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 …
technique for data sequences. In its most common form, it processes high-dimensional …
Modern Koopman theory for dynamical systems
The field of dynamical systems is being transformed by the mathematical tools and
algorithms emerging from modern computing and data science. First-principles derivations …
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 …
descriptions of natural physical laws, capturing a rich variety of phenomenology and …
Universal differential equations for scientific machine learning
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 …
well be" a model is worth a thousand datasets." In this manuscript we introduce the SciML …
Machine learning for molecular simulation
Machine learning (ML) is transforming all areas of science. The complex and time-
consuming calculations in molecular simulations are particularly suitable for an ML …
consuming calculations in molecular simulations are particularly suitable for an ML …
[PDF][PDF] Integrating physics-based modeling with machine learning: A survey
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 …
require novel methodologies that are able to integrate traditional physics-based modeling …
Integrating scientific knowledge with machine learning for engineering and environmental systems
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 …
require novel methodologies that are able to integrate traditional physics-based modeling …
Deep learning for universal linear embeddings of nonlinear dynamics
Identifying coordinate transformations that make strongly nonlinear dynamics approximately
linear has the potential to enable nonlinear prediction, estimation, and control using linear …
linear has the potential to enable nonlinear prediction, estimation, and control using linear …
Data-driven discovery of coordinates and governing equations
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 …
rich fields that lack well-characterized quantitative descriptions. Advances in sparse …
Lift & learn: Physics-informed machine learning for large-scale nonlinear dynamical systems
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 …
models for large-scale dynamical systems. The method exploits knowledge of a system's …