UA-PBR: Physics-Guided Rejection for Safe Classification in Physical Systems
Abstract
Classification models deployed in safety-critical scientific systems—from subsurface reservoir characterization to medical imaging—must handle inputs that violate the governing physical laws due to sensor failure, data corruption, or adversarial interference. Standard classifiers lack mechanisms to detect such violations and produce confident but physically implausible predic-tions, creating unacceptable operational risk. We introduce UA-PBR, a unified rejection frame- work that combines two complementary signals: a physics-informed autoencoder that detects violations of known governing equations via PDE residual analysis, and a Bayesian convolutional network that quantifies predictive uncertainty through Monte Carlo dropout. Inputs are rejected when either signal exceeds a learned threshold, providing a deterministic safety check (physics) coupled with a probabilistic confidence measure (uncertainty). We ground the approach in decision-theoretic risk minimization and derive stability bounds linking PDE residuals to recon-struction and prediction error under explicit coercivity and Lipschitz assumptions (Lemmas 3.1–3.2, Propositions 3.3–3.4). Evaluation on a Darcy flow benchmark with four corruption types (Gaussian noise, salt-and-pepper, structured artifacts, and PDE-inconsistent perturbations) shows that UA-PBR reduces classification risk by 52–93% on heavily corrupted inputs, depend-ing on corruption type, while accepting 89.7% of clean samples at 99.99% accuracy.…
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