Document Type
Article
Publication Date
9-30-2025
Abstract
In many computational problems, using the Markov Chain Monte Carlo (MCMC) can be prohibitively time-consuming. We propose MCMC-Net, a simple yet efficient way to accelerate MCMC via neural networks. The key idea of our approach is to substitute the true likelihood function of the MCMC method with a neural operator based surrogate. We extensively evaluate the accuracy and speedup of our method on three different partial differential equation-based inverse problems where likelihood computations are computationally expensive, namely electrical impedance tomography, diffuse optical tomography, and quantitative photoacoustic tomography. MCMC-Net performs similar to the classical likelihood counterpart but with a significant speedup. We conjecture that the method can be applied to any problem with a sufficiently expensive likelihood function. We also analyze MCMC-Net in a theoretical setting for the different use cases. We prove a universal approximation theorem-type result to show that the proposed network can approximate the mapping resulting from forward model evaluations to a desired accuracy. Furthermore, we establish convergence of the surrogate posterior to the true posterior under Hellinger distance.
Keywords
Bayesian inverse problems, convolutional neural network, deep learning, Markov Chain Monte Carlo
Language
English
Publication Title
Inverse Problems
Rights
© 2025, The Author(s). This is an Open Access work distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
Majee, S., Abhishek, A., Strauss, T., & Khan, T. (2025). MCMC-Net: accelerating Markov Chain Monte Carlo with neural networks for inverse problems. Inverse Problems, 41(9), 095013. https://doi.org/10.1088/1361-6420/ae05c2
Manuscript Version
Final Publisher Version