Gaussian Processes for Fusion
A flexible regression method that reports calibrated uncertainty, well suited to small, expensive datasets.
What a Gaussian process is
A Gaussian process (GP) defines a distribution over functions. Conditioned on observed data, it returns both a prediction and a principled uncertainty at every input. Where data are dense the uncertainty is small; far from data it grows. This built-in honesty about what it does not know suits fusion, where data are scarce and extrapolation matters.
The kernel
A GP's behavior is set by its kernel, which encodes how correlated outputs are as a function of input distance. The kernel choice expresses assumptions about smoothness and length scales, and its parameters are fit to data. A well-chosen kernel is where physical knowledge enters the model.
Uses in fusion
- Profile fitting from noisy diagnostic points with error bars
- Surrogates for expensive simulations with usable uncertainty
- The core of Bayesian optimization for experiment and design
Costs
Standard GP training scales cubically with the number of points, so they are ideal for small-to-moderate datasets and awkward for very large ones. Sparse and approximate GP methods extend them to larger data at some loss of exactness.
Why the uncertainty matters
A GP does not just predict; it says how much to trust the prediction. Downstream, this lets an optimizer explore where uncertainty is high, and lets a controller be cautious where the state is poorly constrained. For fusion, where a confident wrong answer can be costly, calibrated uncertainty is often more valuable than a marginal gain in average accuracy.