Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control. [PDF]
PLoS ONE, 2016 In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions.
Steven L Brunton +3 more
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Koopman operator and its approximations for systems with symmetries [PDF]
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2019 Nonlinear dynamical systems with symmetries exhibit a rich variety of behaviors, often described by complex attractor-basin portraits and enhanced and suppressed bifurcations. Symmetry arguments provide a way to study these collective behaviors and to simplify their analysis.
Anastasiya Salova +4 more
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Model-Based Control Using Koopman Operators
Robotics: Science and Systems XIII, 2017 This paper explores the application of Koopman operator theory to the control of robotic systems. The operator is introduced as a method to generate data-driven models that have utility for model-based control methods. We then motivate the use of the Koopman operator towards augmenting model-based control.
Gerardo De La Torre +2 more
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Closed-loop Koopman operator approximation
Machine Learning: Science and TechnologyThis paper proposes a method to identify a Koopman model of a feedback-controlled system given a known controller. The Koopman operator allows a nonlinear system to be rewritten as an infinite-dimensional linear system by viewing it in terms of an ...
Steven Dahdah, James Richard Forbes
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Learning Hamiltonian neural Koopman operator and simultaneously sustaining and discovering conservation laws [PDF]
Physical Review ResearchAccurately finding and predicting dynamics based on the observational data with noise perturbations is of paramount significance but still a major challenge presently.
Jingdong Zhang, Qunxi Zhu, Wei Lin
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Extraction of nonlinearity in neural networks with Koopman operator [PDF]
Journal of Statistical Mechanics: Theory and ExperimentNonlinearity plays a crucial role in deep neural networks. In this paper, we investigate the degree to which the nonlinearity of the neural network is essential.
Naoki Sugishita, Kayo Kinjo, Jun Ohkubo
semanticscholar +4 more sources
Temporally-consistent koopman autoencoders for forecasting dynamical systems [PDF]
Scientific ReportsAbsence of sufficiently high-quality data often poses a key challenge in data-driven modeling of high-dimensional spatio-temporal dynamical systems.
Indranil Nayak +4 more
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Deep Learning for Koopman Operator Estimation in Idealized Atmospheric Dynamics [PDF]
BigData Congress [Services Society]Deep learning is revolutionizing weather forecasting, with new data-driven models achieving accuracy on par with operational physical models for medium-term predictions.
David Millard +2 more
semanticscholar +3 more sources
Leveraging KANs For Enhanced Deep Koopman Operator Discovery [PDF]
arXiv.orgMulti-layer perceptrons (MLP's) have been extensively utilized in discovering Deep Koopman operators for linearizing nonlinear dynamics. With the emergence of Kolmogorov-Arnold Networks (KANs) as a more efficient and accurate alternative to the MLP ...
George Nehma, Madhur Tiwari
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A Class of Logistic Functions for Approximating State-Inclusive Koopman Operators
, 2017 An outstanding challenge in nonlinear systems theory is identification or learning of a given nonlinear system's Koopman operator directly from data or models.
Charles A. Johnson, Enoch Yeung
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