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cs.LG2026
Geometry-Conditioned Fourier Neural Operators for Cubic Nonlinear Schrodinger Dynamics on Periodic Domains
Emmanuel E. Oguadimma, Victory C. Obieke, Xueying Yu
We consider the cubic nonlinear Schrödinger (NLS) equation on two-dimensional flat tori with varying aspect ratios. In this formulation, the choice of aspect ratio governs the Four…
cs.LG2025
Structure-Preserving Physics-Informed Neural Network for the Korteweg--de Vries (KdV) Equation
Victory Obieke, Emmanuel Oguadimma
Physics-Informed Neural Networks (PINNs) offer a flexible framework for solving nonlinear partial differential equations (PDEs), yet conventional implementations often fail to pres…