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Discovering governing equations from data by sparse identification of nonlinear dynamical systems
TLDR
This work develops a novel framework to discover governing equations underlying a dynamical system simply from data measurements, leveraging advances in sparsity techniques and machine learning and using sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data.
Dynamic mode decomposition - data-driven modeling of complex systems
TLDR
This first book to address the DMD algorithm presents a pedagogical and comprehensive approach to all aspects of DMD currently developed or under development, and blends theoretical development, example codes, and applications to showcase the theory and its many innovations and uses.
Data-driven discovery of partial differential equations
TLDR
The sparse regression method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation.
Dynamic Mode Decomposition with Control
TLDR
This work develops a new method which extends dynamic mode decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems and provides the additional innovation of being able to disambiguate between the underlying dynamics and the effects of actuation, resulting in accurate input-output models.
Chaos as an intermittently forced linear system
TLDR
A universal, data-driven decomposition of chaos as an intermittently forced linear system is presented, combining delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates.
Generalizing Koopman Theory to Allow for Inputs and Control
TLDR
A new generalization of Koopman operator theory that incorporates the effects of inputs and control is developed that is rigorously connected and generalizes a recent development called Dynamic Mode Decomposition with control (DMDc).
Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control
TLDR
This work presents a data-driven strategy to identify relevant observable functions for Koopman analysis by leveraging a new algorithm to determine relevant terms in a dynamical system by ℓ1-regularized regression of the data in a nonlinear function space and demonstrates the usefulness of nonlinear observable subspaces in the design of Koop man operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.
Modeling malaria genomics reveals transmission decline and rebound in Senegal
TLDR
The findings imply that intensive intervention to control malaria results in rapid and dramatic changes in parasite population genomics, and suggest that genomics combined with epidemiological modeling may afford prompt, continuous, and cost-effective tracking of progress toward malaria elimination.
Compressive sampling and dynamic mode decomposition
This work develops compressive sampling strategies for computing the dynamic mode decomposition (DMD) from heavily subsampled or output-projected data. The resulting DMD eigenvalues are equal to DMD
Discovering dynamic patterns from infectious disease data using dynamic mode decomposition
TLDR
Dynamic mode decomposition (DMD) is a recently developed method focused on discovering coherent spatial-temporal modes in high-dimensional data collected from complex systems with time dynamics that is poised to be an effective and efficient computational analysis tool for the study of infectious disease.
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