Abstract Every computer model depends on numerical input parameters that are chosen according to mostly conservative but rigorous numerical or empirical estimates. These parameters could for example be the step size for time integrators, a seed for pseudo-random number generators, a threshold or the number of grid points to discretize a computational domain. In case a numerical model is enhanced with new algorithms and modelling techniques the numerical influence on the quantities of interest, the running time as well as the accuracy is often initially unknown. Usually parameters are chosen on a trial-and-error basis neglecting the computational cost versus accuracy aspects. As a consequence the cost per simulation might be unnecessarily high which wastes computing resources. Hence, it is essential to identify the most critical numerical parameters and to analyse systematically their effect on the result in order to minimize the time-to-solution without losing significantly on accuracy. Relevant parameters are identified by global sensitivity studies where Sobol’ indices are common measures. These sensitivities are obtained by surrogate models based on polynomial chaos expansion. In this paper, we first introduce the general methods for uncertainty quantification. We then demonstrate their use on numerical solver parameters to reduce the computational costs and discuss further model improvements based on the sensitivity analysis. The sensitivities are evaluated for neighbouring bunch simulations of the existing PSI Injector II and PSI Ring as well as the proposed DAE δ ALUS Injector cyclotron and simulations of the rf electron gun of the Argonne Wakefield Accelerator.

中文翻译：

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粒子加速器系统中Particle-In-Cell模型数值求解器参数的全局敏感性分析

摘要 每个计算机模型都依赖于根据大多数保守但严格的数值或经验估计选择的数值输入参数。例如，这些参数可以是时间积分器的步长、伪随机数生成器的种子、阈值或离散化计算域的网格点数。如果使用新算法和建模技术增强数值模型，则数值对感兴趣量、运行时间和精度的影响通常最初是未知的。通常在反复试验的基础上选择参数，忽略计算成本与准确性方面。因此，每次模拟的成本可能会不必要地高，从而浪费计算资源。因此，必须确定最关键的数值参数并系统地分析它们对结果的影响，以便在不显着降低精度的情况下最大限度地缩短求解时间。相关参数由全球敏感性研究确定，其中 Sobol 指数是常用度量。这些敏感性是通过基于多项式混沌展开的代理模型获得的。在本文中，我们首先介绍了不确定性量化的一般方法。然后，我们展示了它们在数值求解器参数上的使用，以降低计算成本，并讨论基于灵敏度分析的进一步模型改进。