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 …

Closed-loop turbulence control: Progress and challenges

SL Brunton, BR Noack - Applied Mechanics …, 2015 - asmedigitalcollection.asme.org
Closed-loop turbulence control is a critical enabler of aerodynamic drag reduction, lift
increase, mixing enhancement, and noise reduction. Current and future applications have …

Deep hidden physics models: Deep learning of nonlinear partial differential equations

M Raissi - Journal of Machine Learning Research, 2018 - jmlr.org
We put forth a deep learning approach for discovering nonlinear partial differential
equations from scattered and potentially noisy observations in space and time. Specifically …

Hidden physics models: Machine learning of nonlinear partial differential equations

M Raissi, GE Karniadakis - Journal of Computational Physics, 2018 - Elsevier
While there is currently a lot of enthusiasm about “big data”, useful data is usually “small”
and expensive to acquire. In this paper, we present a new paradigm of learning partial …

[图书][B] Dynamic mode decomposition: data-driven modeling of complex systems

The integration of data and scientific computation is driving a paradigm shift across the
engineering, natural, and physical sciences. Indeed, there exists an unprecedented …

Data-driven discovery of partial differential equations

SH Rudy, SL Brunton, JL Proctor, JN Kutz - Science advances, 2017 - science.org
We propose a sparse regression method capable of discovering the governing partial
differential equation (s) of a given system by time series measurements in the spatial …

Projection-based model reduction: Formulations for physics-based machine learning

R Swischuk, L Mainini, B Peherstorfer, K Willcox - Computers & Fluids, 2019 - Elsevier
This paper considers the creation of parametric surrogate models for applications in science
and engineering where the goal is to predict high-dimensional output quantities of interest …

Chaos as an intermittently forced linear system

SL Brunton, BW Brunton, JL Proctor, E Kaiser… - Nature …, 2017 - nature.com
Understanding the interplay of order and disorder in chaos is a central challenge in modern
quantitative science. Approximate linear representations of nonlinear dynamics have long …

Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control

SL Brunton, BW Brunton, JL Proctor, JN Kutz - PloS one, 2016 - journals.plos.org
In this work, we explore finite-dimensional linear representations of nonlinear dynamical
systems by restricting the Koopman operator to an invariant subspace spanned by specially …

Data-driven sparse sensor placement for reconstruction: Demonstrating the benefits of exploiting known patterns

K Manohar, BW Brunton, JN Kutz… - IEEE Control Systems …, 2018 - ieeexplore.ieee.org
Optimal sensor and actuator placement is an important unsolved problem in control theory.
Nearly every downstream control decision is affected by these sensor and actuator …