Development of regularization method for physics problems using PINNs and data augmentation using equation discovery technique

This study proposes a regularization method for high-accuracy prediction by machine learning under small data conditions by combining Physics-Informed Neural Networks (PINNs) and data augmentation based on equation discovery using Sparse Identification of Nonlinear Dynamical Systems (SINDy). PINNs incorporate governing equations into the loss function to enforce physical consistency, while SINDy extracts mathematical models from data, enabling interpolation with continuity and physical interpretability. Validation using crack propagation data (25 points) demonstrated that the combination of SINDy- based augmentation and PINNs reduced the sum of squared errors (SSE) by approximately 28% compared to linear interpolation. The effectiveness of the proposed method was also confirmed for different datasets (59 points). These results indicate that the method is particularly effective in improving learning accuracy for engineering problems where only small amounts of data are available.