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<p>Data-driven methods have opened new avenues for modeling nonlinear wave phenomena. In this study, we propose a radial basis function-based Kolmogorov–Arnold Network (RPIKAN) to explore nonlinear wave dynamics in up to (2+1)-dimensions for the first time. We conduct a systematic comparison against a spline function-based PIKAN and conventional physics-informed neural networks (PINNs) over ten numerical cases—solitary wave, kink wave, periodic wave, peakon, periodic peakon, compacton, and multi-soliton. Across all scenarios, our method exceeds or matches PINNs in predictive accuracy and consistently outperforms PIKAN in both convergence speed and final error levels. These results demonstrate that RPIKAN uniquely combines physics-informed modeling with flexible radial basis approximation, making it a highly efficient and high-fidelity solver for difficult and high-dimensional nonlinear wave dynamics.</p>

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Data-driven nonlinear wave dynamics via Kolmogorov–Arnold networks

  • 期刊论文

  • 发表日期：

    2026年1月20日

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  • Kebing Li,
  • Hong-Kun Zhang,
  • Dingshi Li,
  • Zhe Pu

摘要

Data-driven methods have opened new avenues for modeling nonlinear wave phenomena. In this study, we propose a radial basis function-based Kolmogorov–Arnold Network (RPIKAN) to explore nonlinear wave dynamics in up to (2+1)-dimensions for the first time. We conduct a systematic comparison against a spline function-based PIKAN and conventional physics-informed neural networks (PINNs) over ten numerical cases—solitary wave, kink wave, periodic wave, peakon, periodic peakon, compacton, and multi-soliton. Across all scenarios, our method exceeds or matches PINNs in predictive accuracy and consistently outperforms PIKAN in both convergence speed and final error levels. These results demonstrate that RPIKAN uniquely combines physics-informed modeling with flexible radial basis approximation, making it a highly efficient and high-fidelity solver for difficult and high-dimensional nonlinear wave dynamics.