# Bayesian full waveform inversion with sequential surrogate model refinement

arXiv: https://arxiv.org/abs/2505.03246 · HTML: https://mlsanity.com/paper/2505.03246/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 75 references that are in the map.
- First posted on arXiv 6 May 2025.

## Builds on (most cited first, 10 of 10)

- [Survey of multifidelity methods in uncertainty propagation, inference, and optimization](https://mlsanity.com/paper/1806.10761/) (2018)
- [Deep-learning inversion: a next generation seismic velocity-model building method](https://mlsanity.com/paper/1902.06267/) (2019)
- [Sparse Polynomial Chaos Expansions: Literature Survey and Benchmark](https://mlsanity.com/paper/2002.01290/) (2020)
- [Implicit Full Waveform Inversion with Deep Neural Representation](https://mlsanity.com/paper/2209.03525/) (2022)
- [Data-Driven Model Reduction for the Bayesian Solution of Inverse Problems](https://mlsanity.com/paper/1403.4290/) (2014)
- [Automatic selection of basis-adaptive sparse polynomial chaos expansions for engineering applications](https://mlsanity.com/paper/2009.04800/) (2020)
- [Emulating the dynamics of complex systems using autoregressive models on manifolds (mNARX)](https://mlsanity.com/paper/2306.16335/) (2023)
- [Efficient Polynomial Chaos Expansion for Uncertainty Quantification in Power Systems](https://mlsanity.com/paper/1910.06498/) (2019)
- [A new framework for experimental design using Bayesian Evidential Learning: the case of wellhead protection area](https://mlsanity.com/paper/2105.05539/) (2021)
- [Bayesian tomography using polynomial chaos expansion and deep generative networks](https://mlsanity.com/paper/2307.04228/) (2023)

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

- [Surrogate modeling for uncertainty quantification in nonlinear dynamics](https://mlsanity.com/paper/2507.12358/) (2025)

## Abstract (arXiv)

Bayesian formulations of inverse problems are attractive for their ability to incorporate prior knowledge and update probabilistic models as new data become available. Markov chain Monte Carlo (MCMC) methods sample posterior probability density functions (pdfs) but require accurate prior models and many likelihood evaluations. Dimensionality-reduction methods, such as principal component analysis (PCA), can help define the prior and train surrogate models that efficiently approximate costly forward solvers. However, for problems like full waveform inversion, the complex input/output relations often cannot be captured well by surrogate models trained only on prior samples, leading to biased results. Including samples from high-posterior-probability regions can improve accuracy, but these regions are hard to identify in advance. We propose an iterative method that progressively refines the surrogate model. Starting with low-frequency data, we train an initial surrogate and perform an MCMC inversion. The resulting posterior samples are then used to retrain the surrogate, allowing us to expand the frequency bandwidth in the next inversion step. Repeating this process reduces model errors and improves the surrogate's accuracy over the relevant input domain. Ultimately, we obtain a highly accurate surrogate across the full bandwidth, enabling a final MCMC inversion. Numerical results from 2D synthetic crosshole Ground Penetrating Radar (GPR) examples show that our method outperforms ray-based approaches and those relying solely on prior sampling. The overall computational cost is reduced by about two orders of magnitude compared to full finite-difference time-domain modeling.