Incorporating Lasso Regression to Physics-Informed Neural Network for Inverse PDE Problem

Partial Differential Equation (PDE) is among the most fundamental tools employed to model dynamic systems. Existing PDE modeling methods are typically derived from established knowledge and known phenomena, which are time-consuming and labor-intensive. Recently, discovering governing PDEs from collected actual data via Physics Informed Neural Networks (PINNs) provides a more efficient way to analyze fresh dynamic systems and establish PED models. This study proposes Sequentially Threshold Least Squares-Lasso (STLasso), a module constructed by incorporating Lasso regression into the Sequentially Threshold Least Squares (STLS) algorithm, which can complete sparse regression of PDE coefficients with the constraints of l0 norm. It further introduces PINN-STLasso, a physics informed neural network combined with Lasso sparse regression, able to find underlying PDEs from data with reduced data requirements and better interpretability. In addition, this research conducts experiments on canonical inverse PDE problems and compares the results to several recent methods. The results demonstrated that the proposed PINN-STLasso outperforms other methods, achieving lower error rates even with less data.