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

arXiv: https://arxiv.org/abs/2511.12512 · HTML: https://mlsanity.com/paper/2511.12512/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 26 references that are in the map.
- First posted on arXiv 16 Nov 2025.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [xLSTM: Extended Long Short-Term Memory](https://mlsanity.com/paper/2405.04517/) (2024)
- [Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Sampling](https://mlsanity.com/paper/2207.02338/) (2022)
- [PointNet with KAN versus PointNet with MLP for 3D Classification and Segmentation of Point Sets](https://mlsanity.com/paper/2410.10084/) (2024)
- [Understanding and Mitigating Extrapolation Failures in Physics-Informed Neural Networks](https://mlsanity.com/paper/2306.09478/) (2023)
- [Physics-Informed Neural Networks for High-Frequency and Multi-Scale Problems using Transfer Learning](https://mlsanity.com/paper/2401.02810/) (2024)
- [Momentum Diminishes the Effect of Spectral Bias in Physics-Informed Neural Networks](https://mlsanity.com/paper/2206.14862/) (2022)
- [Physics-informed KAN PointNet: Deep learning for simultaneous solutions to inverse problems in incompressible flow on numerous irregular geometries](https://mlsanity.com/paper/2504.06327/) (2025)
- [Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method](https://mlsanity.com/paper/2501.07700/) (2025)
- [LNN-PINN: A Unified Physics-Only Training Framework with Liquid Residual Blocks](https://mlsanity.com/paper/2508.08935/) (2025)

## Abstract (arXiv)

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.