通过记忆门控重构频谱，提升物理信息神经网络对高频现象的建模能力。
xLSTM-PINN: Memory-Gated Spectral Remodeling for Physics-Informed Learning
- 引入记忆门控与残差微步，实现表征层的频谱重塑。
- 在4个不同偏微分方程基准上显著降低频谱误差与均方根误差。
- 无需修改损失函数，适合需高精度外推的物理建模场景。
物理信息神经网络（PINN）受频谱偏差影响，难以建模高频现象且泛化性能受限。本文提出xLSTM-PINN，通过记忆门控与残差微步实现表征级频谱重塑。在四个不同的偏微分方程（PDE）基准测试中，该方法始终显著降低频谱误差与均方根误差（RMSE），并扩大稳定学习率范围。频域分析表明，xLSTM-PINN提升了高频核权重，使可分辨带宽右移，缩短了高波数成分的收敛时间。该方法无需改变自动微分或物理损失约束，为抑制频谱偏差提供了稳健路径，从而提升物理信息学习中的精度、可复现性与迁移能力。
原文摘要 · Abstract (English)
Physics-informed neural networks (PINN) face significant challenges from spectral bias, which impedes their ability to model high-frequency phenomena and limits extrapolation performance. To address this, we introduce xLSTM-PINN, a novel architecture that performs representation-level spectral remodeling through memory gating and residual micro-steps. Our method consistently achieves markedly lower spectral error and root mean square error (RMSE) across four diverse partial differential equation (PDE) benchmarks, along withhhh a broader stable learning-rate window. Frequency-domain analysis confirms that xLSTM-PINN elevates high-frequency kernel weights, shifts the resolvable bandwidth rightward, and shortens the convergence time for high-wavenumber components. Without modifying automatic differentiation or physics loss constraints, this work provides a robust pathway to suppress spectral bias, thereby improving accuracy, reproducibility, and transferability in physics-informed learning.
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