xLSTM-PINN: Memory-Gated Spectral Remodeling for Physics-Informed Learning

TL;DR

This paper introduces xLSTM-PINN, a novel neural network architecture that reduces spectral bias in physics-informed learning, significantly improving high-frequency modeling, accuracy, and stability across multiple PDE benchmarks.

Contribution

xLSTM-PINN employs memory gating and residual micro-steps for spectral remodeling, offering a new approach to mitigate spectral bias without altering existing physics-informed training methods.

Findings

Lower spectral error and RMSE across four PDE benchmarks

Broader stable learning-rate window and faster convergence for high-frequency components

Frequency analysis shows enhanced high-frequency kernel weights and resolvable bandwidth

Abstract

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.