Bayesian Inverse Problems Meet Flow Matching: Efficient and Flexible Inference via Transformers
This provides a faster and more flexible method for researchers and practitioners dealing with complex posterior distributions in fields like disease modeling and PDEs, though it is incremental as it builds on existing flow matching and transformer techniques.
The paper tackles the high computational cost of Bayesian inverse problems by integrating Conditional Flow Matching with transformers, achieving parameter recovery errors as low as 1.5% and inference speed-ups of up to 2000 times compared to MCMC.
The efficient resolution of Bayesian inverse problems remains challenging due to the high computational cost of traditional sampling methods. In this paper, we propose a novel framework that integrates Conditional Flow Matching (CFM) with a transformer-based architecture to enable fast and flexible sampling from complex posterior distributions. The proposed methodology involves the direct learning of conditional probability trajectories from the data, leveraging CFM's ability to bypass iterative simulation and transformers' capacity to process arbitrary numbers of observations. The efficacy of the proposed framework is demonstrated through its application to three problems: a simple nonlinear model, a disease dynamics framework, and a two-dimensional Darcy flow Partial Differential Equation. The primary outcomes demonstrate that the relative errors in parameters recovery are as low as 1.5%, and that the inference time is reduced by up to 2000 times on CPU in comparison with the Monte Carlo Markov Chain. This framework facilitates the expeditious resolution of Bayesian problems through the utilisation of sampling from the learned conditional distribution.