Reservoir Computing with Error Correction: Long-term Behaviors of Stochastic Dynamical Systems

• URL: http://arxiv.org/abs/2305.00669v2
• Date: Sun, 30 Jul 2023 13:35:13 GMT
• Title: Reservoir Computing with Error Correction: Long-term Behaviors of Stochastic Dynamical Systems
• Authors: Cheng Fang, Yubin Lu, Ting Gao, Jinqiao Duan
• Abstract summary: We propose a data-driven framework combining Reservoir Computing and Normalizing Flow to study this issue. We verify the effectiveness of the proposed framework in several experiments, including the Van der Pal, El Nino-Southern Oscillation simplified model, and Lorenz system.
• Score: 5.815325960286111
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The prediction of stochastic dynamical systems and the capture of dynamical behaviors are profound problems. In this article, we propose a data-driven framework combining Reservoir Computing and Normalizing Flow to study this issue, which mimics error modeling to improve traditional Reservoir Computing performance and integrates the virtues of both approaches. With few assumptions about the underlying stochastic dynamical systems, this model-free method successfully predicts the long-term evolution of stochastic dynamical systems and replicates dynamical behaviors. We verify the effectiveness of the proposed framework in several experiments, including the stochastic Van der Pal oscillator, El Ni\~no-Southern Oscillation simplified model, and stochastic Lorenz system. These experiments consist of Markov/non-Markov and stationary/non-stationary stochastic processes which are defined by linear/nonlinear stochastic differential equations or stochastic delay differential equations. Additionally, we explore the noise-induced tipping phenomenon, relaxation oscillation, stochastic mixed-mode oscillation, and replication of the strange attractor.

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