Learning to Test: Physics-Informed Representation for Dynamical Instability Detection

2026-04-13

AI Summary

This work addresses the challenge of efficiently assessing stability in differential-algebraic equation (DAE) systems subject to stochastic dynamic environments, particularly in high-dimensional or real-time settings where repeated simulation is computationally prohibitive. The authors propose a learning framework for testing that uniquely integrates physical constraints with distributional hypothesis testing. By leveraging a neural dynamical surrogate model and uncertainty-aware calibration, the method constructs a physics-informed, regularized latent representation. This enables stability monitoring at deployment to be cast as a distributional hypothesis test in latent space—eliminating the need for repeated DAE solves. The approach provides an efficient, scalable, and statistically reliable means of detecting instability risks under distributional shifts while maintaining strict control over Type I error rates.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: State Estimation

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

Many safety-critical scientific and engineering systems evolve according to differential-algebraic equations (DAEs), where dynamical behavior is constrained by physical laws and admissibility conditions. In practice, these systems operate under stochastically varying environmental inputs, so stability is not a static property but must be reassessed as the context distribution shifts. Repeated large-scale DAE simulation, however, is computationally prohibitive in high-dimensional or real-time settings. This paper proposes a test-oriented learning framework for stability assessment under distribution shift. Rather than re-estimating physical parameters or repeatedly solving the underlying DAE, we learn a physics-informed latent representation of contextual variables that captures stability-relevant structure and is regularized toward a tractable reference distribution. Trained on baseline data from a certified safe regime, the learned representation enables deployment-time safety monitoring to be formulated as a distributional hypothesis test in latent space, with controlled Type I error. By integrating neural dynamical surrogates, uncertainty-aware calibration, and uniformity-based testing, our approach provides a scalable and statistically grounded method for detecting instability risk in stochastic constrained dynamical systems without repeated simulation.

Problem

• dynamical instability
• distribution shift
• differential-algebraic equations
• stochastic systems
• safety monitoring

Innovation

• physics-informed representation
• distributional hypothesis testing
• dynamical instability detection
• neural dynamical surrogates
• distribution shift