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Journal Article
Koopman 이론 기반 비선형 동적 시스템에 대한 결측값 보간 모델
- Issue Date
- 2024-11
- Citation
- 전기학회논문지, v.73, no.11, pp.2004-2010
- ISSN
- 1975-8359
- Publisher
- 대한전기학회
- Language
- Korean
- Type
- Journal Article
- Abstract
- In this paper, we propose a novel deep learning model based on Koopman theory to learn the partial differential equations (PDEs) inherent in data observed from nonlinear dynamical systems for missing data imputation. Since nonlinear PDEs such as the Navier-Stokes equations in fields like fluid dynamics and quantum mechanics still lack solutions, this paper addresses the long-term prediction problem of nonlinear dynamical systems by leveraging the Koopman Autoencoder (KAE) model. To improve the long-term prediction performance of KAE on nonlinear systems, we propose a multi-input-based KAE model that utilizes high temporal resolution multi-input data instead of lowering the temporal resolution of the model prediction. We validated the effectiveness of the proposed method through MSE, MAPE, and SMAPE metrics on three nonlinear dynamical system datasets—Navier-Stokes (smoke), Navier-Stokes (viscous flow), and Shallow-Water, showing significant improvement over baseline models.
- KSP Keywords
- Fluid Dynamics, High temporal resolution, Long-term Prediction, Missing Data Imputation, Multi-input, Navier-Stokes equations, Nonlinear PDEs, Nonlinear dynamical systems, Partial Differential Equations(PDEs), Quantum mechanics(QM), Shallow-water
This work is distributed under the term of Creative Commons License (CCL)
(CC BY NC)
(CC BY NC)
