\begin{figure}[H]
\centering
@@ -142,7 +142,7 @@ The model outputs quantiles that can be used to reconstruct the cumulative distr
The NRV value for a quarter can be sampled from the reconstructed cumulative distribution function. A full-day prediction for the NRV exists of 96 values. This means 96 cumulative distributions need to be reconstructed and samples need to be drawn from each of the distributions.
The model needs to learn the quantiles of the NRV values. These, however, are not available in the training data. Only the historical NRV values are known. A special loss function is needed to train the model to output the quantiles of the NRV values. This loss function is called the pinball loss function. The loss function is defined as: \\
The model needs to learn the quantiles of the NRV values. These, however, are not available in the training data. Only the historical NRV values are known. A special loss function is needed to train the model to output the quantiles of the NRV values. This loss function is called the pinball loss function \cite{team_pinball_nodate}. The loss function is defined as: \\
\begin{equation}
L_\tau(y, \hat{y}) = \begin{cases}
\tau(y - \hat{y}) & \text{if } y \geq \hat{y} \\
@@ -203,7 +203,7 @@ A simple linear model can be used as a baseline to compare the more complex mode
x_1, ..., x_n & = \text{Input features} \\
\end{align*}
This model needs to be adapted to be used for quantile regression. The model needs to output the quantiles for the target value. This can be done by training multiple linear models for each of the quantiles. The model can be trained using the pinball loss function. The number of parameters in this model is quite low which makes it easier and faster to train. The downside of this model is that it is very simple and might not be able to capture the complexity of the data. The number of parameters of this model is $\text{number of quantiles} \times (\text{number of input features} + 1)$.
This model needs to be adapted to be used for quantile regression. The model needs to output the quantiles for the target value. This can be done by training multiple linear models for each of the quantiles. The model can be trained using the pinball loss function. The number of parameters in this model is quite low which makes it easier and faster to train. The downside of this model is that it is very simple and might not be able to capture the complexity of the data. The number of parameters of this model is $\text{number of quantiles} \times (\text{number of input features} + 1)$. The formula for a linear quantile regression model is shown below:
\begin{equation}
\hat{y}_\tau = \beta_{0, \tau} + \beta_{1, \tau} x_1 + \beta_{2, \tau} x_2 + ... + \beta_{n, \tau} x_n
@@ -226,7 +226,7 @@ Another more complex model that can be used is a Recurrent Neural Network (RNN).
The RNN model can be used to model the NRV data. The input features are structured in a way that the model can learn the sequential patterns in the data. The model can be trained to output the quantiles for the NRV based on the input features using the pinball loss function.
Multiple types of RNN models exist. The two most common types of RNNs are the Long Short-Term Memory (LSTM) and the Gated Recurrent Unit (GRU). The GRU is a simpler version of the LSTM. The GRU has fewer parameters which results in faster training times. The GRU still can capture long-term dependencies in the data and can achieve similar performance to the LSTM. The GRU model has two gates, the reset gate and the update gate. The reset gate determines how much of the past information to forget, and the update gate determines how much of the new information to keep.
Multiple types of RNN models exist. The two most common types of RNNs are the Long Short-Term Memory (LSTM) \cite{hochreiter_long_1997} and the Gated Recurrent Unit (GRU) \cite{cho_learning_2014}. The GRU is a simpler version of the LSTM. The GRU has fewer parameters which results in faster training times. The GRU still can capture long-term dependencies in the data and can achieve similar performance to the LSTM. The GRU model has two gates, the reset gate and the update gate. The reset gate determines how much of the past information to forget, and the update gate determines how much of the new information to keep.
\begin{figure}[H]
\centering
@@ -247,7 +247,7 @@ The input feature structure is designed to provide the model with a comprehensiv
\subsection{Diffusion models}
\subsubsection{Overview}
Diffusion models are a type of probabilistic model designed to generate high-quality, diverse samples from complex data distributions. The way this type of model is trained is unique. The model is trained to reverse an iterative noise process that is applied to the data. This process is called the diffusion process. The model denoises the data in each iteration. During the training, the model learns to reverse the diffusion process. A training sample is transformed into a noise sample by applying the diffusion process. The model is then trained to recover the original sample from the noise sample. The model is trained to maximize the likelihood of the data given the noise. By doing this, the model learns to generate samples from the data distribution. Starting from the noise, the model can generate samples that look like the data. The model can also be conditioned on additional information to generate samples that follow other distributions.
Diffusion models are a type of probabilistic model designed to generate high-quality, diverse samples from complex data distributions. The way this type of model is trained is unique. The model is trained to reverse an iterative noise process that is applied to the data. This process is called the diffusion process. The model denoises the data in each iteration. During the training, the model learns to reverse the diffusion process. A training sample is transformed into a noise sample by applying the diffusion process. The model is then trained to recover the original sample from the noise sample. The model is trained to maximize the likelihood of the data given the noise. By doing this, the model learns to generate samples from the data distribution. Starting from the noise, the model can generate samples that look like the data. The model can also be conditioned on additional information to generate samples that follow other distributions. \cite{sohl-dickstein_deep_2015}
\subsubsection{Applications}
Diffusion models gained popularity in the field of computer vision. They are used for inpainting, super-resolution, image generation, image editing etc. The paper introducing "Denoising Diffusion Probabilistic Models" (DDPM) by \citet{ho_denoising_2020} showed that diffusion models can achieve state-of-the-art results in image generation. This type of model was then applied to other fields like text generation, audio generation etc. The most popular application of diffusion models is still image generation. Many different models and products exist that make use of diffusion models to generate images. Some examples are DALL·E, Stable Diffusion, Midjourney, etc. These models can generate or edit images based on a given text description.
@@ -262,7 +262,7 @@ This method can also be applied to other fields like audio generation, text gene
\end{figure}
\subsubsection{Generation process}
The generation process is quite different in comparison to other models. For example, GANs and VAE generate samples by sampling from a noise distribution and then transforming the noise into a sample that looks like the training data in one step using a generator network. Diffusion models generate samples by starting from a noise distribution and then applying a series of denoising steps to the noise. The diffusion process consists of 3 main components: the forward process, the reverse process and the sampling process.
The generation process is quite different in comparison to other models. For example, GANs and VAEs generate samples by sampling from a noise distribution and then transforming the noise into a sample that looks like the training data in one step using a generator network. Diffusion models generate samples by starting from a noise distribution and then applying a series of denoising steps to the noise. The diffusion process consists of 3 main components: the forward process, the reverse process and the sampling process.
\begin{itemize}
\item \textbf{Forward process} \\

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@@ -2,17 +2,14 @@
\label{sec:policies}
Organizations that own a battery and are active in the electricity market have to make decisions on when to charge and discharge their battery. These decisions are based on the current state of the battery, the current state of the market, and the future state of the market. The future state of the market can be predicted using generative models like the ones discussed in previous sections. The organizations want to maximize their profit by buying electricity when it is cheap and selling electricity when it is expensive. The policies used decide when to charge and discharge the battery. Another important aspect of these policies is to keep the battery in a healthy state. Charging and discharging a battery too much can reduce its lifetime. The policies have to take this into account.
In this thesis, a simple policy is used to optimize the profit made by charging and discharging a battery. The policy is based on the Net Regulation Volume (NRV) predictions for the next day. This shows the potential of using NRV predictions to optimize the policy. In the real world, more complex policies can be used to optimize the profit. These policies can be trained using reinforcement learning or other optimization techniques. Multiple baseline policies are defined to compare the performance of the policy based on NRV predictions.
The simple policy uses two thresholds to decide when to charge and discharge the battery based on the imbalance price. When the imbalance price is below the charging threshold, the battery is fully charged. When the imbalance price is above the discharging threshold, the battery is fully discharged again. This policy is very simple and does not take into account some important aspects.
In this thesis, a simple policy is used to optimize the profit made by charging and discharging a battery. The policy is based on imbalance price predictions for the next day. These imbalance prices are reconstructed using the generated full-day NRV samples. This allows showing the potential of using NRV generations to optimize the policy. In the real world, more complex policies can be used to optimize the profit. These policies can be trained using reinforcement learning or other optimization techniques. Multiple baseline policies are defined to compare the performance of the policy based on NRV predictions.
\subsection{Baselines}
% Baseline fixed thresholds
The most simple baseline policy is to define two fixed thresholds for charging and discharging the battery. These thresholds can be determined by the historical data of the imbalance price. The thresholds can be found by doing a simple grid search for the best thresholds. The thresholds that maximize the profit on the historical data are used as the fixed thresholds. During the optimization, a penalty parameter can be added to the profit function to penalize when the battery is charged or discharged too much.
% Baseline thresholds determined on the previous day
Another baseline policy is to determine the thresholds for charging and discharging the battery based on the NRV of the previous day. This policy is based on the assumption that the NRV of the next day will be similar to the NRV of the previous day. The NRV of the previous day can be seen as the NRV prediction for the next day. The thresholds can then be determined by doing a simple grid search for the best thresholds over the NRV prediction. The same penalty parameter can be added to the profit function to reduce the charge cycles of the battery.
Another baseline policy is to determine the thresholds for charging and discharging the battery based on the NRV of the previous day. This policy is based on the assumption that the NRV of the next day will be similar to the NRV of the previous day. The NRV of the previous day can be seen as the NRV prediction for the next day and is used to reconstruct the imbalance prices. The thresholds can then be determined by doing a simple grid search for the best thresholds over the reconstructed imbalance prices. The same penalty parameter can be added to the profit function to reduce the charge cycles of the battery.
\subsection{Policies based on NRV generations}
% Policy based on NRV generations
The simple baseline policy can be used with the NRV predictions for the next day. First, multiple full-day NRV samples are generated using a generative model. Each of these samples will be seen as a prediction for the NRV of the next day. The charge and discharge thresholds are determined for each of these samples using a simple grid search like in the baseline policy. The mean is taken over all the thresholds to determine the final thresholds for the next day. This results in a policy that uses the NRV samples of the generative model. This policy also uses the penalty parameter to reduce the charge cycles of the battery.
A simple policy can be defined that uses multiple predictions for the NRV of the next day. First, multiple full-day NRV samples are generated using a generative model. Each of these samples will be seen as a prediction for the NRV of the next day. For each of these predictions, the imbalance prices are reconstructed. The charge and discharge thresholds are determined for each of these reconstructed imbalance prices using a simple grid search like in the baseline policy. The mean is taken over all the optimal thresholds to determine the final thresholds for the next day. This results in a policy that uses the NRV samples of the generative model. This policy also uses the penalty parameter to reduce the charge cycles of the battery.

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@@ -1,5 +1,5 @@
\section{Results \& Discussion}
As discussed in the background information, the imbalance prices are based on the Net Regulation Volume (NRV). This means that the imbalance prices can be reconstructed from the sampled NRV. Multiple baselines and models will be compared that forecast and model the NRV using different metrics. The data utilized in this thesis is provided by Elia. Elia makes a lot of data public and provides them in quarterly hour or minute intervals. The data used in this thesis is on a quarterly hourly basis. This makes the number of input features and output features way more manageable and makes the training more computationally efficient. A full-day sample of the NRV exists of 96 values. One value for every quarter. Further research could be done using smaller data intervals to see if this improves the models.
As discussed in the background information, the imbalance prices are based on the Net Regulation Volume (NRV). This means that the imbalance prices can be reconstructed from the sampled NRV. Multiple baselines and models will be compared that forecast and model the NRV using different metrics. The data utilized in this thesis is provided by Elia. Elia makes a lot of data public and provides them in quarterly hour or minute intervals. The data used in this thesis is on a quarterly hourly basis. This makes the number of input features and output features way more manageable and makes the training more computationally efficient. A full-day sample of the NRV exists of 96 values. One value for every quarter. Further research could be done using smaller data intervals to see if this improves the models and the profits of the policies.
\subsection{Data}
Elia offers a variety of data on their website \cite{noauthor_welcome_nodate}. They provide data for the following categories:

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@@ -1,4 +1,4 @@
\begin{thebibliography}{32}
\begin{thebibliography}{34}
\providecommand{\natexlab}[1]{#1}
\providecommand{\url}[1]{\texttt{#1}}
\expandafter\ifx\csname urlstyle\endcsname\relax
@@ -18,27 +18,23 @@ De geliberaliseerde elektriciteitsmarkt omvat vele partijen die allen samen moet
Role of {BRP}, {\natexlab{b}}.
\newblock URL \url{https://www.elia.be/en/electricity-market-and-system/role-of-brp}.
\bibitem[noa({\natexlab{c}})]{noauthor_elia_nodate}
Elia: de electriciteitsmarkt en -systeem, {\natexlab{c}}.
\newblock URL \url{https://www.elia.be/nl/elektriciteitsmarkt-en-systeem}.
\bibitem[noa({\natexlab{d}})]{noauthor_fcr_nodate}
{FCR}, {\natexlab{d}}.
\newblock URL \url{https://www.elia.be/en/electricity-market-and-system/system-services/keeping-the-balance/fcr}.
\bibitem[noa({\natexlab{e}})]{noauthor_afrr_nodate}
{aFRR}, {\natexlab{e}}.
\newblock URL \url{https://www.elia.be/en/electricity-market-and-system/system-services/keeping-the-balance/afrr}.
\bibitem[noa({\natexlab{f}})]{noauthor_mfrr_nodate}
{mFRR}, {\natexlab{f}}.
\newblock URL \url{https://www.elia.be/en/electricity-market-and-system/system-services/keeping-the-balance/mfrr}.
\bibitem[{Elia}()]{elia_tariffs_2022}
{Elia}.
\newblock Tariffs for maintaining and restoring the residual balance of individual access responsible parties.
\newblock URL \url{https://www.elia.be/-/media/project/elia/elia-site/customers/tarrifs-and-invoicing/tariffs-and-invoicing/en/grille-tarifaire-desequilibre-2022-en-v20220214s.pdf}.
\bibitem[noa({\natexlab{c}})]{noauthor_fcr_nodate}
{FCR}, {\natexlab{c}}.
\newblock URL \url{https://www.elia.be/en/electricity-market-and-system/system-services/keeping-the-balance/fcr}.
\bibitem[noa({\natexlab{d}})]{noauthor_afrr_nodate}
{aFRR}, {\natexlab{d}}.
\newblock URL \url{https://www.elia.be/en/electricity-market-and-system/system-services/keeping-the-balance/afrr}.
\bibitem[noa({\natexlab{e}})]{noauthor_mfrr_nodate}
{mFRR}, {\natexlab{e}}.
\newblock URL \url{https://www.elia.be/en/electricity-market-and-system/system-services/keeping-the-balance/mfrr}.
\bibitem[Goodfellow et~al.()Goodfellow, Pouget-Abadie, Mirza, Xu, Warde-Farley, Ozair, Courville, and Bengio]{goodfellow_generative_2014}
Ian~J. Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio.
\newblock Generative adversarial networks.
@@ -69,6 +65,24 @@ Roger Koenker and Gilbert Bassett.
\newblock URL \url{https://www.jstor.org/stable/1913643}.
\newblock Publisher: [Wiley, Econometric Society].
\bibitem[team()]{team_pinball_nodate}
Lokad team.
\newblock Pinball loss function definition.
\newblock URL \url{https://www.lokad.com/pinball-loss-function-definition/}.
\bibitem[Hochreiter and Schmidhuber()]{hochreiter_long_1997}
Sepp Hochreiter and Jürgen Schmidhuber.
\newblock Long short-term memory.
\newblock 9\penalty0 (8):\penalty0 1735--1780.
\newblock \doi{10.1162/neco.1997.9.8.1735}.
\newblock Publisher: {MIT} Press.
\bibitem[Cho et~al.()Cho, van Merriënboer, Bahdanau, and Bengio]{cho_learning_2014}
Kyunghyun Cho, Bart van Merriënboer, Dzmitry Bahdanau, and Yoshua Bengio.
\newblock Learning phrase representations using {RNN} encoder-decoder for statistical machine translation.
\newblock In \emph{Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing ({EMNLP})}, pages 1724--1734. Association for Computational Linguistics.
\newblock \doi{10.3115/v1/D14-1179}.
\bibitem[Ho et~al.()Ho, Jain, and Abbeel]{ho_denoising_2020}
Jonathan Ho, Ajay Jain, and Pieter Abbeel.
\newblock Denoising diffusion probabilistic models.
@@ -148,28 +162,28 @@ Michał Narajewski.
\newblock Probabilistic forecasting of german electricity imbalance prices.
\newblock URL \url{http://arxiv.org/abs/2205.11439}.
\bibitem[noa({\natexlab{g}})]{noauthor_welcome_nodate}
Welcome — elia open data portal, {\natexlab{g}}.
\bibitem[noa({\natexlab{f}})]{noauthor_welcome_nodate}
Welcome — elia open data portal, {\natexlab{f}}.
\newblock URL \url{https://opendata.elia.be/pages/home/}.
\bibitem[noa({\natexlab{h}})]{noauthor_imbalance_nodate}
Imbalance prices per quarter-hour (historical data), {\natexlab{h}}.
\bibitem[noa({\natexlab{g}})]{noauthor_imbalance_nodate}
Imbalance prices per quarter-hour (historical data), {\natexlab{g}}.
\newblock URL \url{https://opendata.elia.be/explore/dataset/ods047/information/?sort=datetime}.
\bibitem[noa({\natexlab{i}})]{noauthor_measured_nodate}
Measured and forecasted total load on the belgian grid (historical data), {\natexlab{i}}.
\bibitem[noa({\natexlab{h}})]{noauthor_measured_nodate}
Measured and forecasted total load on the belgian grid (historical data), {\natexlab{h}}.
\newblock URL \url{https://opendata.elia.be/explore/dataset/ods001/table/?sort=datetime}.
\bibitem[noa({\natexlab{j}})]{noauthor_photovoltaic_nodate}
Photovoltaic power production estimation and forecast on belgian grid (historical), {\natexlab{j}}.
\bibitem[noa({\natexlab{i}})]{noauthor_photovoltaic_nodate}
Photovoltaic power production estimation and forecast on belgian grid (historical), {\natexlab{i}}.
\newblock URL \url{https://opendata.elia.be/explore/dataset/ods032/table/?sort=datetime}.
\bibitem[noa({\natexlab{k}})]{noauthor_wind_nodate}
Wind power production estimation and forecast on belgian grid (historical), {\natexlab{k}}.
\bibitem[noa({\natexlab{j}})]{noauthor_wind_nodate}
Wind power production estimation and forecast on belgian grid (historical), {\natexlab{j}}.
\newblock URL \url{https://opendata.elia.be/explore/dataset/ods031/information/}.
\bibitem[noa({\natexlab{l}})]{noauthor_intraday_nodate}
Intraday implicit net position (belgium's balance), {\natexlab{l}}.
\bibitem[noa({\natexlab{k}})]{noauthor_intraday_nodate}
Intraday implicit net position (belgium's balance), {\natexlab{k}}.
\newblock URL \url{https://opendata.elia.be/explore/dataset/ods022/information/?sort=datetime}.
\bibitem[Dhariwal and Nichol()]{dhariwal_diffusion_2021}

83
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@@ -8,8 +8,6 @@ A level-1 auxiliary file: sections/literature_study.aux
The style file: unsrtnat.bst
A level-1 auxiliary file: sections/appendix.aux
Database file #1: references.bib
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--line 2 of file references.bib
Warning--entry type for "noauthor_welcome_nodate" isn't style-file defined
--line 365 of file references.bib
Warning--entry type for "noauthor_imbalance_nodate" isn't style-file defined
@@ -34,14 +32,15 @@ Warning--entry type for "noauthor_afrr_nodate" isn't style-file defined
--line 502 of file references.bib
Warning--entry type for "noauthor_mfrr_nodate" isn't style-file defined
--line 509 of file references.bib
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--line 671 of file references.bib
Warning--empty year in commission_for_electricity_and_gas_regulation_creg_study_2023
Warning--empty year in noauthor_geliberaliseerde_nodate
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Warning--empty year in goodfellow_generative_2014
Warning--empty year in kingma_auto-encoding_2022
Warning--empty year in rezende_variational_2015
@@ -50,6 +49,12 @@ Warning--empty year in sohl-dickstein_deep_2015
Warning--empty journal in koenker_regression_1978
Warning--empty year in koenker_regression_1978
Warning--empty year in koenker_regression_1978
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Warning--empty year in cho_learning_2014
Warning--empty year in ho_denoising_2020
Warning--empty journal in gneiting_strictly_2007
Warning--empty year in gneiting_strictly_2007
@@ -82,45 +87,45 @@ Warning--empty year in noauthor_wind_nodate
Warning--empty year in noauthor_intraday_nodate
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@@ -1824,14 +1820,10 @@ File: images/diffusion/results/samples/Diffusion_Test_Example_7008.jpeg Graphic
<use images/diffusion/results/samples/Diffusion_Test_Example_7008.jpeg>
Package pdftex.def Info: images/diffusion/results/samples/Diffusion_Test_Example_7008.jpeg used on input line 154.
(pdftex.def) Requested size: 172.99498pt x 86.16971pt.
[57
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Package natbib Warning: There were undefined citations.
(./verslag.aux (./sections/introduction.aux) (./sections/background.aux) (./sections/policies.aux) (./sections/literature_study.aux) (./sections/appendix.aux))
] [59]) (./verslag.aux (./sections/introduction.aux) (./sections/background.aux) (./sections/policies.aux) (./sections/literature_study.aux) (./sections/appendix.aux))
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Reports/Thesis/verslag.pdf
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4
Reports/Thesis/verslag.toc
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@@ -16,7 +16,7 @@
\contentsline {subsection}{\numberline {3.5}Evaluation}{18}{subsection.3.5}%
\contentsline {section}{\numberline {4}Policies}{20}{section.4}%
\contentsline {subsection}{\numberline {4.1}Baselines}{20}{subsection.4.1}%
\contentsline {subsection}{\numberline {4.2}Policies based on NRV generations}{21}{subsection.4.2}%
\contentsline {subsection}{\numberline {4.2}Policies based on NRV generations}{20}{subsection.4.2}%
\contentsline {section}{\numberline {5}Literature Study}{22}{section.5}%
\contentsline {subsection}{\numberline {5.1}Day-Ahead Electricity Price Forecasting}{22}{subsection.5.1}%
\contentsline {subsection}{\numberline {5.2}Imbalance Price Forecasting}{23}{subsection.5.2}%
@@ -33,4 +33,4 @@
\contentsline {subsubsection}{\numberline {6.5.1}Baselines}{46}{subsubsection.6.5.1}%
\contentsline {subsubsection}{\numberline {6.5.2}Policy using generated NRV samples}{47}{subsubsection.6.5.2}%
\contentsline {section}{\numberline {7}Conclusion}{51}{section.7}%
\contentsline {section}{\numberline {A}Appendix}{57}{appendix.A}%
\contentsline {section}{\numberline {A}Appendix}{58}{appendix.A}%

25
src/training_scripts/non_autoregressive_quantiles.py
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@@ -5,7 +5,7 @@ clearml_helper = ClearMLHelper(
project_name="Thesis/NrvForecast"
)
task = clearml_helper.get_task(
task_name="NAQR: Non Linear (2 - 256)"
task_name="NAQR: Non Linear (4 - 512)"
)
task.execute_remotely(queue_name="default", exit_process=True)
@@ -45,7 +45,7 @@ data_config.NOMINAL_NET_POSITION = False
data_config = task.connect(data_config, name="data_features")
data_processor = DataProcessor(data_config, path="", lstm=True)
data_processor = DataProcessor(data_config, path="", lstm=False)
data_processor.set_batch_size(64)
data_processor.set_full_day_skip(True)
@@ -68,8 +68,8 @@ else:
model_parameters = {
"learning_rate": 0.0001,
"hidden_size": 256,
"num_layers": 2,
"hidden_size": 512,
"num_layers": 4,
"dropout": 0.2,
}
@@ -77,24 +77,15 @@ model_parameters = task.connect(model_parameters, name="model_parameters")
# linear_model = LinearRegression(inputDim, len(quantiles) * 96)
# non_linear_model = NonLinearRegression(
# inputDim,
# len(quantiles) * 96,
# hiddenSize=model_parameters["hidden_size"],
# numLayers=model_parameters["num_layers"],
# dropout=model_parameters["dropout"],
# )
lstm_model = GRUModel(
non_linear_model = NonLinearRegression(
inputDim,
len(quantiles) * 96,
hidden_size=model_parameters["hidden_size"],
num_layers=model_parameters["num_layers"],
hiddenSize=model_parameters["hidden_size"],
numLayers=model_parameters["num_layers"],
dropout=model_parameters["dropout"],
)
model = lstm_model
model = non_linear_model
model.output_size = 96
optimizer = torch.optim.Adam(model.parameters(), lr=model_parameters["learning_rate"])