Live experiment / 01
Operator
learning lab
Evolve a periodic heat equation with a compact learned spectral operator and compare it against the numerical reference. Everything runs locally in your browser.
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
What is actually learned?
This is a real, deliberately small operator model.
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 instead of hiding it.