Farcaş Ionuţ-Gabriel, Merlo Gabriele, Jenko Frank
Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, TX USA.
Max Planck Institute for Plasma Physics, Garching, Germany.
Commun Eng. 2022;1(1):43. doi: 10.1038/s44172-022-00045-0. Epub 2022 Dec 10.
In many fields of science, comprehensive and realistic computational models are available nowadays. Often, the respective numerical calculations call for the use of powerful supercomputers, and therefore only a limited number of cases can be investigated explicitly. This prevents straightforward approaches to important tasks like uncertainty quantification and sensitivity analysis. This challenge can be overcome via our recently developed sensitivity-driven dimension-adaptive sparse grid interpolation strategy. The method exploits, via adaptivity, the structure of the underlying model (such as lower intrinsic dimensionality and anisotropic coupling of the uncertain inputs) to enable efficient and accurate uncertainty quantification and sensitivity analysis at scale. Here, we demonstrate the efficiency of this adaptive approach in the context of fusion research, in a realistic, computationally expensive scenario of turbulent transport in a magnetic confinement tokamak device with eight uncertain parameters, reducing the effort by at least two orders of magnitude. In addition, we show that this refinement method intrinsically provides an accurate surrogate model that is nine orders of magnitude cheaper than the high-fidelity model.
在当今许多科学领域，都有全面且逼真的计算模型。通常，相应的数值计算需要使用强大的超级计算机，因此只能明确研究有限数量的案例。这阻碍了对不确定性量化和敏感性分析等重要任务采用直接的方法。通过我们最近开发的敏感性驱动的维度自适应稀疏网格插值策略，可以克服这一挑战。该方法通过自适应利用基础模型的结构（例如不确定输入的较低固有维度和各向异性耦合），从而能够在大规模情况下进行高效且准确的不确定性量化和敏感性分析。在此，我们在聚变研究的背景下，展示了这种自适应方法在一个现实的、计算成本高昂的场景中的效率，该场景涉及具有八个不确定参数的磁约束托卡马克装置中的湍流输运，工作量减少了至少两个数量级。此外，我们表明这种细化方法本质上提供了一个精确的替代模型，其成本比高保真模型便宜九个数量级。
