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Operator Learning for Cubic Nonlinear Schr\"odinger Equation on Periodic Domains

arXiv cs.LG · 5d ago Cached

This paper presents a geometry-conditioned Fourier Neural Operator (FNO) to learn the solution operator for the cubic nonlinear Schrödinger equation on periodic domains with varying aspect ratios. Numerical experiments show the model captures distinct Sobolev norm behaviors on rational and irrational tori, demonstrating geometry-aware neural operators for dispersive PDEs.

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