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

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 spatiotemporal 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.

Automated summary

We propose scalable neural networks that can handle translational symmetries in dynamical systems and infer high-dimensional dynamics for different system sizes. By training the networks to predict dynamics for a single size and then driving them with their own predictions, we show that the complex dynamics for larger or smaller system sizes can be accurately predicted. The network learns from a single example and leverages symmetry properties to infer entire bifurcation diagrams.