Uncertainty Quantification at the Exascale (EXA-UQ)

百亿亿级不确定性量化 (EXA-UQ)

• 批准号: EP/W007886/1
• 负责人: Peter Challenor
• 金额: $ 128.19万
• 依托单位: UNIVERSITY OF EXETER
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FW007886%2F1
• 关键词: Uncertainty; Quantification; Exascale; EXA; UQ

Exascale computing offers the prospect of running numerical models, for example of nuclear fusion and the climate, at unprecedented resolution and fidelity, but such models are still subject to uncertainty and we need to able to quantify such uncertainties (and for example use data on model outputs to calibrate the model inputs). Exascale computing comes at a cost. We will never be able to run huge ensembles go models on Exascale computers. Naive methods, such as Monte Carlo where we simply sample from the probability distribution of the model inputs, run a huge ensemble of models and produce a sample from the output distribution, are not going to be feasible. We need to develop uncertainty quantification methodology that allows us to efficiently, and effectively, perform sensitivity and uncertainty calculations with the minimum number of exascale model runs.Our methods are based on the idea of an emulator. An emulator is a statistical approximation linking model inputs and outputs in a fast non-linear way. It also includes a measure of its own uncertainty so we know how well it is approximating the original numerical model. Our emulators are based on Gaussian processes. Normally we would run a designed experiment and use these results to train the emulator. Because of the cost of exascale computing we use a hierarchy of models from fast, low fidelity versions through higher fidelity more computationally expensive ones to the very expensive, very high fidelity one at the apex of the hierarchy. Building a joint emulator for all the models in the hierarchy allows us to gain strength from the low fidelity ones to emulate the exascale models. Although such ideas have been around for a number of years they have not been exploited much for very large models.We will expand on the existing theory on a number of new ways. First we will look at the problem of design. To exploit the hierarchy to its fullest extent we need an experimental design that allocates model runs to the correct layer of the model hierarchy. We will extend existing sequential design methodology to work with hierarchies of model, not only finding the optimal next set of inputs for running the model but also which level it should be run in. We will also ensure that the sequential design is 'batch' sequential, allowing us to run ensembles rather than waiting for each run to return answers.Because the inputs and outputs of exascale models are often fields of correlated values we will develop methods for handling such high dimensional inputs and outputs and how to relate them to other levels of the hierarchy.Finally we will investigate whether AI methods other than Gaussian processes can be used to build efficient emulators.

Exascale Computing提供了运行数值模型的前景，例如核融合和气候，以前所未有的分辨率和忠诚度，但此类模型仍然存在不确定性，我们需要能够量化此类不确定性（例如，例如使用模型输出的数据来校准模型输入）。 Exascale计算是有代价的。我们将永远无法在Exascale计算机上运行巨大的合奏模型。天真的方法，例如蒙特卡洛，我们只是从模型输入的概率分布中进行采样，运行大量模型并从输出分布中产生样本，这是不可行的。我们需要开发不确定性定量方法，使我们能够使用最小数量的Exascale模型运行，并有效地执行灵敏度和不确定性计算。您的方法基于模拟器的概念。模拟器是以快速的非线性方式链接模型输入和输出的统计近似。它还包括一个衡量其自身不确定性的度量，因此我们知道它近似原始数值模型的效果如何。我们的仿真器基于高斯过程。通常，我们会运行设计的实验，并使用这些结果来训练模拟器。由于计算的成本，我们使用了来自快速，低忠诚版本的模型的层次结构，通过更高的保真度，更昂贵的计算机到非常昂贵的，非常高的忠诚度，在层次结构的顶点处。为层次结构中的所有模型构建一个联合模拟器，使我们能够从低忠诚度的模型中获得强度，从而模仿Exascale模型。尽管这些想法已经存在了很多年，但它们并没有被大型模型所利用。我们将以许多新方式扩展现有理论。首先，我们将研究设计问题。为了最大程度地利用层次结构，我们需要一个实验设计，该设计将模型分配到模型层次结构的正确层。我们将将现有的顺序设计方法扩展到与模型的层次结构一起工作，不仅找到了运行模型的最佳下一组输入，还应使用哪个级别进行运行。我们还将确保顺序设计是“批处理”的“顺序”顺​​序，使我们能够运行eNSEMBLES，允许我们等待每个运行的返回答案。输入和输出以及如何将它们与其他层次结构相关联。从本文中，我们将研究是否可以使用高斯流程以外的其他方法来构建有效的仿真器。

项目成果

Cross-Validation--based Adaptive Sampling for Gaussian Process Models

基于交叉验证的高斯过程模型自适应采样

• DOI: 10.1137/21m1404260
• 发表时间: 2022
• 期刊: SIAM/ASA Journal on Uncertainty Quantification
• 作者: Mohammadi H