PosteriorBench: going beyond point reconstructions for scientific inverse-problem to full posterior distributions. Many scientific problems involve indirect or partial observations. Multiple physical fields can explain the same measurements. A solver should capture these possibilities, yet reconstruction accuracy alone is misleading. We spent substantial compute to construct high-fidelity reference posteriors across four tasks: Darcy flow inversion, Poisson source recovery, carbon capture and storage, and light transport material inference. These reference data let researchers directly evaluate their solvers using five complementary metrics. One of our key findings: better reconstruction accuracy can coincide with worse posterior recovery. Even strong generative samplers struggle to get both the mean and variance right, often underestimating the uncertainty. Paper: Code: Thanks to Jiachen Yao, Sean Hsu, Xi Deng, and all our coauthors for making this work possible @Caltech #AIforScience# #InverseProblems# #UncertaintyQuantification#

Excited to share that I’ll be attending the SIAM Conference on Uncertainty Quantification (UQ26) this year! 🎙️ At the conference, I will deliver an invited talk on Physics-Informed Posterior Sampling for Scientific Inverse Problems. Time: Tuesday 3 PM Link: Many scientific inverse problems ask us to reconstruct complex hidden fields from sparse, noisy observations. In these settings, a single best guess is often not enough. What we really need is a way to generate solutions that are both uncertainty-aware and faithful to the underlying physics. 💫 In this talk, I'll present a central message: Function-space diffusion can serve as a foundation for posterior sampling; decoupling prior and physics fixes the low-data bottleneck; and the resulting framework works in realistic scientific applications with verified posterior. I’m especially looking forward to sharing and learning new theories and advances. 🧸 If you’re attending UQ26, I would love to connect! #ScientificMachineLearning# #UncertaintyQuantification# #InverseProblems# #DiffusionModels# #PhysicsInformedAI# #BayesianInference# #MachineLearning#