arXiv Machine Learning

Joint 3D Gravity and Magnetic Inversion via Rectified Flow and Ginzburg-Landau Guidance

arXiv:2603. 06829v2 Announce Type: replace Abstract: Subsurface ore detection is of paramount importance given the rising depletion of shallow mineral resources in recent years.

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
arXiv Machine Learning
Sep 14

Physical-State-Guided Diffusion Sampling for Full-Waveform Inversion

Physical-State-Guided Diffusion Sampling (PSG) couples a persistent physical velocity model to a diffusion prior via a Gaussian bridge, allowing the physical state to be refined by waveform fitting while guiding the reverse diffusion process. This approach separates wave‑equation and denoiser gradients, preserving conventional FWI initialization and optimization history. PSG outperforms classical and diffusion‑based baselines on four OpenFWI families, maintains strong structural recovery under noise, and supports large‑scale models like Marmousi, Overthrust, and BP2004 Salt without retraining.

By Chen Min, Haowen Jiang, Zheng Ma, Xiongbin Yan
arXiv Machine Learning
Sep 21

Generative inversion for early ranking of competing geologic interpretations

The paper introduces a workflow that ranks competing geological interpretations by converting them into spatial priors and assessing their consistency with hydraulic‑head observations. Using a text‑to‑image model to generate 1600 geologic images per interpretation, a variational autoencoder encodes them, and a supervised inverse network maps head data into this latent space, producing log‑conductivity fields for flow simulation. The method is validated on a synthetic Johansen Formation benchmark and applied to two conceptual models of the Culebra Dolomite, yielding compatibility scores that align with independent evidence.

By Harun Ur Rashid, Daniel O'Malley