arXiv:2606. 30230v1 Announce Type: cross Abstract: Learned reconstruction operators for inverse problems are typically trained under a fixed noise model, and generalize poorly when the distribution during testing differs from the one assumed during training.
By Floor van Maarschalkerwaart, Subhadip Mukherjee, Christoph Brune, Marcello Carioni
arXiv:2608.27590v1 Announce Type: cross
Abstract: Inferring elastic constants from resonant ultrasound spectra is a nonlinear and typically overdetermined inverse problem based on finite spectral dat...
By Alejandro Cubillos Mu\~noz, Manuela Rivas, Julian Rincon
The paper evaluates the robustness of Physics‑Informed Neural Networks (PINNs) against noisy data in inverse problems, comparing them to a finite element method (FEM) plus optimizer baseline. Experiments on viscosity identification in 1D Burgers’ equation and 2D/3D Taylor‑Green Vortex with additive Gaussian noise show that PINNs, while requiring less human expertise, are outperformed by the traditional FEM approach in accuracy (e.g., RMSE 0.01 vs. 0.0013 for 2D Taylor‑Green with σ=1). PINNs do, however, exhibit better scaling with problem complexity, and the study highlights specific training failures that must be addressed for PINNs to become more competitive.
By Aleksandra Jekic, Afroditi Natsaridou, Signe Riemer-S{\o}rensen, Helge Langseth, Odd Erik Gundersen
arXiv:2609.13819v1 Announce Type: new
Abstract: Solving inverse problems with differentiable physics simulators holds the potential to revolutionize scientific discovery and engineering design, as it...
By Xiang Chen, Huanhuan Xia
arXiv:2606. 04804v1 Announce Type: new Abstract: Generative models -- diffusion and flow matching -- are increasingly used to solve partial differential equation (PDE) inverse problems, enforcing the governing physics as a \emph{hard constraint} (via projection or guidance) and reporting the resulting samples as a Bayesian posterior with calibrated uncertainty.
By Jian Xu, Delu Zeng, John Paisley, Qibin Zhao
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