DeepAI AI Chat
Log In Sign Up

Extended dynamic mode decomposition with dictionary learning using neural ordinary differential equations

10/01/2021
by   Hiroaki Terao, et al.
Osaka University
0

Nonlinear phenomena can be analyzed via linear techniques using operator-theoretic approaches. Data-driven method called the extended dynamic mode decomposition (EDMD) and its variants, which approximate the Koopman operator associated with the nonlinear phenomena, have been rapidly developing by incorporating machine learning methods. Neural ordinary differential equations (NODEs), which are a neural network equipped with a continuum of layers, and have high parameter and memory efficiencies, have been proposed. In this paper, we propose an algorithm to perform EDMD using NODEs. NODEs are used to find a parameter-efficient dictionary which provides a good finite-dimensional approximation of the Koopman operator. We show the superiority of the parameter efficiency of the proposed method through numerical experiments.

READ FULL TEXT

page 11

page 13

11/14/2021

Numerical methods to evaluate Koopman matrix from system equations

A method that is employed to evaluate a Koopman matrix from a data set o...
10/01/2022

Parameter-varying neural ordinary differential equations with partition-of-unity networks

In this study, we propose parameter-varying neural ordinary differential...
02/07/2020

Adaptive semiparametric Bayesian differential equations via sequential Monte Carlo

Nonlinear differential equations (DEs) are used in a wide range of scien...
01/16/2023

Data-Driven Encoding: A New Numerical Method for Computation of the Koopman Operator

This paper presents a data-driven method for constructing a Koopman line...
06/27/2022

Heterogeneous mixtures of dictionary functions to approximate subspace invariance in Koopman operators

Koopman operators model nonlinear dynamics as a linear dynamic system ac...
01/07/2022

Forecasting emissions through Kaya identity using Neural Ordinary Differential Equations

Starting from the Kaya identity, we used a Neural ODE model to predict t...