Interpretable governing-physics discovery using sparsity-gated neural operator priors

Abstract

The extraction of governing physical laws from observational data represents a fundamental challenge in computational sciences, bridging the gap between empirical observation and theoretical formulation. Recent advances in deep learning have introduced powerful tools for system identification, yet these models often operate as opaque mechanisms lacking physical interpretability. This paper presents a novel framework for interpretable governing-physics discovery utilizing sparsity-gated neural operator priors. By integrating neural operators, which learn resolution-invariant mappings between infinite-dimensional function spaces, with a sparsity-inducing gating mechanism, the proposed architecture identifies the parsimonious underlying partial differential equations governing complex dynamical systems. The sparsity-gated prior acts as a stringent inductive bias, effectively distilling the learned infinite-dimensional mapping into a finite, interpretable dictionary of differential operators. We demonstrate that this approach not only matches the predictive accuracy of conventional black-box models but uniquely yields explicitly readable mathematical descriptions of the underlying physics. Extensive theoretical analysis and empirical validations on canonical nonlinear systems, including fluid dynamics and reaction-diffusion processes, confirm the robustness of the framework against observational noise and varying spatial resolutions. This methodology signifies a critical step toward transparent, physics-aware artificial intelligence, ensuring that machine learning models contribute directly to fundamental scientific discovery.