# Piecewise Deterministic Markov Processes for Bayesian Inference of PDE Coefficients

arXiv: https://arxiv.org/abs/2602.05559 · HTML: https://mlsanity.com/paper/2602.05559/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 35 references that are in the map.
- First posted on arXiv 5 Feb 2026.

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

- [The Bouncy Particle Sampler: A Non-Reversible Rejection-Free Markov Chain Monte Carlo Method](https://mlsanity.com/paper/1510.02451/) (2015)
- [Piecewise Deterministic Markov Processes for Continuous-Time Monte Carlo](https://mlsanity.com/paper/1611.07873/) (2016)
- [The Boomerang Sampler](https://mlsanity.com/paper/2006.13777/) (2020)
- [NuZZ: numerical Zig-Zag sampling for general models](https://mlsanity.com/paper/2003.03636/) (2020)
- [Scaling of Piecewise Deterministic Monte Carlo for Anisotropic Targets](https://mlsanity.com/paper/2305.00694/) (2023)
- [Fused L1/2 prior for large scale linear inverse problem with Gibbs bouncy particle sampler](https://mlsanity.com/paper/2409.07874/) (2024)
- [Integration of Active Learning and MCMC Sampling for Efficient Bayesian Calibration of Mechanical Properties](https://mlsanity.com/paper/2411.13361/) (2024)

## Abstract (arXiv)

We develop a general framework for piecewise deterministic Markov process (PDMP) samplers that enables efficient Bayesian inference in non-linear inverse problems with expensive likelihoods. The key ingredient is a surrogate-assisted thinning scheme in which a surrogate model provides a proposal event rate and a robust correction mechanism enforces an upper bound on the true rate by dynamically adjusting an additive offset whenever violations are detected. This construction is agnostic to the choice of surrogate and PDMP, and we demonstrate it for the Zig-Zag sampler and the Bouncy particle sampler with constant, Laplace, and Gaussian process (GP) surrogates, including gradient-informed and adaptively refined GP variants. As a representative application, we consider Bayesian inference of a spatially varying Young's modulus in a one-dimensional linear elasticity problem. Across dimensions, PDMP samplers equipped with GP-based surrogates achieve substantially higher accuracy and effective sample size per forward model evaluation than Random Walk Metropolis algorithm and the No-U-Turn sampler. The Bouncy particle sampler exhibits the most favorable overall efficiency and scaling, illustrating the potential of the proposed PDMP framework beyond this particular setting.