Learn one size to infer all: Exploiting translational symmetries in delay-dynamical and spatio-temporal systems using scalable neural networks

TL;DR

This paper introduces scalable neural networks that leverage translational symmetries to predict high-dimensional delay-dynamical and spatio-temporal systems across different sizes, enabling efficient inference of complex dynamics from minimal training.

Contribution

The authors develop neural networks that exploit translational symmetries, allowing for scalable predictions of system dynamics across varying sizes from a single trained example.

Findings

Networks successfully predict dynamics for larger and smaller systems.

The approach infers entire bifurcation diagrams from limited training.

Scalability is achieved without retraining for different system sizes.

Abstract

We design scalable neural networks adapted to translational symmetries in dynamical systems, capable of inferring untrained high-dimensional dynamics for different system sizes. We train these networks to predict the dynamics of delay-dynamical and spatio-temporal systems for a single size. Then, we drive the networks by their own predictions. We demonstrate that by scaling the size of the trained network, we can predict the complex dynamics for larger or smaller system sizes. Thus, the network learns from a single example and, by exploiting symmetry properties, infers entire bifurcation diagrams.