xLSTM-PINN: Memory-Gated Spectral Remodeling for Physics-Informed Learning
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917126974996480 |
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| author | Tao, Ze Zhao, Darui Liu, Fujun Xu, Ke Hu, Xiangsheng |
| author_facet | Tao, Ze Zhao, Darui Liu, Fujun Xu, Ke Hu, Xiangsheng |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12512 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | xLSTM-PINN: Memory-Gated Spectral Remodeling for Physics-Informed Learning Tao, Ze Zhao, Darui Liu, Fujun Xu, Ke Hu, Xiangsheng Machine Learning 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. |
| title | xLSTM-PINN: Memory-Gated Spectral Remodeling for Physics-Informed Learning |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2511.12512 |