PDE-Net: Learning PDEs from data

Zichao Long, Yiping Lu, Xianzhong Ma, Bin Dong

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

Partial differential equations (PDEs) play a prominent role in many disciplines of science and engineering. PDEs are commonly derived based on empirical observations. However, with the rapid development of sensors, computational power, and data storage in the past decade, huge quantities of data can be easily collected and efficiently stored. Such vast quantity of data offers new opportunities for data-driven discovery of physical laws. Inspired by the latest development of neural network designs in deep learning, we propose a new feed-forward deep network, called PDE- Net, to fulfill two objectives at the same time: To accurately predict dynamics of complex sys-tems and to uncover the underlying hidden PDE models. Comparing with existing approaches, our approach has the most flexibility by learning both differential operators and the nonlinear response function of the underlying PDE model. A special feature of the proposed PDE-Net is that all filters are properly constrained, which enables us to easily identify the governing PDE models while still maintaining the expressive and predictive power of the network. These constrains are carefully designed by fully exploiting the relation between the orders of differential operators and the orders of sum rules of filters (an important concept originated from wavelet theory). Numerical experiments show that the PDE-Net has the potential to uncover the hidden PDE of the observed dynamics, and predict the dynamical behavior for a relatively long time, even in a noisy environment.

Original languageEnglish (US)
Title of host publication35th International Conference on Machine Learning, ICML 2018
EditorsJennifer Dy, Andreas Krause
PublisherInternational Machine Learning Society (IMLS)
Pages5067-5078
Number of pages12
ISBN (Electronic)9781510867963
StatePublished - Jan 1 2018
Event35th International Conference on Machine Learning, ICML 2018 - Stockholm, Sweden
Duration: Jul 10 2018Jul 15 2018

Publication series

Name35th International Conference on Machine Learning, ICML 2018
Volume7

Other

Other35th International Conference on Machine Learning, ICML 2018
CountrySweden
CityStockholm
Period7/10/187/15/18

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Human-Computer Interaction
  • Software

Fingerprint Dive into the research topics of 'PDE-Net: Learning PDEs from data'. Together they form a unique fingerprint.

  • Cite this

    Long, Z., Lu, Y., Ma, X., & Dong, B. (2018). PDE-Net: Learning PDEs from data. In J. Dy, & A. Krause (Eds.), 35th International Conference on Machine Learning, ICML 2018 (pp. 5067-5078). (35th International Conference on Machine Learning, ICML 2018; Vol. 7). International Machine Learning Society (IMLS).