Deep dim reduction

Here we present techniques which can be used to project timeseries onto dominant processes aided by deep neural networks. In order to use the implementations provided by deeptime, a working installation of PyTorch is required.

In particular, the following methods are implemented:

• VAMPNets
• Time-lagged autoencoders
  • Autoencoders
  • Variational autoencoders

VAMPNets [1] belong to the family of Koopman methods and try to maximize a variational score which is described, e.g., here. They can be used to find transformations of the observed data such that the estimated Koopman operator is particularly close to the real and underlying Koopman operator.

Time-lagged autoencoders [2] on the other hand can also to some degree be related to Koopman theory (see the reference for details), but at their core try to learn a mapping of the input data to a latent code which can then be transformed back to the next point in time, i.e., they try to find mappings \(E: \mathbb{R}^N \to\mathbb{R}^n\) and \(D: \mathbb{R}^n\to\mathbb{R}^N\) with \(n < N\) such that \(x_{t+\tau}\approx (D\circ E)(x_t)\).

References

[1]

Andreas Mardt, Luca Pasquali, Hao Wu, and Frank Noé. Vampnets for deep learning of molecular kinetics. Nature communications, 9(1):1–11, 2018.

[2]

Christoph Wehmeyer and Frank Noé. Time-lagged autoencoders: deep learning of slow collective variables for molecular kinetics. J. Chem. Phys., 148(24):241703, jun 2018. doi:10.1063/1.5011399.