A Case Study in Adjoint Sensitivity Analysis of Parameter Calibration

Adjoint sensitivity computation of parameter estimation problems is a widely used technique in the field of computational science and engineering for retrieving derivatives of a cost functional with respect to parameters efficiently. Those derivatives can be used, e.g. for sensitivity analysis, optimization, or robustness analysis. Deriving and implementing adjoint code is an error-prone, non-trivial task which can be avoided by using Algorithmic Differentiation (AD) software. Generating adjoint code by AD software has the downside of usually requiring a huge amount of memory as well as a non-optimal run time. In this article, we couple two approaches for achieving both, a robust and efficient adjoint code: symbolically derived adjoint formulations and AD. Comparisons are carried out for a real-world case study originating from the remote atmospheric sensing simulation software JURASSIC developed at the Institute of Energy and Climate Research – Stratosphere, Research Center Jülich. We show, that the coupled approach outperforms the fully algorithmic approach by AD in terms of run time and memory requirement and argue that this can be achieved while still preserving the desireable feature of AD being automatic.