Generating simulated training data needed for constructing sufficiently accurate surrogate models to be used for efficient optimization or parameter identification can incur a huge computational effort in the offline phase. We consider a fully adaptive greedy approach to the computational design of experiments problem using gradient-enhanced Gaussian process regression as surrogates. Designs are incrementally defined by solving an optimization problem for accuracy given a certain computational budget. We address not only the choice of evaluation points but also of required simulation accuracy, both of values and gradients of the forward model. Numerical results show a significant reduction of the computational effort compared to just position-adaptive and static designs as well as a clear benefit of including gradient information into the surrogate training.

翻译：生成模拟训练数据以构建足够精确的代理模型，从而用于高效优化或参数识别，在离线阶段可能产生巨大的计算负担。我们提出一种完全自适应的贪婪方法，利用梯度增强高斯过程回归作为代理模型，解决计算实验设计问题。设计方案通过求解给定计算预算下的精度优化问题来逐步定义。我们不仅考虑评估点的选择，还考虑正向模型的值和梯度所需的仿真精度。数值结果表明，与仅位置自适应和静态设计方案相比，该方法显著降低了计算量，并且将梯度信息纳入代理模型训练具有明显优势。