Dynamic mode decomposition and its variants

PJ Schmid - Annual Review of Fluid Mechanics, 2022 - annualreviews.org
Dynamic mode decomposition (DMD) is a factorization and dimensionality reduction
technique for data sequences. In its most common form, it processes high-dimensional …

Modern Koopman theory for dynamical systems

SL Brunton, M Budišić, E Kaiser, JN Kutz - arXiv preprint arXiv:2102.12086, 2021 - arxiv.org
The field of dynamical systems is being transformed by the mathematical tools and
algorithms emerging from modern computing and data science. First-principles derivations …

Promising directions of machine learning for partial differential equations

SL Brunton, JN Kutz - Nature Computational Science, 2024 - nature.com
Partial differential equations (PDEs) are among the most universal and parsimonious
descriptions of natural physical laws, capturing a rich variety of phenomenology and …

Universal differential equations for scientific machine learning

C Rackauckas, Y Ma, J Martensen, C Warner… - arXiv preprint arXiv …, 2020 - arxiv.org
In the context of science, the well-known adage" a picture is worth a thousand words" might
well be" a model is worth a thousand datasets." In this manuscript we introduce the SciML …

Machine learning for molecular simulation

F Noé, A Tkatchenko, KR Müller… - Annual review of …, 2020 - annualreviews.org
Machine learning (ML) is transforming all areas of science. The complex and time-
consuming calculations in molecular simulations are particularly suitable for an ML …

[PDF][PDF] Integrating physics-based modeling with machine learning: A survey

J Willard, X Jia, S Xu, M Steinbach… - arXiv preprint arXiv …, 2020 - beiyulincs.github.io
There is a growing consensus that solutions to complex science and engineering problems
require novel methodologies that are able to integrate traditional physics-based modeling …

Integrating scientific knowledge with machine learning for engineering and environmental systems

J Willard, X Jia, S Xu, M Steinbach, V Kumar - ACM Computing Surveys, 2022 - dl.acm.org
There is a growing consensus that solutions to complex science and engineering problems
require novel methodologies that are able to integrate traditional physics-based modeling …

Deep learning for universal linear embeddings of nonlinear dynamics

B Lusch, JN Kutz, SL Brunton - Nature communications, 2018 - nature.com
Identifying coordinate transformations that make strongly nonlinear dynamics approximately
linear has the potential to enable nonlinear prediction, estimation, and control using linear …

Data-driven discovery of coordinates and governing equations

K Champion, B Lusch, JN Kutz… - Proceedings of the …, 2019 - National Acad Sciences
The discovery of governing equations from scientific data has the potential to transform data-
rich fields that lack well-characterized quantitative descriptions. Advances in sparse …

Lift & learn: Physics-informed machine learning for large-scale nonlinear dynamical systems

E Qian, B Kramer, B Peherstorfer, K Willcox - Physica D: Nonlinear …, 2020 - Elsevier
Abstract We present Lift & Learn, a physics-informed method for learning low-dimensional
models for large-scale dynamical systems. The method exploits knowledge of a system's …