Benchmarking sparse system identification with low-dimensional chaos

AA Kaptanoglu, L Zhang, ZG Nicolaou, U Fasel… - Nonlinear …, 2023 - Springer
Sparse system identification is the data-driven process of obtaining parsimonious differential
equations that describe the evolution of a dynamical system, balancing model complexity …

[HTML][HTML] Coarse-graining Hamiltonian systems using WSINDy

DA Messenger, JW Burby, DM Bortz - Scientific Reports, 2024 - nature.com
Weak form equation learning and surrogate modeling has proven to be computationally
efficient and robust to measurement noise in a wide range of applications including ODE …

The Occupation Kernel Method for Nonlinear System Identification

JA Rosenfeld, BP Russo, R Kamalapurkar… - SIAM Journal on Control …, 2024 - SIAM
This manuscript presents a novel approach to nonlinear system identification leveraging
densely defined Liouville operators and a new “kernel” function that represents an …

[HTML][HTML] Sparse regression for plasma physics

AA Kaptanoglu, C Hansen, JD Lore, M Landreman… - Physics of …, 2023 - pubs.aip.org
Many scientific problems can be formulated as sparse regression, ie, regression onto a set
of parameters when there is a desire or expectation that some of the parameters are exactly …

The weak form is stronger than you think

DA Messenger, A Tran, V Dukic, DM Bortz - arXiv preprint arXiv …, 2024 - arxiv.org
The weak form is a ubiquitous, well-studied, and widely-utilized mathematical tool in modern
computational and applied mathematics. In this work we provide a survey of both the history …

Fourier Features for Identifying Differential Equations (FourierIdent)

M Tang, H Liu, W Liao, SH Kang - arXiv preprint arXiv:2311.16608, 2023 - arxiv.org
We investigate the benefits and challenges of utilizing the frequency information in
differential equation identification. Solving differential equations and Fourier analysis are …