Uncertainty Quantification at the Exascale (EXA-UQ)

Exascale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，但这些模型仍然受到不确定性的影响，我们需要能够量化这些不确定性（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。简单的方法，如蒙特卡洛，我们简单地从模型输入的概率分布中采样，运行一个巨大的模型集合，并从输出分布中产生一个样本，是不可行的。我们需要开发不确定性量化方法，使我们能够高效地，有效地，执行灵敏度和不确定性计算与最小数量的exascale模型运行。我们的方法是基于模拟器的想法。仿真器是以快速非线性方式连接模型输入和输出的统计近似。它还包括对自身不确定性的测量，因此我们知道它对原始数值模型的近似程度。我们的仿真器基于高斯过程。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仿真器。由于百亿亿次计算的成本，我们使用了一个层次结构的模型，从快速，低保真度的版本，通过更高的保真度，计算更昂贵的，非常昂贵的，非常高保真的一个在层次结构的顶点。为层次结构中的所有模型构建联合仿真器使我们能够从低保真度模型中获得力量来仿真兆兆级模型。虽然这些想法已经存在了很多年，但它们还没有被用于非常大的模型。我们将在现有理论的基础上扩展一些新的方法。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来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，而且还应该在哪个级别运行。我们还将确保顺序设计是“批量”顺序设计，允许我们运行集合，而不是等待每次运行返回答案。由于exascale模型的输入和输出通常是相关值的字段，因此我们将开发处理此类高维输入和输出的方法，以及如何将它们与层次结构的其他级别相关联。最后，我们将研究除了高斯过程之外的AI方法是否可以用来构建高效的仿真器。

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.