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.

百亿亿次计算提供了以前所未有的分辨率和保真度运行数值模型的前景，例如核聚变和气候，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（例如使用模型输出的数据来校准模型输入）。百亿亿次计算是有代价的。我们永远无法在百亿亿次计算机上运行巨大的集成围棋模型。简单的方法，例如蒙特卡罗，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生成样本，这是不可行的。我们需要开发不确定性量化方法，使我们能够以最少的百亿亿次模型运行次数高效、有效地执行灵敏度和不确定性计算。我们的方法基于模拟器的理念。模拟器是一种以快速非线性方式链接模型输入和输出的统计近似。它还包括对其自身不确定性的测量，因此我们知道它与原始数值模型的近似程度。我们的模拟器基于高斯过程。通常我们会运行一个设计好的实验并使用这些结果来训练模拟器。由于百亿亿级计算的成本，我们使用一系列模型，从快速、低保真度版本到更高保真度、计算成本更高的版本，再到位于层次结构顶端的非常昂贵、非常高保真度版本。为层次结构中的所有模型构建联合模拟器使我们能够从低保真度模型中获得力量来模拟百亿亿次模型。尽管这样的想法已经存在了很多年，但它们还没有在非常大的模型中得到充分利用。我们将以许多新的方式扩展现有的理论。首先我们来看看设计的问题。为了充分利用层次结构，我们需要一个实验设计，将模型运行分配到模型层次结构的正确层。我们将扩展现有的顺序设计方法以处理模型的层次结构，不仅找到运行模型的最佳下一组输入，而且还确定模型应该在哪个级别运行。我们还将确保顺序设计是“批量”顺序的，使我们能够运行集成而不是等待每次运行返回答案。因为百亿亿次模型的输入和输出通常是相关值的字段，我们将开发处理如此高维的方法 输入和输出以及如何将它们与层次结构的其他级别相关联。最后，我们将研究是否可以使用高斯过程以外的人工智能方法来构建高效的模拟器。

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