20221204Deep Learning to Discover Coordinates for Dynamics: Autoencoders & Physics Informed ML

原视频https://www.youtube.com/watch?v=KmQkDgu-Qp0​​​​​​​

        In complex systems,we know that there are low dimentional patterns and a few degrees of freedom that matter

Deep autoencoder for dynamics

        需要在普通的encoder-decoder基础上加一个f来学习系统的变化

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right coordinate system的重要性 

        选择以太阳为中心比地球为中心的系统要简单的多

提到sindy+autoencoder的paper作为方法之一：

        Data-driven discovery of coordinates and governing equations

提到的其他paper作为方法之二：

        Mardt, Pasquali, Wu, & Noé, Nat. Comm. 20 18 [arXiv:I7 10.06012] ——Deep learning of molecular kinetics

        Wehmeyer and Noé, J. Chem. Phys. 2018 [arXiv:l710.I 1239] ——Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics

        Yeung, Kundu, Hodas, 2017 [arXiv: 1708.06850]——Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems

        Takeishi, Kawahara, & Yairi, NeurlPS 2017 [arXiv:I710.04340] ——

        Otto and Rowley, SIADS 2019 [arXiv:I7 12.01378]——Linearly-Recurrent Autoencoder Networks for Learning Dynamics

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Other         

        constrictive autoencoder might be more interpretable，you might be able to tease out relationships

conclude

        i've shown you two examples one is where f is sparse andnon-linear using our sindy approach,another perspective is where you try to find a coordinate embedding where f is actually linear this is a matrix and both of those are you know getting widely explored in the literature.

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