arXiv:2512. 09165v2 Announce Type: replace Abstract: Deep Operator Networks (DeepONets) have emerged as a powerful framework for data-driven operator learning, providing flexible surrogates for nonlinear mappings arising in partial differential equations (PDEs).
By Muhammad Abid, Omer San
The paper introduces WaSP, a Wasserstein Data Synthesis Pipeline that trains neural operators on manufactured input‑solution pairs while progressively reducing distribution shift toward the target input distribution. By iteratively generating new pairs through a learned surrogate and the exact PDE operator, WaSP achieves a stepwise error‑propagation bound and empirically reduces solution error by 3.9× to 9.5× on PDE benchmarks such as Allen‑Cahn, Kuramoto‑Sivashinsky, and Ginzburg‑Landau.
By Ryan Liu, Chuwei Wang, Ricardo Baptista, Andrew Stuart, Anima Anandkumar
arXiv:2605. 08170v2 Announce Type: replace Abstract: Neural operators have emerged as a powerful tool for learning mappings between infinite-dimensional function spaces.
By Nicole Hao
arXiv:2609.36709v1 Announce Type: cross
Abstract: Out-of-distribution (OOD) generalization is a central challenge in scientific machine learning. We study regression problems in which the test distri...
By Ben Adcock, Simone Brugiapaglia, Xuemeng Wang
arXiv:2609.36047v1 Announce Type: cross
Abstract: Given a functional dependent on the spectrum of a differential operator, we address the problem of finding a domain which optimizes this functional....
By Alexis de Villeroch\'e, Beniamin Bogosel, St\'ephane Breuils, Dorin Bucur, Jacques-Olivier Lachaud
arXiv:2606. 02427v1 Announce Type: cross Abstract: Existing evaluations of neural operators and in-context operator learning rely primarily on prediction error, but accurate output prediction does not guarantee the correct local dynamical structure.
By Zhiwei Gao, Liu Yang, George Em Karniadakis