# Stochastic embeddings of dynamical phenomena through variational autoencoders

System identification in scenarios where the observed number of variables is less than
the degrees of freedom in the dynamics is an important challenge. In this work we
tackle this problem by using a recognition network to increase the observed space
dimensionality during the reconstruction of the phase space. The phase space is forced
to have approximately Markovian dynamics described by a Stochastic Differential Equation
(SDE), which is also to be discovered. To enable robust learning from stochastic data we
use the Bayesian paradigm and place priors on the drift and diffusion terms. To handle
the complexity of learning the posteriors, a set of mean field variational approximations to
the true posteriors are introduced, enabling efficient statistical inference. Finally, a decoder
network is used to obtain plausible reconstructions of the experimental data. The main
advantage of this approach is that the resulting model is interpretable within the paradigm
of statistical physics. Our validation shows that this approach not only recovers a state
space that resembles the original one, but it is also able to synthesize new time series
capturing the main properties of the experimental data.

keywords: Stochastic Differential Equation, Gaussian process state space model, Structured variational autoencoder

Publication: Article

1654594487114

June 7, 2022

/research/publications/stochastic-embeddings-of-dynamical-phenomena-through-variational-autoencoders

System identification in scenarios where the observed number of variables is less than
the degrees of freedom in the dynamics is an important challenge. In this work we
tackle this problem by using a recognition network to increase the observed space
dimensionality during the reconstruction of the phase space. The phase space is forced
to have approximately Markovian dynamics described by a Stochastic Differential Equation
(SDE), which is also to be discovered. To enable robust learning from stochastic data we
use the Bayesian paradigm and place priors on the drift and diffusion terms. To handle
the complexity of learning the posteriors, a set of mean field variational approximations to
the true posteriors are introduced, enabling efficient statistical inference. Finally, a decoder
network is used to obtain plausible reconstructions of the experimental data. The main
advantage of this approach is that the resulting model is interpretable within the paradigm
of statistical physics. Our validation shows that this approach not only recovers a state
space that resembles the original one, but it is also able to synthesize new time series
capturing the main properties of the experimental data. - Constantino A. García, Paulo Félix, Jesús M. Presedo, Abraham Otero - 10.1016/j.jcp.2022.110970

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