Physics-informed learning of governing equations from scarce data

By Zhao Chen, Yang Liu. Nature Communications, 2020

661 citations recorded by the source corpus.

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 approach called physics-informed neural network with sparse regression to discover governing partial differential equations from scarce and noisy data for nonlinear spatiotemporal systems. In particular, this discovery approach seamlessly integrates the strengths of deep neural networks for rich representation learning, physics embedding, automatic differentiation and sparse regression to approximate the solution of system variables, compute essential derivatives, as well as identify the key derivative terms and parameters that form the structure and explicit expression of the equations. The efficacy and robustness of this method are demonstrated, both numerically and experimentally, on discovering a variety of partial differential equation 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. Recovery of underlying governing laws or equations describing the evolution of complex systems from data can be challenging if dataset is damaged or incomplete. The authors propose a learning approach which allows to discover governing partial differential equations from scarce and noisy data.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e596988b1df3a0bc78bf72c0bfdb21c85eaab6c9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. T. Nissen‐Meyer
2. Benjamin Moseley
3. Andrew Markham

In Statistical and Nonlinear Physics

1. T. Nissen‐Meyer
2. Fujin Wang
3. Benjamin Moseley
4. Zhi Zhai
5. Yi Di
6. Xuefeng Chen
7. Andrew Markham
8. Zhibin Zhao

In Statistics and Probability

1. T. Nissen‐Meyer
2. Benjamin Moseley
3. Andrew Markham

Citations in the corpus

• Physics-informed neural network for lithium-ion battery degradation stable modeling and prognosis (2024, positive): “The promising prospect of physics-informed neural network (PINN) 36,37 lies in amalgamating the strengths of physics-based and data-driven approaches, potentially addressing the aforementioned challenges.”
• Finite basis physics-informed neural networks (FBPINNs): a scalable domain decomposition approach for solving differential equations (2021, methodology): “PINNs have been extended to fractional differential equations [Pang et al., 2019], stochastic differential equations [Yang et al., 2020, Zhang et al., 2019], and have even been used to discover the underlying differential equations themselves [Chen et al., 2020a].”