Disentangling Aleatoric and Epistemic Uncertainty in Physics‐Informed Neural Networks: Application to Insulation Material Degradation Prognostics

Physics‐Informed Neural Networks (PINNs) provide a framework for integrating physical laws with data. However, their application to Prognostics and Health Management (PHM) remains constrained by the limited uncertainty quantification (UQ) capabilities. Most existing PINN‐based prognostics approaches are deterministic or account only for epistemic uncertainty, limiting their suitability for risk‐aware decision‐making. This work introduces a heteroscedastic Bayesian Physics‐Informed Neural Network (B‐PINN) framework that jointly models epistemic and aleatoric uncertainty, yielding full predictive posteriors for spatiotemporal insulation material aging estimation. The approach integrates Bayesian Neural Networks (BNNs) with physics‐based residual enforcement and prior distributions, enabling probabilistic inference within a physics‐informed learning architecture. The framework is evaluated on transformer insulation ageing application, validated with a finite‐element thermal model and field measurements from a solar power plant, and benchmarked against deterministic PINNs, dropout‐based PINNs (d‐PINNs), and alternative B‐PINN variants. Results show that the proposed B‐PINN provides improved predictive accuracy and better‐calibrated uncertainty estimates than competing approaches. A systematic sensitivity study further analyzes the impact of boundary‐condition, initial‐condition, and residual sampling strategies on accuracy, calibration, and generalization, and the influence of measurement noise on aleatoric uncertainty. Overall, the findings highlight the capability of Bayesian physics‐informed learning to support uncertainty‐aware prognostics and informed decision‐making in transformer asset management by tracking aleatoric and epistemic sources of uncertainty.