Uncertainty-Aware Classifier with Physics-Based Rejection (UA-PBR): A Proof-of-Concept Under Computational Constraints—Revised Version

Deep learning classifiers deployed in scientific applications often encounter inputs that violate physical laws (e.g., due to sensor failure or corruption). Standard methods cannot detect such violations and may produce confident but wrong predictions. We propose UA-PBR, a framework that combines a physics-informed autoencoder (to detect physics violations) with a Bayesian CNN (to quantify predictive uncertainty). Inputs are rejected if either the PDE residual exceeds a threshold or the predictive entropy is too high. As a proof-of-concept, we evaluate UA-PBR on a synthetic Darcy flow dataset (32 × 32 grid) under severe computational constraints (Google Colab, 10 seeds). Despite these limitations, UA-PBR reduces classification risk by over 90% on heavily corrupted samples while accepting 89.7% of clean inputs with 99.99% accuracy on accepted samples. Ablation studies confirm that both components contribute synergistically. These preliminary results on a synthetic benchmark illustrate the potential of physics-aware rejection and motivate further investigation with larger-scale experiments. Code is available at: https://github.com/UA-PBR/UA-PBR.