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

• URL: http://arxiv.org/abs/2604.10967v1
• Date: Mon, 13 Apr 2026 04:12:40 GMT
• Title: Learning to Test: Physics-Informed Representation for Dynamical Instability Detection
• Abstract summary: This paper proposes a test-oriented learning framework for stability assessment under distribution shift.<n>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.
• Score: 12.003388826045928
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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