CombOpNet: Scaling SINDy for High-Dimensional Dynamical Systems

March 7, 2025

TIME: 3:30 PM

LOCATION: GMCS 314

SPEAKER: Siyuan Xing, California Polytechnic State University, San Luis Obispo

ABSTRACT: In this talk, we introduce the Combinatorial Operation Neural Network (CombOpNet), a compact neural architecture designed to overcome the curse of dimensionality in Sparse Identification of Nonlinear Dynamics. Within CombOpNet, nonlinear terms in dynamical equations are represented by a chain of multiplication of univariate functions. These functions correspond to neurons of a multi-layer neural network that allows the construction of nonlinear terms in dynamical equations by employing forward propagation. This way, CombOpNet dramatically reduces the computational complexity from exponential to polynomial level, enabling SINDy to scale to high-dimensional systems previously considered intractable. Unlike traditional neural networks that struggle with untrained data, CombOpNet excels at extrapolation by precisely recovering governing equations, enabling reliable predictions of coherent structures in complex systems. Our method demonstrates remarkable noise tolerance even with incomplete or imperfect data. We’ll demonstrate the efficacy of this approach through several complex nonlinear dynamical systems, highlighting CombOpNet’s potential for advancing our understanding of large-scale, real-world systems.

HOST: Stahtis Charalampidis

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