{"ID":2869118,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.14568","arxiv_id":"2509.14568","title":"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.","short_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...","url_abs":"https://arxiv.org/abs/2509.14568","url_pdf":"https://arxiv.org/pdf/2509.14568v3","authors":"[\"Hai Siong Tan\",\"Kuancheng Wang\",\"Rafe McBeth\"]","published":"2025-09-18T03:06:14Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"physics.comp-ph\"]","methods":"[]","has_code":false}