Extended dynamic mode decomposition with dictionary learning using neural ordinary differential equations
| Autor: | Sho Shirasaka, Hideyuki Suzuki, Hiroaki Terao |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Signal Processing (eess.SP)
FOS: Computer and information sciences Computer Science - Machine Learning Polymers and Plastics Computer science FOS: Physical sciences Dynamical Systems (math.DS) Machine Learning (cs.LG) Operator (computer programming) Dynamic mode decomposition FOS: Mathematics FOS: Electrical engineering electronic engineering information engineering Mathematics - Numerical Analysis Electrical Engineering and Systems Science - Signal Processing Mathematics - Dynamical Systems General Environmental Science Nonlinear phenomena Artificial neural network Continuum (topology) Numerical Analysis (math.NA) Nonlinear Sciences - Chaotic Dynamics Physics - Data Analysis Statistics and Probability Ordinary differential equation Chaotic Dynamics (nlin.CD) Dictionary learning Algorithm Data Analysis Statistics and Probability (physics.data-an) |
| DOI: | 10.48550/arxiv.2110.01450 |
| Popis: | 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. Comment: Corrigendum: The loss function in Eq. (20) is not what we have used in our code. Please replace the sum of squared error in Eq. (20) with the mean squared error |
| Databáze: | OpenAIRE |
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