# Adaptive Physics-Informed Neural Networks for Markov-Chain Monte Carlo

arXiv: https://arxiv.org/abs/2008.01604 · HTML: https://mlsanity.com/paper/2008.01604/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Aug 2020.

## Built on by (most cited first, 6 of 6)

- [Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing](https://mlsanity.com/paper/2211.07377/) (2022)
- [Adaptive operator learning for infinite-dimensional Bayesian inverse problems](https://mlsanity.com/paper/2310.17844/) (2023)
- [Active Learning with Multifidelity Modeling for Efficient Rare Event Simulation](https://mlsanity.com/paper/2106.13790/) (2021)
- [Damper-B-PINN: Damper Characteristics-Based Bayesian Physics-Informed Neural Network for Vehicle State Estimation](https://mlsanity.com/paper/2502.20772/) (2025)
- [Hamiltonian Neural Networks approach to fuzzball geodesics](https://mlsanity.com/paper/2502.20881/) (2025)
- [DBPnet: Damper Characteristics-Based Bayesian Physics-Informed Neural Network for Wheel Load Estimation](https://mlsanity.com/paper/2605.24860/) (2026)

## Abstract (arXiv)

In this paper, we propose the Adaptive Physics-Informed Neural Networks (APINNs) for accurate and efficient simulation-free Bayesian parameter estimation via Markov-Chain Monte Carlo (MCMC). We specifically focus on a class of parameter estimation problems for which computing the likelihood function requires solving a PDE. The proposed method consists of: (1) constructing an offline PINN-UQ model as an approximation to the forward model; and (2) refining this approximate model on the fly using samples generated from the MCMC sampler. The proposed APINN method constantly refines this approximate model on the fly and guarantees that the approximation error is always less than a user-defined residual error threshold. We numerically demonstrate the performance of the proposed APINN method in solving a parameter estimation problem for a system governed by the Poisson equation.