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Found 10 papers, 0 papers with code
Learning Invariant Subspaces of Koopman Operators--Part 1: A Methodology for Demonstrating a Dictionary's Approximate Subspace Invariance
Recently, deep learning combined with EDMD has been used to learn novel dictionary functions in an algorithm called deep dynamic mode decomposition (deepDMD).
Learning Invariant Subspaces of Koopman Operators--Part 2: Heterogeneous Dictionary Mixing to Approximate Subspace Invariance
The SILL dictionary's nonlinear functions are homogeneous, a norm in data-driven dictionary learning of Koopman operators.
Heterogeneous mixtures of dictionary functions to approximate subspace invariance in Koopman operators
We discover a novel class of dictionary functions to approximate Koopman observables.
Towards Scalable Koopman Operator Learning: Convergence Rates and A Distributed Learning Algorithm
We propose an alternating optimization algorithm to the nonconvex Koopman operator learning problem for nonlinear dynamic systems.
A Constructive Approach for One-Shot Training of Neural Networks Using Hypercube-Based Topological Coverings
In this paper we presented a novel constructive approach for training deep neural networks using geometric approaches.
Enforcing constraints for interpolation and extrapolation in Generative Adversarial Networks
We suggest ways to enforce given constraints in the output of a Generative Adversarial Network (GAN) generator both for interpolation and extrapolation (prediction).
A Class of Logistic Functions for Approximating State-Inclusive Koopman Operators
An outstanding challenge in nonlinear systems theory is identification or learning of a given nonlinear system's Koopman operator directly from data or models.
Solving differential equations with unknown constitutive relations as recurrent neural networks
We solve a system of ordinary differential equations with an unknown functional form of a sink (reaction rate) term.
Decomposition of Nonlinear Dynamical Systems Using Koopman Gramians
In this paper we propose a new Koopman operator approach to the decomposition of nonlinear dynamical systems using Koopman Gramians.
Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems
The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery.
