arXiv:2608. 06107v1 Announce Type: new Abstract: Machine learning offers a promising avenue to accelerate physical simulations by replacing computationally expensive traditional Partial Differential Equation (PDE) solvers with fast, differentiable surrogate models.
By Guillaume Couairon, Alexis Jacq, Yu-Han Wu, Renu Singh, Yana Hasson, Quentin Berthet, Romuald Elie
arXiv:2606. 16219v1 Announce Type: cross Abstract: Digital twin modeling, including control and data assimilation under model uncertainty, often faces an open-ended fidelity problem: adding variables, data streams, and time scales can indefinitely increase model complexity, ultimately producing systems that are difficult to maintain, validate, interpret, and use for stress or safety testing.
By Zongren Zou, Th\'eo Bourdais, Ricardo Baptista, Houman Owhadi
arXiv:2608. 05702v1 Announce Type: new Abstract: Scientific machine learning commonly validates models at the level of a subdomain, a benchmark split, or an explanation for one prediction.
By Gnankan Landry Regis N'guessan, Bum Jun Kim
arXiv:2608. 11746v1 Announce Type: new Abstract: Modern systems are increasingly expected to transfer across tasks not specified during training.
By Ellen Su, Andres Potapczynski, Shikai Qiu, Edward Hughes, Andrew Gordon Wilson
arXiv:2606. 15637v1 Announce Type: new Abstract: A digital twin (DT) of a patient-specific heart offers significant potential in personalized medicine.
By Sumeet Vadhavkar, Xiajun Jiang, Yubo Ye, Maryam Toloubidokhti, Linwei Wang
The paper introduces a new federated learning protocol for partial differential equations called solution-space PDE-Dirichlet, which transforms continuous supervised responses into reusable solution bins and measures client separation via optimal transport. It establishes an exact inverse relationship between population allocation heterogeneity and Dirichlet concentration, and shows how response heterogeneity can cause gradient disagreement, local-update dispersion, and parameter divergence. Experiments on seven PDE tasks, three neural-operator families, and five random seeds demonstrate that lower concentration consistently increases solution distance and optimization heterogeneity, with the most pronounced error increase observed in low-viscosity Burgers equations.
By Ping Luo, Jiahuan Wang, Ziqing Wen, Tao Sun, Dongsheng Li