Physics-informed learning of governing equations from scarce data

Abstract

Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and engineering disciplines. This work introduces a novel physics-informed deep learning framework to discover governing partial differential equations (PDEs) from scarce and noisy data for nonlinear spatiotemporal systems. In particular, this approach seamlessly integrates the strengths of deep neural networks for rich representation learning, physics embedding, automatic differentiation and sparse regression to (1) approximate the solution of system variables, (2) compute essential derivatives, as well as (3) identify the key derivative terms and parameters that form the structure and explicit expression of the PDEs. The efficacy and robustness of this method are demonstrated, both numerically and experimentally, on discovering a variety of PDE systems with different levels of data scarcity and noise accounting for different initial/boundary conditions. The resulting computational framework shows the potential for closed-form model discovery in practical applications where large and accurate datasets are intractable to capture.

46 pages; 1 table, 6 figures and 3 extended data figures in main text; 2 tables and 12 figures in supplementary information

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Cited by in corpus (24)

• Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations
• Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems
• PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs
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