2023/05/01 by Cheng Fang, Fang, Cheng, Yubin Lu +5 · 1 citation
Computer Science · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Neural Networks and Applications #Neural Networks and Reservoir Computing
paper · pdf · doi:10.48550/arxiv.2305.00669
openalex publication_date 2023/05/01 · openalex created_date 2023/05/03 · openalex updated_date 2026/07/28
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 Niño-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.