Intelligent Solution of Multiphysics Inverse Problems via Equation-Regularized Neural Networks with Data Scarcity Adaptation

Abstract

Conventional data-intensive AI paradigms for coupled multiphysics systems exhibit fundamental deficiencies: degraded extrapolation performance under measurement-constrained scenarios, absence of governing law constraints in network architecture, and instability when addressing strongly nonlinear ill-posed problems. This work presents a novel computational framework that synergizes differential-equation-constrained deep learning with limited-measurement information recovery. Diverging from standard neural network training, the proposed methodology incorporates governing equation residuals as implicit regularization terms and implements dynamic coefficient balancing for multi-objective optimization, substantially improving solution reliability and physical consistency. Additionally, a noise-suppressing feature reconstruction component is engineered to distill actionable intelligence from corrupted and incomplete observational records. Benchmark evaluations on representative multiphysics parameter identification tasks demonstrate that the developed approach surpasses prevailing physics-guided learning variants and classical discretization techniques in both reconstruction fidelity and computational efficiency. The framework maintains predictive integrity under severely under-sampled operational regimes, furnishing a robust computational tool for automated characterization and inverse reconstruction of intricate coupled-field systems in scientific and industrial contexts.