论文标题

一个大规模量化不确定性的一般框架

A general framework for quantifying uncertainty at scale

论文作者

Farcas, Ionut-Gabriel, Merlo, Gabriele, Jenko, Frank

论文摘要

在许多科学领域,如今已获得全面和现实的计算模型。通常,相应的数值计算要求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。这样可以防止直接的方法处理重要任务,例如不确定性量化和灵敏度分析。可以通过我们最近开发的敏感性自适应稀疏网格插值策略来克服这一挑战。该方法通过适应性利用了基础模型的结构(例如,不确定输入的较低的内在维度和各向异性耦合),以促进有效,准确的不确定性量化和敏感性分析。在融合研究的背景下,我们在磁性限制的tokamak设备中具有八个不确定参数的湍流传输方案,在融合研究的背景下证明了我们的方法的效率,从而将努力减少了至少两个数量级。此外,我们表明我们的方法本质上提供了一个准确的替代模型,该模型比高保真模型便宜九个数量级。

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. We demonstrate the efficiency of our 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 our method intrinsically provides an accurate surrogate model that is nine orders of magnitude cheaper than the high-fidelity model.

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