Algorithmic Differentiation for adjoint sensitivity calculation in plasma edge codes

In the framework of fusion energy research, divertor design and model calibration based on plasma edge codes currently rely either on manual iterative tuning of parameters, or alternatively on parameter scans. This, combined with the complex and computationally expensive nature of plasma edge codes, makes these procedures extremely cumbersome. Gradient-based optimization methods can significantly reduce this effort, but require an efficient strategy for sensitivity calculation. Algorithmic Differentiation (AD) offers an efficient and accurate solution, allowing semi-automatic sensitivity computation in complex, continuously developed codes. The adjoint AD mode is especially attractive, as its cost is independent of the number of input parameters. In this paper, adjoint AD sensitivity calculation is deployed for the first time in plasma edge codes, applying the TAPENADE AD tool to SOLPS-ITER. Adjoint AD results are verified to be machine precision accurate compared to tangent AD mode, and up to 10 −9 compared to finite differences. Scalings of AD computational efforts prove the advantages of adjoint compared to tangent AD, while memory requirements rapidly increase for adjoint, showing the need for an improved checkpointing strategy. With the new tool, a wealth of information becomes accessible to the modeler. An adjoint sensitivity analysis for a COMPASS density scan identifies the input parameters with largest impact on the solution, and 2D sensitivity maps show their spatial dependence.