Gaussian-Process Regression for Plasma
Gaussian processes fit smooth plasma profiles from scattered measurements while returning principled uncertainty and gradient estimates.
A nonparametric fit with error bars
A Gaussian process (GP) defines a distribution over functions and conditions it on observed data to produce a smooth fit with pointwise uncertainty. For plasma profiles measured at scattered radii, a GP yields both the profile and its gradient, with error bands, without assuming a fixed functional form.
Why gradients matter
Transport is driven by gradients of temperature and density, so profile fitting must estimate derivatives accurately. Because differentiation is a linear operation, a GP provides the derivative and its uncertainty analytically from the same fit, which is a major advantage over ad hoc spline fits.
# GP profile fit, schematic
from sklearn.gaussian_process import GaussianProcessRegressor
from sklearn.gaussian_process.kernels import RBF, WhiteKernel
k = RBF(length_scale=0.1) + WhiteKernel(noise_level=1e-2)
gp = GaussianProcessRegressor(kernel=k, normalize_y=True)
gp.fit(r.reshape(-1,1), Te) # radius vs temperature
mean, std = gp.predict(r_fine.reshape(-1,1), return_std=True)Kernel choice
The kernel encodes assumptions about smoothness and length scale. A length scale that is too short overfits noise; too long oversmooths real structure such as a pedestal. Hyperparameters are learned by maximizing the marginal likelihood, and non-stationary kernels handle regions of differing smoothness.
Strengths and limits
- Principled uncertainty on both value and gradient
- No fixed profile shape imposed
- Handles heteroscedastic noise across diagnostics
- Cost grows cubically with the number of points, limiting very large datasets
GP profile fitting is a workhorse for diagnostic analysis and feeds transport studies. In Kronos design work it is applied to simulated profiles for the breeder concept, providing the gradient estimates that turbulence surrogates consume, with all results understood as computational until measured on hardware that does not yet exist.