Reproduce “Efficient Prior Calibration From Indirect Data” on OpenResearch

About this paper

O. Deniz Akyildiz, Mark Girolami, Andrew M. Stuart, Arnaud Vadeboncoeur

Researchers from Imperial College London, The Alan Turing Institute, University of Cambridge, and Caltech developed a methodology for efficiently learning prior distributions in Bayesian inverse problems using only indirect and noisy observational data. This framework integrates generative models, optimal transport, and concurrent neural operator learning to accurately estimate prior parameters and surrogate models, demonstrating robust performance with <2% relative errors for prior parameters in 2D Darcy flow scenarios.

Key insights

• Data-driven prior calibration can be effectively performed from indirect observations by matching probability distributions in the data space using robust optimal transport metrics.
• The concurrent learning of both the prior's generative model and a neural operator surrogate via bilevel optimization offers a principled way to manage computational cost without explicit loss term balancing.
• The proposed distributional matching approach is theoretically linked to Bayesian posterior recovery, providing a strong foundation for its use in prior calibration.

Summary by alphaXiv.