Physics-informed learning of governing equations from scarce data
This work addresses the challenge of model discovery in science and engineering where large datasets are unavailable, offering a method to derive explicit equations from limited data, though it is incremental as it builds on existing physics-informed and sparse regression techniques.
The authors tackled the problem of discovering governing partial differential equations (PDEs) from scarce and noisy data for nonlinear spatiotemporal systems, introducing a physics-informed deep learning framework that integrates neural networks, physics embedding, and sparse regression to identify PDE structures and parameters, demonstrating efficacy on various PDE systems with different data conditions.
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.