arXiv:2606.27459v1 Announce Type: new Abstract: We consider the cubic nonlinear Schr\"odinger (NLS) equation on two-dimensional flat tori with varying aspect ratios. In this formulation, the choice of aspect ratio governs the Fourier resonance structure, so rational and irrational geometries can exhibit different high-frequency cascade behaviors. We present a geometry-conditioned Fourier neural operator (FNO) for the cubic defocusing NLS equation, where the input consists of the real and imaginary parts of the solution together with the aspect-ratio parameter \(\omega^2\). The model is trained
Source: arXiv cs.LG — read the full report at the original publisher.