arXiv:2607. 06252v1 Announce Type: cross Abstract: Many problems in science and engineering are difficult to model accurately, either due to unknown physical mechanisms, poorly quantified measurement uncertainty, or prohibitive computational costs of high-fidelity simulations.
By Fabian Schneider, Tapio Helin, Leila Taghizadeh
PosteriorBench is a new benchmark that evaluates how well generative inverse solvers recover full posterior distributions rather than just a single reconstruction. It tests four physics-based inverse problems—Darcy flow inversion, Poisson source recovery, carbon capture and storage, and light transport material inference—using high-fidelity reference posteriors generated by rejection sampling and MCMC. The benchmark employs five metrics (posterior-mean error, posterior-standard-deviation error, maximum mean discrepancy, sliced Wasserstein distance, and radially averaged power-spectrum error) to assess pointwise accuracy, uncertainty, distributional alignment, and global frequency fidelity, revealing significant distribution-matching gaps in current solvers and highlighting the importance of neural operators, guidance weights, and generation noise for posterior-variance calibration.
By Jiachen Yao, Zi-Siang Hsu, Xi Deng, Aditi Gupta, Xin Ju, Sally M Benson, Gege Wen, Anima Anandkumar
arXiv:2602.01176v2 Announce Type: replace
Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physica...
By Olaf Yunus Laitinen Imanov
The paper introduces an active diffusion-based inverse problem solver that trains a diffusion model to map between parameter and observable spaces. By iteratively detecting and correcting model misspecification through posterior uncertainty, the method can discover and learn the correct parameter region even when initial training bounds exclude the true parameters. The authors demonstrate the solver on a toy inverse problem with infinite solutions and on parameterizing quantum correlation functions for a Quantum Chromodynamics analysis of nucleon structure.
By Jitao Xu, Nobuo Sato, Yaohang Li
arXiv:2603. 14798v2 Announce Type: replace-cross Abstract: We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime.
By Zilan Cheng, Li-Lian Wang, Zhongjian Wang
arXiv:2512.12749v3 Announce Type: replace-cross
Abstract: Learning surrogate models for physical systems with latent uncertainty remains challenging in data-scarce regimes: deterministic neural opera...
By Sahil Bhola, Karthik Duraisamy