638 citations · 3k across the 32 of their papers we have counts for
6 papers · 1 filter
Structured Time-Delay Models for Dynamical Systems with Connections to Frenet-Serret Frame
Seth M. Hirsh, Sara M. Ichinaga, Steven L. Brunton +2
Time-delay embeddings and dimensionality reduction are powerful techniques for discovering effective coordinate systems to represent the dynamics of physical systems. Recently, it…
Numerical differentiation of noisy data: A unifying multi-objective optimization framework
Floris van Breugel, J. Nathan Kutz, Bingni W. Brunton
Computing derivatives of noisy measurement data is ubiquitous in the physical, engineering, and biological sciences, and it is often a critical step in developing dynamic models or…
Inferring Causal Networks of Dynamical Systems through Transient Dynamics and Perturbation
George Stepaniants, Bingni W. Brunton, J. Nathan Kutz
Inferring causal relations from time series measurements is an ill-posed mathematical problem, where typically an infinite number of potential solutions can reproduce the given dat…
Centering Data Improves the Dynamic Mode Decomposition
Seth M. Hirsh, Kameron Decker Harris, J. Nathan Kutz +1
Dynamic mode decomposition (DMD) is a data-driven method that models high-dimensional time series as a sum of spatiotemporal modes, where the temporal modes are constrained by line…
Chaos as an Intermittently Forced Linear System
Steven L. Brunton, Bingni W. Brunton, Joshua L. Proctor +2
Understanding the interplay of order and disorder in chaotic systems is a central challenge in modern quantitative science. We present a universal, data-driven decomposition of cha…
Koopman invariant subspaces and finite linear representations of nonlinear dynamical systems for control
Steven L. Brunton, Bingni W. Brunton, Joshua L. Proctor +1
In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace. The Koopman operator…