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.
@article{arxiv.2511.12512,
title = {xLSTM-PINN: Memory-Gated Spectral Remodeling for Physics-Informed Learning},
author = {Ze Tao and Darui Zhao and Fujun Liu and Ke Xu and Xiangsheng Hu},
journal= {arXiv preprint arXiv:2511.12512},
year = {2025}
}