{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T04:19:24Z","timestamp":1778645964722,"version":"3.51.4"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"8","license":[{"start":{"date-parts":[[2022,8,3]],"date-time":"2022-08-03T00:00:00Z","timestamp":1659484800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,8,3]],"date-time":"2022-08-03T00:00:00Z","timestamp":1659484800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Helmholtz Association\u2019s Initiative and Networking Fund through Helmholtz AI."},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["2153"],"award-info":[{"award-number":["2153"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Helmholtz Association\u2019s Initiative and Networking Fund through Helmholtz Metadata Collaboration"},{"name":"Helmholtz Association under the Program \u201dEnergy System Design\u201d"},{"name":"Karlsruher Institut f\u00fcr Technologie (KIT)"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Intell"],"published-print":{"date-parts":[[2023,4]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Generated synthetic time series aim to be both realistic by mirroring the characteristics of real-world time series and useful by including characteristics that are useful for subsequent applications, such as forecasting and missing value imputation. To generate such realistic and useful time series, we require generation methods capable of controlling the non-stationarity and periodicities of the generated time series. However, existing approaches do not consider such explicit control. Therefore, in the present paper, we present a novel approach to control non-stationarity and periodicities with calendar and statistical information when generating time series. We first define the requirements for methods to generate time series with non-stationarity and periodicities, which we show are not fulfilled by existing generation methods. Second, we formally describe the novel approach for controlling non-stationarity and periodicities in generated time series. Thirdly, we introduce an exemplary implementation of this approach using a conditional Invertible Neural Network (cINN). We evaluate this cINN empirically in experiments with real-world data sets and compare it to state-of-the-art time series generation methods. Our experiments show that the evaluated cINN can generate time series with controlled periodicities and non-stationarity, and it also generally outperforms the selected benchmarks.<\/jats:p>","DOI":"10.1007\/s10489-022-03742-7","type":"journal-article","created":{"date-parts":[[2022,8,3]],"date-time":"2022-08-03T06:02:30Z","timestamp":1659506550000},"page":"8826-8843","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Controlling non-stationarity and periodicities in time series generation using conditional invertible neural networks"],"prefix":"10.1007","volume":"53","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1923-0848","authenticated-orcid":false,"given":"Benedikt","family":"Heidrich","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3776-2215","authenticated-orcid":false,"given":"Marian","family":"Turowski","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9197-1739","authenticated-orcid":false,"given":"Kaleb","family":"Phipps","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1171-1428","authenticated-orcid":false,"given":"Kai","family":"Schmieder","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2785-7736","authenticated-orcid":false,"given":"Wolfgang","family":"S\u00fc\u00df","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9100-5496","authenticated-orcid":false,"given":"Ralf","family":"Mikut","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3572-9083","authenticated-orcid":false,"given":"Veit","family":"Hagenmeyer","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,8,3]]},"reference":[{"key":"3742_CR1","unstructured":"Abadi M, Agarwal A, Barham P et al (2015) TensorFlow: large-scale machine learning on heterogeneous systems. https:\/\/www.tensorflow.org\/"},{"key":"3742_CR2","unstructured":"Ardizzone L, L\u00fcth C, Kruse J et al (2019) Guided image generation with conditional invertible neural networks. arXiv:1907.023921907.02392"},{"key":"3742_CR3","unstructured":"Chollet F, et al. (2015) Keras. https:\/\/keras.io"},{"key":"3742_CR4","unstructured":"Dinh L, Sohl-Dickstein J, Bengio S (2017) Density estimation using Real NVP. In: 5th International conference on learning representations, ICLR 2017 - conference track proceedings. arXiv:1605.08803"},{"key":"3742_CR5","unstructured":"Donahue C, McAuley J, Puckette M (2019) Adversarial audio synthesis. In: 7th International conference on learning representations, ICLR 2019. arXiv:1802.04208"},{"key":"3742_CR6","doi-asserted-by":"crossref","unstructured":"Dong HW, Hsiao WY, Yang LC et al (2018) MuseGAN: multi-track sequential generative adversarial networks for symbolic music generation and accompaniment. In: The thirty-second AAAI conference on artificial intelligence (AAAI-18), pp 34\u201341. https:\/\/ojs.aaai.org\/index.php\/AAAI\/article\/view\/11312","DOI":"10.1609\/aaai.v32i1.11312"},{"key":"3742_CR7","unstructured":"Dua D, Graff C (2019) UCI machine learning repository. http:\/\/archive.ics.uci.edu\/ml"},{"key":"3742_CR8","unstructured":"Esteban C, Hyland SL, R\u00e4tsch G (2017) Real-valued (medical) time series generation with recurrent conditional GANs. arXiv:1706.0.2633"},{"key":"3742_CR9","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1007\/s13748-013-0040-3","volume":"2","author":"TH Fanaee","year":"2014","unstructured":"Fanaee TH, Gama J (2014) Event labeling combining ensemble detectors and background knowledge. Progress Artif Intell 2:113\u2013127. https:\/\/doi.org\/10.1007\/s13748-013-0040-3","journal-title":"Progress Artif Intell"},{"key":"3742_CR10","doi-asserted-by":"publisher","first-page":"77,587","DOI":"10.1109\/ACCESS.2020.2989350","volume":"8","author":"L Ge","year":"2020","unstructured":"Ge L, Liao W, Wang S et al (2020) Modeling daily load profiles of distribution network for scenario generation using flow-based generative network. IEEE Access 8:77,587\u201377,597. https:\/\/doi.org\/10.1109\/ACCESS.2020.2989350","journal-title":"IEEE Access"},{"key":"3742_CR11","unstructured":"Goodfellow I, Pouget-Abadie J, Mirza M et al (2014) Generative adversarial nets. In: Ghahramani Z, Welling M, Cortes C et al (eds) Advances in neural information processing systems. https:\/\/proceedings.neurips.cc\/paper\/2014\/file\/5ca3e9b122f61f8f06494c97b1afccf3-Paper.pdf, pp 4089\u20134099"},{"key":"3742_CR12","unstructured":"Heidrich B, Bartschat A, Turowski M et al (2021) pywatts: Python workflow automation tool for time series. arXiv:2106.10157"},{"key":"3742_CR13","unstructured":"Hyndman R, Athanasopoulos G (2018) Forecasting: principles and practice, 2nd edn. OTexts: Melbourne, Australia. OTexts.com\/fpp2. accessed on 24.05.2021"},{"key":"3742_CR14","unstructured":"Kingma DP, Dhariwal P (2018) Glow: generative flow with invertible 1x1 convolutions. In: Bengio S, Wallach H, Larochelle H et al (eds) Advances in neural information processing systems, pp 10,215\u201310,224. https:\/\/proceedings.neurips.cc\/paper\/2018\/file\/d139db6a236200b21cc7f752979132d0-Paper.pdf"},{"key":"3742_CR15","unstructured":"Kingma DP, Welling M (2014) Auto-encoding variational Bayes. arXiv:1312.6114"},{"key":"3742_CR16","doi-asserted-by":"publisher","first-page":"1188","DOI":"10.1016\/j.egypro.2018.09.157","volume":"152","author":"J Lan","year":"2018","unstructured":"Lan J, Guo Q, Sun H (2018) Demand side data generating based on conditional generative adversarial networks. Energy Procedia 152:1188\u20131193. https:\/\/doi.org\/10.1016\/j.egypro.2018.09.157","journal-title":"Energy Procedia"},{"key":"3742_CR17","unstructured":"van den Oord A, Dieleman S, Zen H et al (2016) WaveNet: a generative model for raw audio. arXiv:1609.03499"},{"key":"3742_CR18","unstructured":"Paszke A, Gross S, Massa F et al (2019) Pytorch: an imperative style, high-performance deep learning library. In: Wallach H, Larochelle H, Beygelzimer A et al (eds) Advances in neural information processing systems. https:\/\/proceedings.neurips.cc\/paper\/2019\/file\/bdbca288fee7f92f2bfa9f7012727740-Paper.pdf, pp 8024\u20138035"},{"key":"3742_CR19","doi-asserted-by":"publisher","unstructured":"Prenger R, Valle R, Catanzaro B (2019) WaveGlow: a flow-based generative network for speech synthesis. In: 2019 IEEE International conference on acoustics, speech and signal processing (ICASSP), pp 3617\u20133621. https:\/\/doi.org\/10.1109\/ICASSP.2019.8683143","DOI":"10.1109\/ICASSP.2019.8683143"},{"key":"3742_CR20","unstructured":"Ramponi G, Protopapas P, Brambilla M et al (2018) T-CGAN: conditional generative adversarial network for data augmentation in noisy time series with irregular sampling. arXiv:1811.08295"},{"key":"3742_CR21","doi-asserted-by":"publisher","unstructured":"Ross SM (2010) Introduction to probability models, 10th edn. Academic Press. https:\/\/doi.org\/10.1016\/C2009-0-30640-6","DOI":"10.1016\/C2009-0-30640-6"},{"key":"3742_CR22","unstructured":"Xu T, Wenliang LK, Munn M et al (2020) COT-GAN: generating sequential data via causal optimal transport. In: Larochelle H, Ranzato M, Hadsell R et al (eds) Advances in neural information processing systems, pp 8798\u20138809. https:\/\/papers.nips.cc\/paper\/2020\/file\/641d77dd5271fca28764612a028d9c8e-Paper.pdf"},{"key":"3742_CR23","unstructured":"Yoon J, Jarrett D, van der Schaar M (2019) Time-series generative adversarial networks. In: Wallach H, Larochelle H, Beygelzimer A et al (eds) Advances in neural information processing systems, pp 5508\u20135518. https:\/\/proceedings.neurips.cc\/paper\/2019\/file\/c9efe5f26cd17ba6216bbe2a7d26d490-Paper.pdf"}],"container-title":["Applied Intelligence"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-022-03742-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10489-022-03742-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10489-022-03742-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,30]],"date-time":"2023-04-30T09:16:25Z","timestamp":1682846185000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10489-022-03742-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,8,3]]},"references-count":23,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2023,4]]}},"alternative-id":["3742"],"URL":"https:\/\/doi.org\/10.1007\/s10489-022-03742-7","relation":{},"ISSN":["0924-669X","1573-7497"],"issn-type":[{"value":"0924-669X","type":"print"},{"value":"1573-7497","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,8,3]]},"assertion":[{"value":"7 May 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 August 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors have no competing interests to declare that are relevant to the content of this article.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"<!--Emphasis Type='Bold' removed-->Competing interests"}}]}}