Researchers have developed a geometry-conditioned Fourier neural operator (FNO) to model the cubic nonlinear Schrödinger (NLS) equation on two-dimensional flat tori. This operator learns from the real and imaginary parts of the solution and the aspect-ratio parameter to predict the one-step solution. Numerical experiments demonstrate that the FNO accurately captures dynamics and distinguishes between rational and irrational geometries, showing stronger Sobolev norm growth on rational tori. Ablation studies confirmed the importance of geometry conditioning and retained Fourier modes for long-time predictive accuracy, particularly in rational geometries. AI
IMPACT Demonstrates potential for AI to model complex physical phenomena and accelerate scientific discovery.
RANK_REASON Academic paper on a novel application of neural operators to a physics problem. [lever_c_demoted from research: ic=1 ai=1.0]
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