arXiv:2509. 08765v4 Announce Type: replace-cross Abstract: Data-driven acceleration of scientific computing workflows has been a high-profile aim of machine learning (ML) for science, with numerical simulation of transient partial differential equations (PDEs) being one of the main applications.
By Mikhail Khodak, Min Ki Jung, Brian Wynne, Edmond Chow, Egemen Kolemen
arXiv:2606. 27354v1 Announce Type: cross Abstract: Neural surrogate models offer fast approximate mappings from PDE parameters to solutions, but they typically treat solving as a purely statistical task: once trained, they struggle to correct their own constraint violations and extrapolate beyond the training distribution.
By Haina Jiang, Liam Wang, Peng-Chen Chen, Min Seop Kwak, Seungryong Kim, Brian Bell, Jeong Joon Park
arXiv:2607. 28036v1 Announce Type: new Abstract: It is well known that Newton's method converges faster when the initial guess is closer to a root of a system of nonlinear equations.
By R\'emy Vallot (CB, Michelin), Florian de Vuyst (BMBI), Thibault Dairay (CB, Michelin), Mathilde Mougeot (CB, ENSIIE, ENS Paris Saclay)
arXiv:2601. 16510v3 Announce Type: replace-cross Abstract: Solving massive-scale optimization problems requires scalable first-order methods with low per-iteration cost.
By Liping Tao, Xindi Tong, Chee Wei Tan
arXiv:2607. 18256v1 Announce Type: new Abstract: Optimization modeling is the process of translating real-world decision problems, often described in natural language, into formal mathematical formulations and executable solver code.
By Hongliang Lu, Zhong Li, Yuxuan Chen, Yuan Lan, Fan Zhang, Zaiwen Wen
arXiv:2602. 09530v2 Announce Type: replace-cross Abstract: We introduce AutoSpec, a neural network framework for discovering iterative spectral algorithms for large-scale numerical linear algebra and numerical optimization.
By Zihang Liu, Oleg Balabanov, Yaoqing Yang, Michael W. Mahoney