Xiangsheng Hu | Searcharxiv

arXiv2025

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

cs.LG↗

arXiv2025

Operator-Consistent Physics-Informed Learning for Wafer Thermal Reconstruction in Lithography

Thermal field reconstruction in post-exposure bake (PEB) is critical for advanced lithography, yet current physics-informed neural networks (PINNs) suffer from inconsistent accuracy due to a misalignment between geometric coordinates, physical fields, and differential operators. To resolve this, we introduce a novel architecture that unifies these elements on a single computation graph by integrating LSTM-gated mechanisms within a Liquid Neural Network (LNN) backbone. This specific combination of gated liquid layers is necessary to dynamically regulate the network's spectral behavior and enforce operator-level consistency, which ensures stable training and high-fidelity predictions. Applied to a 2D PEB scenario with internal heat generation and convective boundaries, our model formulates residuals via differential forms and a composite loss functional. The results demonstrate rapid convergence, uniformly low errors, strong agreement with FEM benchmarks, and stable training without late-stage oscillations, outperforming existing baselines in accuracy and robustness. Our framework thus establishes a reliable foundation for high-fidelity thermal modeling and offers a transferable strategy for operator-consistent neural surrogates in other physical domains.

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