Learning Iterated Function Systems from Time Series of Partial Observations

2025/08/19 by Gibson, Emilia, Lamb, Jeroen S. W.
#37B10 #37B55 #37H05 #37H99 #37M10 #65P9910 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.13794

Abstract

We develop a methodology to learn finitely generated random iterated function systems from time-series of partial observations using delay embeddings. We obtain a minimal model representation for the observed dynamics, using a hidden variable representation, that is diffeomorphic to the original system.

Citations

• Discovering dynamics and parameters of nonlinear oscillatory and chaotic systems from partial observations
• Delay Embeddings for Forced Systems. II. Stochastic Forcing
• Practical method for determining the minimum embedding dimension of a scalar time series
• Determining embedding dimension for phase-space reconstruction using a geometrical construction

Related

• Learning the Dynamics of Sparsely Observed Interacting Systems
• Learning theory for dynamical systems
• Parameter Inference of Time Series by Delay Embeddings and Learning Differentiable Operators
• Functional Latent Dynamics for Irregularly Sampled Time Series Forecasting
• Research Program: Theory of Learning in Dynamical Systems