2021/11/05 by Mirko Goldmann, Cláudio R. Mirasso, Goldmann, Mirko +5
Computer Science · Mathematics · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Artificial intelligence #Artificial neural network #Bifurcation #Computer science #Dynamical systems theory #Dynamics (music) #FOS: Computer and information sciences #FOS: Physical sciences #Homogeneous space #Machine Learning (cs.LG) #Mathematics #Network dynamics #Neural Networks and Reservoir Computing #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Physics #Scalability #Scaling #Statistical physics #Symmetry (geometry) #Theoretical computer science #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2111.03706
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2021/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.