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

TL;DR

This paper introduces a Bayesian physics-informed neural network framework that jointly models aleatoric and epistemic uncertainties, improving prognostics accuracy and uncertainty calibration for insulation material aging in transformers.

Contribution

It presents a novel heteroscedastic Bayesian PINN that integrates Bayesian neural networks with physics-based constraints for comprehensive uncertainty quantification in prognostics.

Findings

Enhanced predictive accuracy over deterministic PINNs

Better-calibrated uncertainty estimates compared to existing methods

Systematic analysis of sampling strategies on model performance

Abstract

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 ageing 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. Overall, the findings highlight the potential of Bayesian physics-informed learning to support uncertainty-aware prognostics and informed decision-making in transformer asset management.