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Data-driven discovery of PDEs in complex datasets
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2019 (English)In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 384, p. 239-252Article in journal (Refereed) Published
Abstract [en]

Many processes in science and engineering can be described by partial differential equations (PDEs). Traditionally, PDEs are derived by considering first principles of physics to derive the relations between the involved physical quantities of interest. A different approach is to measure the quantities of interest and use deep learning to reverse engineer the PDEs which are describing the physical process. In this paper we use machine learning, and deep learning in particular, to discover PDEs hidden in complex data sets from measurement data. We include examples of data from a known model problem, and real data from weather station measurements. We show how necessary transformations of the input data amounts to coordinate transformations in the discovered PDE, and we elaborate on feature and model selection. It is shown that the dynamics of a non-linear, second order PDE can be accurately described by an ordinary differential equation which is automatically discovered by our deep learning algorithm. Even more interestingly, we show that similar results apply in the context of more complex simulations of the Swedish temperature distribution

Place, publisher, year, edition, pages
2019. Vol. 384, p. 239-252
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-361162DOI: 10.1016/j.jcp.2019.01.036ISI: 000460888400013OAI: oai:DiVA.org:uu-361162DiVA, id: diva2:1250010
Funder
Swedish National Infrastructure for Computing (SNIC), SNIC 2017/7-131Göran Gustafsson Foundation for Research in Natural Sciences and MedicineAvailable from: 2018-09-21 Created: 2018-09-21 Last updated: 2019-04-02Bibliographically approved

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