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Controlling nonlinear dynamical systems into arbitrary states using machine learning.

ABSTRACT: Controlling nonlinear dynamical systems is a central task in many different areas of science and engineering. Chaotic systems can be stabilized (or chaotified) with small perturbations, yet existing approaches either require knowledge about the underlying system equations or large data sets as they rely on phase space methods. In this work we propose a novel and fully data driven scheme relying on machine learning (ML), which generalizes control techniques of chaotic systems without requiring a mathematical model for its dynamics. Exploiting recently developed ML-based prediction capabilities, we demonstrate that nonlinear systems can be forced to stay in arbitrary dynamical target states coming from any initial state. We outline and validate our approach using the examples of the Lorenz and the Rössler system and show how these systems can very accurately be brought not only to periodic, but even to intermittent and different chaotic behavior. Having this highly flexible control scheme with little demands on the amount of required data on hand, we briefly discuss possible applications ranging from engineering to medicine.

SUBMITTER: Haluszczynski A

PROVIDER: S-EPMC8217470 | biostudies-literature | 2021 Jun

REPOSITORIES: biostudies-literature

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Controlling nonlinear dynamical systems into arbitrary states using machine learning.

Haluszczynski Alexander A Räth Christoph C

Scientific reports 20210621 1

Controlling nonlinear dynamical systems is a central task in many different areas of science and engineering. Chaotic systems can be stabilized (or chaotified) with small perturbations, yet existing approaches either require knowledge about the underlying system equations or large data sets as they rely on phase space methods. In this work we propose a novel and fully data driven scheme relying on machine learning (ML), which generalizes control techniques of chaotic systems without requiring a ...[more]

PMID: 34155228

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Project description:Objective. To study the neural control of movement, it is often necessary to estimate how muscles are activated across a variety of behavioral conditions. One approach is to try extracting the underlying neural command signal to muscles by applying latent variable modeling methods to electromyographic (EMG) recordings. However, estimating the latent command signal that underlies muscle activation is challenging due to its complex relation with recorded EMG signals. Common approaches estimate each muscle's activation independently or require manual tuning of model hyperparameters to preserve behaviorally-relevant features.Approach. Here, we adapted AutoLFADS, a large-scale, unsupervised deep learning approach originally designed to de-noise cortical spiking data, to estimate muscle activation from multi-muscle EMG signals. AutoLFADS uses recurrent neural networks to model the spatial and temporal regularities that underlie multi-muscle activation.Main results. We first tested AutoLFADS on muscle activity from the rat hindlimb during locomotion and found that it dynamically adjusts its frequency response characteristics across different phases of behavior. The model produced single-trial estimates of muscle activation that improved prediction of joint kinematics as compared to low-pass or Bayesian filtering. We also applied AutoLFADS to monkey forearm muscle activity recorded during an isometric wrist force task. AutoLFADS uncovered previously uncharacterized high-frequency oscillations in the EMG that enhanced the correlation with measured force. The AutoLFADS-inferred estimates of muscle activation were also more closely correlated with simultaneously-recorded motor cortical activity than were other tested approaches.Significance.This method leverages dynamical systems modeling and artificial neural networks to provide estimates of muscle activation for multiple muscles. Ultimately, the approach can be used for further studies of multi-muscle coordination and its control by upstream brain areas, and for improving brain-machine interfaces that rely on myoelectric control signals.

Dataset Information

Controlling nonlinear dynamical systems into arbitrary states using machine learning.

Publications

Controlling nonlinear dynamical systems into arbitrary states using machine learning.

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