Bayesian maximum a posteriori-estimation of κ turbulence model parameters using algorithmic differentiation in SOLPS-ITER

Radial anomalous diffusion coefficients are among the largest sources of uncertainty in mean-field plasma-edge codes such as SOLPS-ITER. These coefficients are machine, scenario, and space-dependent, thus hampering the predictive and interpretive capability of these codes. In fact, modellers usually adjust these coefficients manually, based on expert judgement or on large, computationally expensive, parameter scans. Matching data from various diagnostics, each with their own experimental uncertainties, additionally complicates the problem of finding a good parameter set. In addition, standard non-linear regression techniques have shown to become prohibitive for expensive plasma-edge simulations with many unknown parameters, as gradient calculation was based on finite differences. In this paper, we apply algorithmic differentiation (AD) as an efficient and more accurate alternative for gradient calculation in large, continuously developed codes as SOLPS-ITER. In addition, the lack of uncertainty information and danger of data overfitting, key limitations of regression techniques, are overcome by combining data and uncertainties from different diagnostics in a Bayesian framework. We implement for the first time such a Bayesian inference framework into SOLPS-ITER, using gradient-based optimization with gradients obtained through tangent AD to find the maximum a posteriori (MAP) values of the parameters. The recently developed kappa turbulence model is employed to limit the number of unknown parameters compared to full spatial profiles of diffusion coefficients. The Bayesian MAP-estimation is compared to standard regression techniques on a small-scale tokamak. We adopt fictitious experimental data obtained from a reference SOLPS-ITER solution with artificial measurement noise.