The field of nonlinear dynamics modeling and forecasting is experiencing significant growth, driven by advances in machine learning, data assimilation, and reduced-order modeling. Researchers are developing innovative methods to improve the accuracy and efficiency of models, including the use of reservoir computing, ensemble Kalman filters, and generative models. These approaches are being applied to a range of complex systems, from ocean turbulence and chaotic flows to sea surface temperature prediction. A key trend is the integration of data-driven techniques with physical models, enabling the development of more accurate and robust forecasting systems. Notably, studies have demonstrated the importance of matching the nonlinearity of the reservoir computer to that of the input data, and the potential of tailored minimal reservoir computing for improving predictive performance. Noteworthy papers include: Denoising and Reconstruction of Nonlinear Dynamics using Truncated Reservoir Computing, which presents a novel reservoir computing method for noise filtering and reconstructing nonlinear dynamics. Generative emulation of chaotic dynamics with coherent prior, which introduces an efficient generative framework for dynamics emulation, achieving superior long-range forecasting skill. Data-Assimilated Model-Based Reinforcement Learning for Partially Observed Chaotic Flows, which proposes a framework for controlling turbulent flows with partial observability and noisy measurements. Tailored minimal reservoir computing, which explores the connection between nonlinearities in the reservoir and in data, and proposes a method for estimating the minimal nonlinearity in unknown time series.
Advances in Nonlinear Dynamics Modeling and Forecasting
Sources
Randomized Proper Orthogonal Decomposition for data-driven reduced order modeling of a two-layer quasi-geostrophic ocean model
Fourier analysis of the physics of transfer learning for data-driven subgrid-scale models of ocean turbulence