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<p>The Nonlinear Schrödinger (NLS) equation is fundamental to modeling nonlinear wave phenomena across optics, plasma physics, and quantum systems, where soliton solutions serve as key localized structures. This study introduces an enhanced neural operator framework for soliton modeling based on the DeepOKAN architecture. By integrating the FitNets knowledge distillation strategy, the proposed model achieves improved accuracy and robustness in solving diverse NLS-type equations. Quantitative experiments demonstrate that the FitNets-based distillation reduces relative <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(l_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>l</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> errors by over 16.4% compared to logits-only schemes, while activation adjustments such as tanh fail to yield further gains. The results confirm the model’s strong expressive capacity even with compact architectures, highlighting the feasibility of embedding structured knowledge into operator learning for complex nonlinear dynamics. This work provides a novel and generalizable pathway for advancing neural-operator-based scientific computing.</p>

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Fit-deepokan: enhancing neural operator learning of soliton dynamics via FitNets distillation

  • 期刊论文

  • 发表日期：

    2026年2月26日

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  • Lan Chen,
  • Houhui Yi,
  • Zhiyang Zhang,
  • Muwei Liu,
  • Wenjun Liu

摘要

The Nonlinear Schrödinger (NLS) equation is fundamental to modeling nonlinear wave phenomena across optics, plasma physics, and quantum systems, where soliton solutions serve as key localized structures. This study introduces an enhanced neural operator framework for soliton modeling based on the DeepOKAN architecture. By integrating the FitNets knowledge distillation strategy, the proposed model achieves improved accuracy and robustness in solving diverse NLS-type equations. Quantitative experiments demonstrate that the FitNets-based distillation reduces relative \(l_2\) l 2 errors by over 16.4% compared to logits-only schemes, while activation adjustments such as tanh fail to yield further gains. The results confirm the model’s strong expressive capacity even with compact architectures, highlighting the feasibility of embedding structured knowledge into operator learning for complex nonlinear dynamics. This work provides a novel and generalizable pathway for advancing neural-operator-based scientific computing.