Empirical Stability Analysis of Kolmogorov-Arnold Networks in Hard-Constrained Recurrent Physics-Informed Discovery

• URL: http://arxiv.org/abs/2602.09988v1
• Date: Tue, 10 Feb 2026 17:13:51 GMT
• Title: Empirical Stability Analysis of Kolmogorov-Arnold Networks in Hard-Constrained Recurrent Physics-Informed Discovery
• Authors: Enzo Nicolas Spotorno, Josafat Leal Filho, Antonio Augusto Medeiros Frohlich,
• Abstract summary: We investigate the integration of Kolmogorov-Arnold Networks (KANs) into hard-constrained recurrent physics architectures (HRPINN)<n>We show that KANs exhibit severe fragility, instability in deeper configurations, and consistent failure on multiplicative terms (Van der Pol)<n>These empirical challenges highlight limitations of the additive inductive bias in the original KAN formulation and provide preliminary empirical evidence of inductive bias limitations for future hybrid modeling.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate the integration of Kolmogorov-Arnold Networks (KANs) into hard-constrained recurrent physics-informed architectures (HRPINN) to evaluate the fidelity of learned residual manifolds in oscillatory systems. Motivated by the Kolmogorov-Arnold representation theorem and preliminary gray-box results, we hypothesized that KANs would enable efficient recovery of unknown terms compared to MLPs. Through initial sensitivity analysis on configuration sensitivity, parameter scale, and training paradigm, we found that while small KANs are competitive on univariate polynomial residuals (Duffing), they exhibit severe hyperparameter fragility, instability in deeper configurations, and consistent failure on multiplicative terms (Van der Pol), generally outperformed by standard MLPs. These empirical challenges highlight limitations of the additive inductive bias in the original KAN formulation for state coupling and provide preliminary empirical evidence of inductive bias limitations for future hybrid modeling.

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