Reproduce “Physics-informed learning of governing equations from scarce data” on OpenResearch

About this paper

Zhao Chen, Yang Liu, Hao Sun

Researchers at Northeastern University and MIT developed the Physics-informed Deep Learning (PiDL) framework, which integrates deep neural networks with sparse regression and automatic differentiation to discover governing partial differential equations. The framework robustly identifies explicit PDE structures and coefficients from scarce and noisy spatiotemporal data, demonstrating superior performance over existing methods in challenging data conditions and successfully deriving a biological model from experimental measurements.

Key insights

• Integrating deep neural networks for spatiotemporal solution approximation and automatic differentiation with sparse regression allows robust discovery of explicit governing partial differential equations from limited data.
• Embedding physical laws into the loss function through collocation points enforces physical consistency and enables generalization of the discovered PDEs beyond the specific training data.
• An alternating direction optimization algorithm effectively manages the complex, non-convex optimization of both neural network parameters and sparse PDE coefficients, leading to stable convergence.

Summary by alphaXiv.