Lennon J. Shikhman
Scientific Machine Learning · Applied Mathematics
Operator learning demonstration
Compare a learned spectral operator with the reference solution of the heat equation. Adjust the initial condition, viscosity, and prediction horizon to examine approximation error.
8 learned modes · 600 training pairsNear training regime
Relative L2 error 0.07%
Initial fieldNumerical referenceLearned operator
Equation1D periodic heat
ModelSpectral neural operator
ExecutionLocal browser inference
Method
The model learned one-step Fourier multipliers from 600 synthetic input-output function pairs at a single viscosity. At inference time, it transforms the full initial function, applies its learned spectral map, and rolls that map forward repeatedly.
The reference uses the analytical spectral evolution at the viscosity you select. Moving away from the training viscosity or choosing a sharp pulse exposes truncation and distribution-shift error.