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

2026-01-07

arXiv.org

AI Summary

This work addresses the challenge of jointly quantifying aleatoric and epistemic uncertainties in physics-informed neural networks (PINNs) for predictive health management, a limitation that hinders risk-aware decision-making. To overcome this, we propose a heteroscedastic Bayesian PINN framework that, for the first time, decouples and jointly models both types of uncertainty within a unified architecture. By integrating Bayesian neural networks, physics-based residual constraints, and heteroscedastic noise modeling, our approach enables full spatiotemporal probabilistic posterior estimation. Evaluated on transformer insulation aging prediction using a finite-element thermal model and real-world field data, the method significantly outperforms deterministic PINNs and Dropout-PINNs, achieving higher predictive accuracy alongside well-calibrated, reliable uncertainty quantification. Furthermore, sensitivity analysis is leveraged to optimize data sampling strategies.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• uncertainty quantification
• Physics-Informed Neural Networks
• Prognostics and Health Management
• aleatoric uncertainty
• epistemic uncertainty

Innovation

• Bayesian Physics-Informed Neural Networks
• Aleatoric Uncertainty
• Epistemic Uncertainty
• Uncertainty Quantification
• Prognostics and Health Management