Learning emergent partial differential equations in a learned emergent space.

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 colle

SUBMITTER: Kemeth FP 

PROVIDER: S-EPMC9184577 | biostudies-literature | 2022 Jun

REPOSITORIES: biostudies-literature