Physics-informed architecture search with interpretable constraints for sparsely observed nonlinear governing systems identification

Abstract

The identification of nonlinear governing equations from sparsely observed data remains a fundamental challenge in computational physics and applied mathematics. Traditional data-driven approaches often struggle with sparse datasets, leading to overfitting and models that violate underlying physical laws. While physics-informed neural networks mitigate some of these issues by embedding physical symmetries into the optimization process, their reliance on manually designed architectures limits their adaptability across diverse dynamical systems. This paper introduces a novel framework that integrates neural architecture search with physics-informed learning, augmented by interpretable constraints. By treating the architecture itself as a differentiable variable, the proposed method automates the discovery of optimal network topologies tailored to specific governing systems. Furthermore, we introduce interpretable constraints that enforce sparsity and structural simplicity within the latent representations, enabling the extraction of symbolic mathematical terms directly from the optimized architecture. Extensive analysis demonstrates that this approach significantly enhances predictive accuracy and equation recovery in regimes characterized by high noise and low data volume. The integration of structural priors ensures that the discovered models remain physically consistent and scientifically interpretable, bridging the gap between automated machine learning and classical analytical physics.