Gaussian Process Surrogates
Gaussian processes are surrogates that return both a prediction and a calibrated uncertainty, ideal where data is scarce and honesty matters.
Predictions with error bars
A Gaussian process is a probabilistic surrogate that models an unknown function as a distribution over functions. Given training points, it returns for any new input both a mean prediction and a variance, an honest statement of how uncertain that prediction is. This built-in uncertainty is why Gaussian processes are favored in twins where trusting a fast approximation blindly would be dangerous.
How it works
The method assumes that outputs at nearby inputs are correlated, with the strength of correlation set by a kernel function. Near training data the prediction is confident and the variance small; far from any data the prediction reverts toward the prior mean and the variance grows. The surrogate therefore signals its own ignorance, which is exactly what a twin needs when a query leaves the trained region.
Where it fits
- Smaller datasets, since fitting cost grows steeply with the number of points
- Smooth functions of modest input dimension
- Situations where calibrated uncertainty is more valuable than raw speed
Limits and remedies
Standard Gaussian processes scale poorly to very large datasets and high input dimensions. Sparse approximations and specialized methods extend them, but for very large problems neural networks are often preferred. The kernel choice encodes assumptions about smoothness and must be selected with care.
Use in the Kronos twins
Gaussian process surrogates suit the parts of a fusion twin where expensive simulations are few and uncertainty must be reported honestly: mapping a small set of costly neutronics runs of the Hyperion blanket, or interpolating structural-life results across load cases. Their uncertainty feeds directly into the twin's decision layer, so a recommendation carries a defensible confidence rather than a bare number. See uncertainty quantification and calibration.