Learning emergent partial differential equations in a learned emergent space
Loading...
Date
2022-06-09
Open Access Location
Journal Title
Journal ISSN
Volume Title
Publisher
Springer Nature Limited
Rights
(c) 2022 The Author/s
CC BY 4.0
CC BY 4.0
Abstract
We propose an approach to learn effective evolution equations for large systems of interacting agents. This is demonstrated on two examples, a well-studied system of coupled normal form oscillators and a biologically motivated example of coupled Hodgkin-Huxley-like neurons. For such types of systems there is no obvious space coordinate in which to learn effective evolution laws in the form of partial differential equations. In our approach, we accomplish this by learning embedding coordinates from the time series data of the system using manifold learning as a first step. In these emergent coordinates, we then show how one can learn effective partial differential equations, using neural networks, that do not only reproduce the dynamics of the oscillator ensemble, but also capture the collective bifurcations when system parameters vary. The proposed approach thus integrates the automatic, data-driven extraction of emergent space coordinates parametrizing the agent dynamics, with machine-learning assisted identification of an emergent PDE description of the dynamics in this parametrization.
Description
Keywords
Machine Learning, Neural Networks, Computer, Neurons
Citation
Kemeth FP, Bertalan T, Thiem T, Dietrich F, Moon SJ, Laing CR, Kevrekidis IG. (2022). Learning emergent partial differential equations in a learned emergent space.. Nat Commun. 13. 1. (pp. 3318-).