The paper introduces the Ensemble-conditioned Inverse Problem (EIP), a multivariate statistical framework for inferring an ensemble that follows the pushforward of a prior through a forward process. It applies to fields such as high‑energy physics, full waveform inversion, and inverse imaging, and proposes non‑iterative inference‑time methods using ensemble inverse generative models that avoid explicit forward model use during inference. The authors demonstrate the approach on synthetic and real datasets and provide code for replication.
By Zhengyan Huan, Camila Pazos, Martin Klassen, Vincent Croft, Pierre-Hugues Beauchemin, Shuchin Aeron
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:2508. 20330v5 Announce Type: replace Abstract: Combinatorial optimization problems are ubiquitous in science and engineering.
By Zohair Shafi, Serdar Kadioglu
arXiv:2606. 30699v1 Announce Type: new Abstract: Discovering governing equations directly from observational data is a key step towards interpretable scientific machine learning.
By Hao Xu, Siyu Lou, Yuntian Chen, Dongxiao Zhang
arXiv:2603. 17216v2 Announce Type: replace Abstract: With the advent of AI agents, automated scientific discovery is becoming an increasingly plausible goal.
By Ziyang Cai, Amir Saeidi, Harkirat Behl
arXiv:2610.09890v1 Announce Type: cross
Abstract: Inverse optimization estimates the weights of an objective function that explain observed decisions as optimal solutions, and is used in a variety of...
By Akira Kitaoka