Data-Driven Discovery of High-Dimensional Dynamical Systems with Sparse Interpretable Neural Networks

Abstract

Existing approaches to explicit data-driven discovery of nonlinear dynamical systems face a curse of dimensionality because candidate libraries grow combinatorially with system dimension. This challenge is particularly severe for high-dimensional systems arising from spatially discretized fields and large complex networks. We develop sparse regression embedded interpretable network (SREINet), a machine-learning framework that embeds sparse regression in an interpretable neural network and uses a sparsity-promoting periodic pruning scheme. Across six paradigmatic systems, SREINet accurately identifies velocity fields with more than 100 dimensions and extrapolates coherent structures from untrained data. Head-to-head benchmarks against representative equation-discovery and predictive methods on clean and noisy systems show that SREINet combines scalable computation with accurate, parsimonious equation recovery, particularly in high-dimensional settings. We further validate the framework using empirical data from a triple-pendulum experiment. These results demonstrate a practical route toward interpretable model discovery for large-scale nonlinear systems and suggest that the framework can be extended to systems with thousands of dimensions.