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

• URL: http://arxiv.org/abs/2601.03673v1
• Date: Wed, 07 Jan 2026 07:54:09 GMT
• Title: Disentangling Aleatoric and Epistemic Uncertainty in Physics-Informed Neural Networks. Application to Insulation Material Degradation Prognostics
• Authors: Ibai Ramirez, Jokin Alcibar, Joel Pino, Mikel Sanz, Jose I. Aizpurua,
• Abstract summary: Most existing PIN-based prognostics approaches are deterministic or account only for uncertainty, limiting their suitability for risk-aware decision-making.<n>This work introduces a heteroscedastic Bayesian Physics-Informed Neural Network (B-PINN) framework that integrates BNNs with physics-based residual enforcement and prior distributions.<n>Results show that the proposed B-PINN provides improved predictive accuracy and better systematic uncertainty estimates than competing approaches.
• Score: 1.1417805445492082
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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