# Evidential Physics-Informed Neural Networks for Scientific Discovery

arXiv: https://arxiv.org/abs/2509.14568 · HTML: https://mlsanity.com/paper/2509.14568/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 25 references that are in the map.
- First posted on arXiv 18 Sep 2025.

## Builds on (most cited first, 8 of 8)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Ensemble deep learning: A review](https://mlsanity.com/paper/2104.02395/) (2021)
- [Assessing Reliability and Challenges of Uncertainty Estimations for Medical Image Segmentation](https://mlsanity.com/paper/1907.03338/) (2019)

## Built on by (most cited first, 2 of 2)

- [Inferring Cosmological Parameters with Evidential Physics-Informed Neural Networks](https://mlsanity.com/paper/2509.24327/) (2025)
- [Uncertainty quantification in neural network-based glucose prediction for diabetes](https://mlsanity.com/paper/2603.04955/) (2026)

## Abstract (arXiv)

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.