īenjamin Erichson N, Manohar K et al (2020) Randomized CP tensor decomposition. īai Z, Kaiser E et al (2020) Dynamic mode decomposition for compressive. īaek SH, Garcia-Diaz A, Dai Y (2020) Multi-choice wavelet thresholding based binary classification method. Advanced deep learning methods like autoencoders, recurrent neural networks, convolutional neural networks, and reinforcement learning are used in modeling of dynamical systems.Ītencia M, Joya G, Sandoval F (2005) Hopfield neural networks for parametric identification of dynamical systems. Machine learning provides advanced new and powerful algorithms for nonlinear dynamics. The identification of dynamical systems through deep learning techniques succeeds in inferring physical systems.
Data-driven models drive to discover the governing equations and give laws of physics. Dimensionality reduction methods are used for projecting dynamical methods in reduced form, and these methods perform computational efficiency on real-world data. Machine learning is providing new and powerful techniques for both challenges. The two chief challenges are (1) nonlinear dynamics and (2) unknown or partially known dynamics. We explore various challenges in modern dynamical systems, along with emerging techniques in data science and machine learning to tackle them. In particular, our review focuses on the key challenges of discovering dynamics from data and finding data-driven representations that make nonlinear systems amenable to linear analysis. This review presents a modern perspective on dynamical systems in the context of current goals and open challenges.
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