arXiv:2607. 23753v1 Announce Type: new Abstract: Partial differential equation (PDE) discovery aims to identify from data the governing law of a physical system.
By Baptiste Mathevon, Farah Cherfaoui, Amaury Habrard, Marc Sebban
arXiv:2607. 10546v1 Announce Type: new Abstract: Discovering governing partial differential equations (PDEs) from noisy observational data is a fundamental challenge in scientific machine learning.
By Jinyang Du, Hao Ma, Xiaohu Shi, Bo Yang, Yanchun Liang, Heow Pueh Lee, Chunguo Wu
arXiv:2606. 05191v1 Announce Type: new Abstract: Data-driven equation discovery is fundamentally an inverse problem that seeks to infer the governing differential equations of a system directly from time-series measurements.
By Federico J. Gonzalez
arXiv:2606. 09638v1 Announce Type: new Abstract: Differential equations play a critical role in scientific discovery because they provide a mathematical framework to describe the behaviour of physical phenomena.
By Siyu Lou, Hao Xu, Wenguan Wang, Lu Lu, Hao Sun, Yang Liu, Linfeng Zhang, Dongxiao Zhang, Yuntian Chen
arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).
By Heechang Kim, Qianying Cao, Hyomin Shin, Seungchul Lee, George Em Karniadakis, Minseok Choi
The paper introduces Neptune, a method that uses independent coordinate neural networks to infer parameter fields in multi-physics PDEs from sparse measurements. Neptune can accurately estimate parameters with nonlinear, spatiotemporal variations, outperforming existing techniques by reducing estimation errors by up to two orders of magnitude and improving dynamic response predictions by a factor of ten. It also demonstrates strong physical extrapolation, enabling reliable predictions beyond the training data.
By Xuyang Li, Mahdi Masmoudi, Rami Gharbi, Nizar Lajnef, Vishnu Naresh Boddeti