Linking Physical Fidelity to Downstream Performance in Physics-Informed Fault Diagnosis

A critical question in Scientific Machine Learning is whether improving a Physics-Informed Neural Network’s (PINN) physical fidelity translates into downstream task performance. We investigate this link using a three-stage diagnostic framework: PINN-based residual generation, Extreme Value Theory anomaly detection, and Siamese Neural Network (SNN) open-set recognition. To overcome optimization costs, we propose a hierarchical three-phase evaluation protocol that progressively filters models based on physical fidelity (Phase 1), linear separability (Phase 2), and downstream robustness (Phase 3). Applying this to a ring bearing system, we evaluated adaptive PINNs against rigorous, architecturally identical data-driven baselines. Results revealed a paradox: unconstrained baselines achieved superior linear separability on known faults yet over-generalized on novel ones. In contrast, PINNs selected for high physical fidelity produced residuals with lower initial separability but a significantly richer latent structure and topological compactness. We demonstrate that the physics loss acts as an inductive bias for invariance, preventing "shortcut" features. This results in enhanced learnability, quantified by the improvement in cluster quality, leading to a state-of-the-art OSR F1-score of 84.0%. This work empirically establishes that optimizing for physical fidelity improves system robustness and provides a tractable methodology for guiding PINN-based applications.