Evidential Physics-Informed Neural Networks for Scientific Discovery
Abstract
We present the fundamental theory and implementation guidelines underlying Evidential Physics-Informed Neural Network (E-PINN) -- a novel class of uncertainty-aware PINN. It leverages the marginal distribution loss function of evidential deep learning for estimating uncertainty of outputs, and infers unknown parameters of the PDE via a learned posterior distribution. Validating our model on two illustrative case studies -- the 1D Poisson equation with a Gaussian source and the 2D Fisher-KPP equation, we found that E-PINN generated empirical coverage probabilities that were calibrated significantly better than Bayesian PINN and Deep Ensemble methods. To demonstrate real-world applicability, we also present a brief case study on applying E-PINN to analyze clinical glucose-insulin datasets that have featured in medical research on diabetes pathophysiology.
Cite
@article{arxiv.2509.14568,
title = {Evidential Physics-Informed Neural Networks for Scientific Discovery},
author = {Hai Siong Tan and Kuancheng Wang and Rafe McBeth},
journal= {arXiv preprint arXiv:2509.14568},
year = {2025}
}
Comments
v3: minor revisions. To appear in TAAI 2025. Code available at https://github.com/HaiSiong-Tan/E-PINN