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
需要在普通的encoder-decoder基础上加一个f来学习系统的变化
选择以太阳为中心比地球为中心的系统要简单的多
Data-driven discovery of coordinates and governing equations
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
constrictive autoencoder might be more interpretable,you might be able to tease out relationships
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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Deep Auto_encoder
https://blog.csdn.net/one_super_dreamer/article/details/104198573
【机器学习】降维——SVD原理以及示例
https://www.imooc.com/article/267351?block_id=tuijian_wz
qr factorization
最优化方法——QR Factorization_显然易证的博客-CSDN博客