Learn one size to infer all: Exploiting translational symmetries in delay-dynamical and spatio-temporal systems using scalable neural networks
This work addresses the challenge of scaling neural network predictions in dynamical systems for researchers in physics and engineering, though it appears incremental as it builds on existing symmetry-exploiting methods.
The authors tackled the problem of predicting high-dimensional dynamics for different system sizes by designing scalable neural networks that exploit translational symmetries in delay-dynamical and spatio-temporal systems, demonstrating that training on a single size allows inference of entire bifurcation diagrams for larger or smaller sizes.
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.