8.2.1.2 Gradient Computation Phase

After the optimizer successfully identified an improved set of parameters, it is necessary to compute the Jacobian of the model. This means at least one evaluation of the model must be performed for each parameter which is selected for optimization. The number of system jobs will therefore be a multiple (times the number of free parameters) compared to the test evaluation phase. Since all model evaluations are independent from each other, and so are their associated system jobs, they can be processed in parallel. In contrast to single evaluation there will be excess system jobs compared to the number of workstations and as a consequence, job farming will use any available workstation as far as allowed (depending on their load limit) and take care that neither a workstation is overloaded nor is underemployed.

Gradient computation impressively demonstrates the power of SIESTA's job farming capabilities. Unless job farming were available for an optimization, the whole procedure would require large amounts of real time. Job farming scales down computation time linearly during this phase of an optimization. SIESTA was successfully employed for a rigorous optimization of doping profiles [O10], where 62 (!) parameters of a discretized doping profile were optimized. The optimization took approximately one day on a cluster of 20 workstations.