# Bayesian PINNs for uncertainty-aware inverse problems (BPINN-IP)

arXiv: https://arxiv.org/abs/2602.04459 · HTML: https://mlsanity.com/paper/2602.04459/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 16 references that are in the map.
- First posted on arXiv 4 Feb 2026.

## Builds on (most cited first, 7 of 7)

- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Functional Variational Bayesian Neural Networks](https://mlsanity.com/paper/1903.05779/) (2019)
- [Tractable Function-Space Variational Inference in Bayesian Neural Networks](https://mlsanity.com/paper/2312.17199/) (2023)
- [Deep learning electromagnetic inversion with convolutional neural networks](https://mlsanity.com/paper/1812.10247/) (2018)

## Built on by (most cited first, 1 of 1)

- [Multi-fidelity surrogates for mechanics of composites: from co-kriging to multi-fidelity neural networks](https://mlsanity.com/paper/2605.02871/) (2026)

## Abstract (arXiv)

The main contribution of this paper is to develop a hierarchical Bayesian formulation of PINNs for linear inverse problems, which is called BPINN-IP. The proposed methodology extends PINN to account for prior knowledge on the nature of the expected NN output, as well as its weights. Also, as we can have access to the posterior probability distributions, naturally uncertainties can be quantified. Also, variational inference and Monte Carlo dropout are employed to provide predictive means and variances for reconstructed images. Un example of applications to deconvolution and super-resolution is considered, details of the different steps of implementations are given, and some preliminary results are presented.