arXiv Machine Learning By Floor van Maarschalkerwaart, Subhadip Mukherjee, Christoph Brune, Marcello Carioni

A Distributionally Robust Framework for Learned Reconstructions in Inverse Problems

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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.

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arXiv Machine Learning
Jun 30

Learning from samples: inverse problems over measures

arXiv:2505. 07124v3 Announce Type: replace Abstract: We study inverse problems where an unknown potential is observed only through samples from the measure it induces by a convex variational principle.

By Francisco Andrade, Gabriel Peyr\'e, Clarice Poon
arXiv Machine Learning
Sep 1

Sensitivity-Constrained Neural Operators for Data-Efficient Forward and Inverse Modeling of Partial Differential Equation Systems

The paper introduces Sensitivity‑Constrained Neural Operators (SC‑NOs), which augment standard neural operator training with sampled Jacobian supervision from differentiable solvers or discrete adjoints. By matching selected sensitivities during training, SC‑NOs improve forward prediction accuracy and significantly enhance gradient‑based inverse reconstruction for distributed fields. Experiments on advection–diffusion, RANS–Spalart–Allmaras, high‑dimensional gridded inputs, and a shallow‑water tsunami source‑inversion case demonstrate that SC‑NOs achieve a better accuracy–cost trade‑off and enable near‑real‑time wave‑propagation forecasting from sparse observations.

By Abdolmehdi Behroozi, Chaopeng Shen, Daniel Kifer, Kathryn Lawson