Scholarlink

<p>Physics-Informed Neural Networks (PINNs) offer a mesh-free paradigm for solving partial differential equations but struggle with stiff, multi-scale systems due to spectral bias in standard multilayer perceptron architectures. We introduce the Adaptive Spectral Physics-Enabled Network (ASPEN), integrating an adaptive spectral layer with learnable Fourier features that dynamically tunes its spectral basis during training to efficiently capture required frequency content. We demonstrate ASPEN on the complex Ginzburg-Landau equation (CGLE), a canonical benchmark for nonlinear, stiff spatio-temporal dynamics. While standard PINNs catastrophically fail with non-physical oscillations, ASPEN successfully solves the CGLE with exceptional accuracy. The predicted solution is visually indistinguishable from high-resolution ground truth, achieving a median physics residual of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(5.10 \times 10^{-3}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>5.10</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>. ASPEN’s solution is pointwise accurate and physically consistent, correctly capturing emergent properties including rapid free energy relaxation and long-term domain wall stability. This work demonstrates that incorporating an adaptive spectral basis provides a robust, physically-consistent solver for complex dynamical systems where standard PINNs fail, opening new avenues for machine learning in challenging physical domains.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

An adaptive spectral physics-enabled network for Ginzburg-Landau dynamics

  • 期刊论文

  • 发表日期：

    2026年2月26日

查看全文
  • Julian Evan Chrisnanto,
  • Nurfauzi Fadillah,
  • Yulison Herry Chrisnanto

摘要

Physics-Informed Neural Networks (PINNs) offer a mesh-free paradigm for solving partial differential equations but struggle with stiff, multi-scale systems due to spectral bias in standard multilayer perceptron architectures. We introduce the Adaptive Spectral Physics-Enabled Network (ASPEN), integrating an adaptive spectral layer with learnable Fourier features that dynamically tunes its spectral basis during training to efficiently capture required frequency content. We demonstrate ASPEN on the complex Ginzburg-Landau equation (CGLE), a canonical benchmark for nonlinear, stiff spatio-temporal dynamics. While standard PINNs catastrophically fail with non-physical oscillations, ASPEN successfully solves the CGLE with exceptional accuracy. The predicted solution is visually indistinguishable from high-resolution ground truth, achieving a median physics residual of \(5.10 \times 10^{-3}\) 5.10 × 10 - 3 . ASPEN’s solution is pointwise accurate and physically consistent, correctly capturing emergent properties including rapid free energy relaxation and long-term domain wall stability. This work demonstrates that incorporating an adaptive spectral basis provides a robust, physically-consistent solver for complex dynamical systems where standard PINNs fail, opening new avenues for machine learning in challenging physical domains.