Identifying the governing equations of complex dynamical systems remains a fundamental challenge across science and engineering. While early approaches relied on empirical data and heuristics, modern data-driven methods offer greater flexibility and fewer assumptions.
arXiv:2606. 12182v1 Announce Type: new Abstract: Identifying the governing equations of complex dynamical systems remains a fundamental challenge across science and engineering.
By Ana Larra\~naga, Urban Fasel, Steven L. Brunton
arXiv:2606. 15690v1 Announce Type: new Abstract: Data from simulations and experiments are rarely noise-free and often exhibit heterogeneous levels of fidelity.
By Filippo Zacchei, Ana Larra\~naga, Attilio Frangi, Andrea Manzoni, Steven L. Brunton
arXiv:2604. 20141v2 Announce Type: replace Abstract: We introduce Fourier Weak SINDy, a minimal noise-robust and interpretable derivative-free equation learning method that combines weak-form sparse equation learning with spectral density estimation for data-driven test function selection.
By Zhiheng Chen, Urban Fasel, Anastasia Bizyaeva
arXiv:2609.09434v1 Announce Type: cross
Abstract: In recent years, weak-form methods have made significant advances in data-driven discovery of dynamical systems. However, in high-dimensional setting...
By Will Houser, Vanja Dukic, David M. Bortz
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