Learning generative neural networks with physics knowledge

Journal Article · 16 May 2022 · Research in the Mathematical Sciences

DOI: https://doi.org/10.1007/s40687-022-00329-z · OSTI ID:2481112

Xu, Kailai ^[1]; Zhu, Weiqiang ^[1]; Darve, Eric  ^[1]

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1. Stanford University, CA (United States)

Deep generative neural networks have enabled modeling complex distributions, but incorporating physics knowledge into the neural networks is still challenging and is at the core of current physics-based machine learning research. To this end, we propose a physics generative neural network (PhysGNN), a new class of generative neural networks for learning unknown distributions in a physical system described by partial differential equations (PDE). PhysGNN couples PDE systems with generative neural networks. It is a fully differentiable model that allows back-propagation of gradients through both numerical PDE solvers and generative neural networks, and is trained by minimizing the discrete Wasserstein distance between generated and observed probability distributions of the PDE outputs using the stochastic gradient descent method. Moreover, PhysGNN does not require adversarial training like standard generative neural networks, which offers better stability than adversarial training. We show that PhysGNN can learn complex distributions in stochastic inverse problems, where conventional methods such as maximum likelihood estimation and momentum matching methods may be inapplicable when little knowledge is known about the form of unknown distributions or the physical model is too complex. Furthermore, our method allows physics-based generative neural network training for learning complex distributions in the context of differential equations.

• Research Organization: Stanford University, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• Grant/Contract Number: SC0019205; SC0019453
• OSTI ID: 2481112
• Journal Information: Research in the Mathematical Sciences, Journal Name: Research in the Mathematical Sciences Journal Issue: 2 Vol. 9; ISSN 2522-0144
• Publisher: SpringerCopyright Statement
• Country of Publication: United States
• Language: English