Diffusion Guided Particle Sampling for Bayesian Inverse PDE Problems
Nicholas Bai
Ongoing — AI + Science Lab, Caltech
Advised by Jiachen Yao, Xi Deng, Anima Anandkumar
Leveraging diffusion priors to recover the full posterior for inverse PDE problems, instead of a single MAP estimate.
Many scientific inverse problems are ill-posed: several different parameter fields all explain the same observations. Standard maximum-a-posteriori approaches return a single solution and disregard the distributional perspective entirely.
This project designs diffusion-prior, particle-based samplers for Bayesian inverse PDE problems, with the goal of recovering the full multimodal posterior. The diffusion model supplies a learned prior over plausible fields; the particle method carries the multimodality through inference.
This is ongoing work in Prof. Anima Anandkumar's AI + Science Lab at Caltech, supported by a Carl F. Braun SURF Fellowship.