← Back to all news
arXiv Machine Learning By Ethan Hanold, Nicholas M. Boffi, Qin Li, Leonardo Zepeda-N\'u\~nez

AdjointFlow: Accelerating Scientific Inverse Problems with Physics-Based Transport

Read the original on arXiv Machine Learning →

AdjointFlow is a new framework that accelerates scientific inverse problems by embedding known physics directly into a generative transport model. It uses stochastic interpolants, an adjoint-based initialization, and a modified transport velocity to handle concentrated target distributions, enabling accurate reconstructions at much lower computational cost than traditional generative or plug‑and‑play methods. Experiments on inverse scattering, seismic imaging, and black hole imaging demonstrate that AdjointFlow outperforms conditional diffusion models and can be up to five orders of magnitude faster than plug‑and‑play inference while still allowing optional refinement for improved data consistency.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

Related stories

arXiv Machine Learning
Aug 19

Composing Flow-Matching Energies with Known Physics: Generation, OOD Detection, and Inversion on PDE Fields

The paper presents a method that combines flow‑matching models with energy‑based modeling to explicitly construct scalar energy functions for physical fields. These energies are derived from a matching regression objective on a linear Gaussian interpolation, avoiding variational approximations or extra MCMC steps, and can be used for energy‑corrected data generation, out‑of‑distribution detection, and posterior sampling in inverse problems. The approach enables general MCMC samplers that reduce PDE residuals and spectral distance, and it demonstrates that combining data‑driven and physics‑based energies improves OOD detection accuracy.

By Yixuan Sun, Anirban Samaddar, Sandeep Madireddy
diffusion
More like this →
arXiv AI
Jul 20

Energy-based Transport for Amortized Bayesian Inference

arXiv:2605. 15407v3 Announce Type: replace-cross Abstract: We consider amortized Bayesian inference for nonlinear inverse problems using only samples from the joint distribution of parameters and observations, including problems with unknown functions in a Banach space.

By Ricardo Baptista, Hojjat Kaveh, Andrew M. Stuart
More like this →
arXiv Machine Learning
Sep 18

PosteriorBench: From Point Estimates to Posterior Matching in Evaluating Generative Inverse Solvers

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
multimodalbenchmarkssafety
More like this →
arXiv Machine Learning
Oct 16

Learn Only Where You Can't Compute: Structured Corrections to Gaussian Process Posteriors

The paper introduces a structured posterior‑correction framework that blends a tractable Gaussian reference with data‑driven corrections learned via diffusion models. After applying mean correction and covariance calibration, the diffusion model focuses on a low‑dimensional subspace that captures discrepancies from the Gaussian reference, while the remaining space stays Gaussian. Experiments on three scientific inference tasks show that these corrections recover hidden modes, improve sample structure, and reduce prediction error compared to the Gaussian reference, with trade‑offs between accuracy and computational cost relative to full‑field generative models.

By Tobias Weber, Carla Sagebiel, Philipp Hennig
diffusion
More like this →