arXiv:2606. 12182v1 Announce Type: new Abstract: Identifying the governing equations of complex dynamical systems remains a fundamental challenge across science and engineering.
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:2607. 15077v1 Announce Type: new Abstract: Many engineering problems involve phenomena whose governing equations are poorly characterized or only partially known.
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.
arXiv:2606. 15690v1 Announce Type: new Abstract: Data from simulations and experiments are rarely noise-free and often exhibit heterogeneous levels of fidelity.
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...
arXiv:2608. 13504v1 Announce Type: new Abstract: We develop the Sparse Orthogonal Regression Technique (SORT), a sparse spectral framework for learning orthonormal-basis expansions from noisy and irregularly sampled data.
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.
arXiv:2609.37083v1 Announce Type: cross Abstract: We study the problem of recovering the governing ODE of a dynamical system from unstructured, high-dimensional observations such as images. Existing...
The paper presents an active learning framework that enhances data-driven reduced-order models (ROMs) for parametric dynamical systems by intelligently selecting training parameters. Using a Bayesian linear regression version of operator inference, the method quantifies prediction uncertainty to guide sequential adaptive sampling, aiming to improve ROM stability and accuracy across the parameter domain. Numerical experiments on nonlinear PDE systems show that this adaptive strategy outperforms random sampling under the same computational budget.
arXiv:2607. 29036v1 Announce Type: new Abstract: Sparse identification of nonlinear dynamics (SINDy) and PDE functional identification (PDE-FIND) recover parsimonious ordinary and partial differential equations (ODEs and PDEs) from data.
arXiv:2606. 25039v1 Announce Type: new Abstract: Recovering governing Ordinary Differential Equations (ODEs) from data is a central challenge in modeling dynamical systems across scientific domains.
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.