Journal Article

Identifying nonlinear dynamical systems via generative recurrent neural networks with applications to fMRI

Lis, Stefanie, Koppe, Georgia, Toutounji, Hazem, Durstewitz, Daniel, Kirsch, Peter

2019

Overview

A major tenet in theoretical neuroscience is that cognitive and behavioral processes are ultimately implemented in terms of the neural system dynamics. Accordingly, a major aim for the analysis of neurophysiological measurements should lie in the identification of the computational dynamics underlying task processing. Here we advance a state space model (SSM) based on generative piecewise-linear recurrent neural networks (PLRNN) to assess dynamics from neuroimaging data. In contrast to many other nonlinear time series models which have been proposed for reconstructing latent dynamics, our model is easily interpretable in neural terms, amenable to systematic dynamical systems analysis of the resulting set of equations, and can straightforwardly be transformed into an equivalent continuous-time dynamical system. The major contributions of this paper are the introduction of a new observation model suitable for functional magnetic resonance imaging (fMRI) coupled to the latent PLRNN, an efficient stepwise training procedure that forces the latent model to capture the 'true' underlying dynamics rather than just fitting (or predicting) the observations, and of an empirical measure based on the Kullback-Leibler divergence to evaluate from empirical time series how well this goal of approximating the underlying dynamics has been achieved. We validate and illustrate the power of our approach on simulated 'ground-truth' dynamical systems as well as on experimental fMRI time series, and demonstrate that the learnt dynamics harbors task-related nonlinear structure that a linear dynamical model fails to capture. Given that fMRI is one of the most common techniques for measuring brain activity non-invasively in human subjects, this approach may provide a novel step toward analyzing aberrant (nonlinear) dynamics for clinical assessment or neuroscientific research.

• Publisher: Public Library of Science,Public Library of Science (PLoS)
• Subject: Algorithms / Analysis / Artificial neural networks / Biology and Life Sciences / Brain - diagnostic imaging / Brain - physiology / Brain mapping / Cognitive ability / Computational Biology / Computational neuroscience / Computer and Information Sciences / Computer simulation / Continuous time systems / Divergence / Dynamic structural analysis / Dynamical systems / Empirical analysis / Functional magnetic resonance imaging / Functional Neuroimaging - statistics & numerical data / Humans / Identification and classification / Magnetic resonance imaging / Magnetic Resonance Imaging - statistics & numerical data / Medical imaging / Medical research / Medicine and Health Sciences / Memory / Mental health / Methods / Models, Neurological / Nerve Net - physiology / Nervous system / Neural networks / Neural Networks, Computer / Neuroimaging / Neurology / Neurosciences / Nonlinear analysis / Nonlinear Dynamics / Nonlinear systems / Physical Sciences / Pipelines / Psychotherapy / Recurrent neural networks / Research and Analysis Methods / Schizophrenia / Software / State space models / Supervision / System dynamics / Systems Analysis / Technology application / Time series