ASPEN通过自适应频谱机制,让神经网络精准捕捉复杂物理系统的高频动态。
ASPEN: An Adaptive Spectral Physics-Enabled Network for Ginzburg-Landau Dynamics
- 在输入层引入可学习傅里叶特征与自适应频谱层,动态调整频率表示能力
- 在复数型吉涅-兰道方程上实现低至5.10×10⁻³的中位物理残差,成功收敛
- 适合求解高阶非线性、多尺度、刚性物理系统,尤其对传统PINN失效场景有效
物理信息神经网络(PINNs)作为求解偏微分方程的无网格范式,因标准多层感知机(MLP)固有的谱偏差,在处理刚性、多尺度和非线性系统时表现不佳,难以表征高频成分。本文提出自适应频谱物理增强网络(ASPEN),通过在输入阶段集成可学习傅里叶特征与自适应频谱层,使模型在训练中动态调节自身频谱基,高效学习并表达解所需的精确频率内容。我们以复数型吉涅-兰道方程(CGLE)为挑战性基准测试,标准PINN在此问题上严重失败,导致非物理解振荡。而ASPEN则成功求解,预测解与高分辨率真值视觉一致,中位物理残差低至5.10×10⁻³。进一步验证表明,其解不仅点态准确,且物理一致,正确捕捉快速自由能松弛及域壁前沿的长期稳定性等涌现特性。本工作证明,引入自适应频谱基可构建鲁棒且物理解一致的复杂动力系统求解器,为机器学习在高难度物理领域应用开辟新路径。
原文摘要 · Abstract (English)
Physics-Informed Neural Networks (PINNs) have emerged as a powerful, mesh-free paradigm for solving partial differential equations (PDEs). However, they notoriously struggle with stiff, multi-scale, and nonlinear systems due to the inherent spectral bias of standard multilayer perceptron (MLP) architectures, which prevents them from adequately representing high-frequency components. In this work, we introduce the Adaptive Spectral Physics-Enabled Network (ASPEN), a novel architecture designed to overcome this critical limitation. ASPEN integrates an adaptive spectral layer with learnable Fourier features directly into the network's input stage. This mechanism allows the model to dynamically tune its own spectral basis during training, enabling it to efficiently learn and represent the precise frequency content required by the solution. We demonstrate the efficacy of ASPEN by applying it to the complex Ginzburg-Landau equation (CGLE), a canonical and challenging benchmark for nonlinear, stiff spatio-temporal dynamics. Our results show that a standard PINN architecture catastrophically fails on this problem, diverging into non-physical oscillations. In contrast, ASPEN successfully solves the CGLE with exceptional accuracy. The predicted solution is visually indistinguishable from the high-resolution ground truth, achieving a low median physics residual of 5.10 x 10^-3. Furthermore, we validate that ASPEN's solution is not only pointwise accurate but also physically consistent, correctly capturing emergent physical properties, including the rapid free energy relaxation and the long-term stability of the domain wall front. This work demonstrates that by incorporating an adaptive spectral basis, our framework provides a robust and physically-consistent solver for complex dynamical systems where standard PINNs fail, opening new options for machine learning in challenging physical domains.
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