{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:13:08Z","timestamp":1760058788495,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2025,4,27]],"date-time":"2025-04-27T00:00:00Z","timestamp":1745712000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Department of Mathematics at RPTU Kaiserslautern"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Sparse data and an unknown conditional distribution of future values are challenges for managing risks inherent in the evolution of time series. This contribution addresses both aspects through the application of ForGAN, a special form of a generative adversarial network (GAN), to German electricity consumption data. Electricity consumption time series have been selected due to their typical combination of (non-linear) seasonal behavior on different time scales and of local random effects. The primary objective is to demonstrate that ForGAN is able to capture such complicated seasonal figures and to generate data with the correct underlying conditional distribution without data preparation, such as de-seasonalization. In particular, ForGAN does so without assuming an underlying model for the evolution of the time series and is purely data-based. The training and validation procedures are described in great detail. Specifically, a long iteration process of the interplay between the generator and discriminator is required to obtain convergence of the parameters that determine the conditional distribution from which additional artificial data can be generated. Additionally, extensive quality assessments of the generated data are conducted by looking at histograms, auto-correlation structures, and further features comparing the real and the generated data. As a result, the generated data match the conditional distribution of the next consumption value of the training data well. Thus, the trained generator of ForGAN can be used to simulate additional time series of German electricity consumption. This can be seen as a kind of proof for the applicabilty of ForGAN. Through a detailed descriptions of the necessary steps of training and validation procedures, a detailed quality check before the actual use of the simulated data, and by providing the intuition and mathematical background behind ForGAN, this contribution aims to demystify the application of GANs to motivate both theorists and researchers in applied sciences to use them for data generation in similar applications. The proposed framework has laid out a plan for doing so.<\/jats:p>","DOI":"10.3390\/a18050256","type":"journal-article","created":{"date-parts":[[2025,4,28]],"date-time":"2025-04-28T06:23:32Z","timestamp":1745821412000},"page":"256","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Simulating Intraday Electricity Consumption with ForGAN"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9123-3883","authenticated-orcid":false,"given":"Ralf","family":"Korn","sequence":"first","affiliation":[{"name":"Department of Mathematics, RPTU Kaiserslautern-Landau, 67663 Kaiserslautern, Germany"},{"name":"Fraunhofer ITWM, Financial Mathematics, Fraunhofer-Platz 1, 67661 Kaiserslautern, Germany"}]},{"given":"Laurena","family":"Ramadani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, RPTU Kaiserslautern-Landau, 67663 Kaiserslautern, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,27]]},"reference":[{"key":"ref_1","unstructured":"Box, G.E.P., Jenkins, G.M., Reinsel, G.C., and Ljung, G.M. (2015). Time Series Analysis: Forecasting and Control, Wiley."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Hamilton, J.D. (1994). Time Series Analysis, Princeton University Press.","DOI":"10.1515\/9780691218632"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1016\/j.jenvman.2018.04.101","article-title":"The impact of electricity consumption on CO2 emission, carbon footprint, water footprint and ecological footprint: The role of hydropower in an emerging economy","volume":"219","author":"Bello","year":"2018","journal-title":"J. Environ. Manag."},{"key":"ref_4","first-page":"102725","article-title":"Interpolating functions for CO2 emission factors in dynamic simulations: The special case of a heat pump","volume":"53","author":"Valdiserri","year":"2022","journal-title":"Sustain. Energy Technol. Assess."},{"key":"ref_5","unstructured":"Karras, T., Aila, T., Laine, S., and Lehtinen, J. (2018). Progressive Growing of GANs for Improved Quality, Stability, and Variation. arXiv."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Zhu, J., Park, T., Isola, P., and Efros, A. (2017, January 22\u201329). Unpaired Image-to-Image Translation Using Cycle-Consistent Adversarial Networks. Proceedings of the IEEE International Conference on Computer Vision (ICCV), Venice, Italy.","DOI":"10.1109\/ICCV.2017.244"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Isola, P., Zhu, J., Zhou, T., and Efros, A. (2017, January 21\u201326). Image-to-Image Translation with Conditional Adversarial Networks. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Honolulu, HI, USA.","DOI":"10.1109\/CVPR.2017.632"},{"key":"ref_8","unstructured":"Wu, J., Zhang, C., Xue, T., Freeman, W., and Tenenbaum, J. (2016). Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling. arXiv."},{"key":"ref_9","unstructured":"Donahue, C., McAuley, J., and Puckette, M. (2018). Synthesizing Audio with Generative Adversarial Networks. arXiv."},{"key":"ref_10","unstructured":"Vondrick, C., Pirsiavash, H., and Torralba, A. (2016, January 5\u201310). Generating Videos with Scene Dynamics. Proceedings of the Neural Information Processing Systems (NIPS), Barcelona, Spain."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"63868","DOI":"10.1109\/ACCESS.2019.2915544","article-title":"Probabilistic Forecasting of Sensory Data with Generative Adversarial Networks\u2014ForGAN","volume":"7","author":"Koochali","year":"2019","journal-title":"IEEE Access"},{"key":"ref_12","unstructured":"Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., and Bengio, Y. (2014). Generative Adversarial Nets. Advances in Neural Information Processing Systems, MIT Press."},{"key":"ref_13","unstructured":"Korn, R. (2024, September 05). Can We Use GANs for Portfolio Optimization?. Actuview, Available online: https:\/\/actuview.com\/videos\/can-we-use-gans-for-portfolio-optimization-3845."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Saxena, D., and Cao, J. (2020). Generative Adversarial Networks (GANs): Challenges, Solutions, and Future Directions. arXiv.","DOI":"10.1145\/3446374"},{"key":"ref_15","unstructured":"Donahue, J., Kr\u00e4henb\u00fchl, P., and Darrell, T. (2017). Adversarial feature learning. arXiv."},{"key":"ref_16","first-page":"234","article-title":"Understanding the mathematical background of Generative Adversarial Networks (GANs)","volume":"3","author":"Yilmaz","year":"2023","journal-title":"Math. Model. Numer. Simul. Appl."},{"key":"ref_17","unstructured":"Langr, J., and Bok, V. (2019). GANs in Action, Manning."},{"key":"ref_18","unstructured":"Njuki, S. (2024, September 22). MQL5 Wizard Techniques You Should Know (Part 28): GANs Revisited with a Primer on Learning Rates. MetaTrader 5\u2014Trading Systems. Available online: https:\/\/www.mql5.com\/en\/articles\/15349."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1419","DOI":"10.1080\/14697688.2020.1730426","article-title":"Quant GANs: Deep Generation of Financial Time Series","volume":"20","author":"Wiese","year":"2020","journal-title":"Quant. Financ."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long Short-term Memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Comput."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Cho, K., van Merrienboer, B., Bahdanau, D., and Bengio, Y. (2014). On the Properties of Neural Machine Translation: Encoder-Decoder Approaches. arXiv.","DOI":"10.3115\/v1\/W14-4012"},{"key":"ref_22","unstructured":"Zhang, A., Lipton, Z.C., Li, M., and Smola, A.J. (2023). Dive into Deep Learning, Cambridge University Press. Available online: https:\/\/d2l.ai\/d2l-en.pdf."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/18\/5\/256\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T17:22:54Z","timestamp":1760030574000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/18\/5\/256"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,4,27]]},"references-count":22,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2025,5]]}},"alternative-id":["a18050256"],"URL":"https:\/\/doi.org\/10.3390\/a18050256","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2025,4,27]]}}}