Hard-Constrained Neural Networks with Physics-Embedded Architecture for Residual Dynamics Learning and Invariant Enforcement in Cyber-Physical Systems

TL;DR

This paper introduces physics-embedded neural network architectures that learn residual dynamics and enforce invariants in cyber-physical systems, improving accuracy and data efficiency with theoretical and empirical validation.

Contribution

It proposes HRPINN and PHRPINN architectures that embed physics constraints directly into neural networks for better residual dynamics learning and invariant enforcement.

Findings

High accuracy on battery prognostics DAE

Effective invariant enforcement in benchmarks

Trade-offs between physical consistency and computational cost

Abstract

This paper presents a framework for physics-informed learning in complex cyber-physical systems governed by differential equations with both unknown dynamics and algebraic invariants. First, we formalize the Hybrid Recurrent Physics-Informed Neural Network (HRPINN), a general-purpose architecture that embeds known physics as a hard structural constraint within a recurrent integrator to learn only residual dynamics. Second, we introduce the Projected HRPINN (PHRPINN), a novel extension that integrates a predict-project mechanism to strictly enforce algebraic invariants by design. The framework is supported by a theoretical analysis of its representational capacity. We validate HRPINN on a real-world battery prognostics DAE and evaluate PHRPINN on a suite of standard constrained benchmarks. The results demonstrate the framework's potential for achieving high accuracy and data efficiency, while also highlighting critical trade-offs between physical consistency, computational cost, and numerical stability, providing practical guidance for its deployment.