Model discovery for dynamical systems with complex-valued product units

• URL: http://arxiv.org/abs/2605.27158v1
• Date: Tue, 26 May 2026 15:18:47 GMT
• Title: Model discovery for dynamical systems with complex-valued product units
• Abstract summary: We present a data-driven approach to model discovery based on complex-valued product-unit networks.<n>We recover the exact governing equations in 90% of trials for the first three systems, and in 70-90% of trials for the fractional case.<n>The model produced stable trajectories with bounded prediction errors, corresponding to an RMSE of approximately 12-14% of the signal amplitude range over a test horizon three times longer than the training interval.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Discovering the governing equations of a dynamical system from observed trajectories provides deeper insight into its structure than mere prediction of future states. We present a data-driven approach to model discovery based on complex-valued product-unit networks, in which each unit represents a complex monomial and the network output is a sparse linear combination of such monomials. In contrast to established library-based methods such as SINDy, our approach does not require a predefined set of candidate functions: the relevant monomials, including those with fractional or negative exponents, are learned directly from data. Across four chaotic benchmark systems (Lorenz63, Lorenz84, the Four-Wing attractor, and a fractional variant of Lorenz63), we recover the exact governing equations in 90% of trials for the first three systems, and in 70-90% of trials for the fractional case, using at least 3000 training points. Applied to real-world human-gait accelerometer signals, the model produced stable trajectories with bounded prediction errors, corresponding to an RMSE of approximately 12-14% of the signal amplitude range over a test horizon three times longer than the training interval, demonstrating its potential for high-dimensional systems in which analytic equations are unavailable.

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