Learn one size to infer all: Exploiting symmetries in dynamical systems using scalable neural networks

Tackling unavailable analytical models, machine learning methods emerged that learn from large amounts of data to forecast the dynamics of complex systems. Yet such predictions are mainly restricted to the dynamical regime observed during training. Here, we attempt to answer the question - Is it possible to infer untrained (size-dependent) dynamical regimes of a complex system while learning from one example related to a certain system size only? Therefore, we design scalable neural networks 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 network by its own predictions. Subsequently, by scaling the size of the trained network, we can predict 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.

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Tobias Galla

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