Technology Category
Computer Vision: Low Level & Physics-based VisionCognitive Modeling & Cognitive Systems: Conceptual Inference and ReasoningHumans and AI: Human-Aware Planning and Behavior Prediction
Hard-Constrained Neural Networks with Physics-Embedded Architecture for Residual Dynamics Learning and Invariant Enforcement in Cyber-Physical Systems
🤖 AI Summary
Modeling inconsistency arises in complex cyber-physical systems where unknown dynamics coexist with known algebraic invariants. Method: We propose physics-embedded neural network frameworks—HRPINN and PHRPINN—that hard-embed known differential equations into a recurrent integrator and enforce algebraic invariants via a prediction-projection mechanism. Our approach integrates physics-informed neural networks, differential-algebraic equation modeling, and projection-based regularization to learn residual dynamics while preserving physical consistency. Contribution/Results: Theoretical analysis and numerical experiments demonstrate high accuracy and data efficiency on battery lifetime prediction and standard constrained benchmarks. Notably, this work is the first to systematically characterize the intrinsic trade-off among physical consistency, computational cost, and numerical stability—providing foundational insights for robust, interpretable learning in constrained dynamical systems.
Technology Category
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Learning residual dynamics in cyber-physical systems with unknown dynamics
Enforcing algebraic invariants through hard structural constraints
Balancing physical consistency with computational cost and stability
Innovation
Methods, ideas, or system contributions that make the work stand out.
Hard-constrained recurrent neural network embeds physics for residual learning
Predict-project mechanism enforces algebraic invariants by design
Theoretical analysis supports representational capacity and practical deployment trade-offs
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