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

@article{Goldmann2021LearnOS,
  title={Learn one size to infer all: Exploiting translational symmetries in delay-dynamical and spatiotemporal systems using scalable neural networks.},
  author={Mirko Goldmann and Claudio R. Mirasso and Ingo Fischer and Miguel C. Soriano},
  journal={Physical review. E},
  year={2021},
  volume={106 4-1},
  pages={
          044211
        }
}
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… 
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