Dynamics-based predictions of infinite-dimensional complex systems using dynamical system deep learning method

• DOI: 10.1088/2632-2153/adc53b
• Publication Date: 2025-03-25T23:49:40Z
• Authors: Hao Li; Jianping Li; Zixiang Wu; Mingyu Wang; Guangcan Liu; Ruipeng Sun; Ruize Li; Ning Wang; Houbin Song; Shixin Zhen
• Keywords: Dynamics; Complex system; Complex dynamics

Abstract Predicting complex nonlinear chaotic dynamical systems constitutes a critical and formidable challenge across various disciplines. A novel methodology termed Dynamical System Deep Learning (DSDL) has recently been introduced utilized for the prediction of systems. This method not only exceeds current techniques but also extracts key variables target systems, thereby providing feasible resolution to “black box” problem. Nonetheless, present focus this chiefly on predicting finite-dimensional real-world phenomena are mainly governed by partial differential equations. research selects Lorenz’ 96 system, set coupled ordinary equations with spatiotemporal dynamics, Kuramoto-Sivashinsky equation as representative examples infinite-dimensional evaluate effectiveness DSDL. We conduct comparisons several mainstream DL methods including ANN, RC-ESN, LSTM NG-RC. The findings demonstrate that DSDL exhibits outstanding performance In long-term predictions, DSDL’s results align most accurately statistical characteristics reference true values, outperforming other mentioned above. Finally, study discusses efficacy, efficiency superiority in well its significant contributions variable extraction.