一种图形化多保真高斯过程模型及其在重离子碰撞仿真中的应用
A graphical multi-fidelity Gaussian process model, with application to emulation of heavy-ion collisions
AI总结：
本文提出图形化多保真高斯过程模型GMGP，将科学依赖的DAG结构嵌入高斯过程框架，支持递归后验计算与实验设计，并通过数值实验和重离子碰撞仿真验证其优势。
摘要：
随着科学计算和数学建模的进步，诸如星系形成和火箭推进等复杂科学现象如今已能被可靠地模拟。然而，这类模拟可能非常耗时，需要数百万CPU小时才能完成。一种解决方案是多保真仿真（emulation），它利用不同保真度的数据训练一个高效的预测模型来仿真昂贵的模拟器。对于复杂的科学问题，并且在科学家仔细引导下，这类多保真数据往往可以通过一个有向无环图（DAG）来关联，该图表示其科学模型依赖关系。因此，我们提出了一种新的图形化多保真高斯过程（GMGP）模型，该模型将这种DAG结构（捕捉科学依赖关系）嵌入到高斯过程框架中。我们证明GMGP通过两个马尔可夫性质具有良好的建模特性，并支持一种可扩展算法，用于沿DAG的每个深度层级递归计算后验均值和方差。我们还提出了一种在给定实验预算下针对DAG的新型实验设计方法，并通过深度高斯过程提出了GMGP的非线性扩展。随后，通过一系列数值实验以及在重离子碰撞仿真中的应用，展示了GMGP的优势；该应用可用于研究大爆炸后不久宇宙中物质的状态。所提出的模型在具有图形结构的数据融合应用中具有更广泛的用途，我们对此进行了进一步讨论。
英文摘要：
With advances in scientific computing and mathematical modeling, complex scientific phenomena such as galaxy formations and rocket propulsion can now be reliably simulated. Such simulations can however be very time-intensive, requiring millions of CPU hours to perform. One solution is multi-fidelity emulation, which uses data of different fidelities to train an efficient predictive model which emulates the expensive simulator. For complex scientific problems and with careful elicitation from scientists, such multi-fidelity data may often be linked by a directed acyclic graph (DAG) representing its scientific model dependencies. We thus propose a new Graphical Multi-fidelity Gaussian Process (GMGP) model, which embeds this DAG structure (capturing scientific dependencies) within a Gaussian process framework. We show that the GMGP has desirable modeling traits via two Markov properties, and admits a scalable algorithm for recursive computation of the posterior mean and variance along at each depth level of the DAG. We also present a novel experimental design methodology over the DAG given an experimental budget, and propose a nonlinear extension of the GMGP via deep Gaussian processes. The advantages of the GMGP are then demonstrated via a suite of numerical experiments and an application to emulation of heavy-ion collisions, which can be used to study the conditions of matter in the Universe shortly after the Big Bang. The proposed model has broader uses in data fusion applications with graphical structure, which we further discuss.
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