基于离散化多级马尔可夫链蒙特卡罗的高性能不确定性量化
High Performance Uncertainty Quantification with Parallelized Multilevel Markov Chain Monte Carlo
摘要：
复杂现实世界现象的数值模型通常需要高性能计算（HPC）。不确定性进一步增加了问题的维度，并提出了更大的挑战。我们提出了一个并行化策略的多级马尔可夫链蒙特卡罗，一个国家的最先进的，算法可扩展的不确定性量化（UQ）算法的贝叶斯逆问题，和一个新的软件框架，允许大规模的并行跨前向模型评估和UQ算法本身。主要的可扩展性挑战以MLMCMC方法引入的强数据依赖性的形式出现，禁止琐碎的并行化。我们的软件是作为模块化和开源的MIT UQ库（MUQ）的一部分发布的，可以很容易地与任意用户代码耦合。我们使用DUNE和ExaHyPE引擎进行演示。后者提供了一个现实的，大规模的海啸模型，其中确定海啸的来源，从海拔高度的数据。
英文摘要：
Numerical models of complex real-world phenomena often necessitate High Performance Computing (HPC). Uncertainties increase problem dimensionality further and pose even greater challenges. We present a parallelization strategy for multilevel Markov chain Monte Carlo, a state-of-the-art, algorithmically scalable Uncertainty Quantification (UQ) algorithm for Bayesian inverse problems, and a new software framework allowing for large-scale parallelism across forward model evaluations and the UQ algorithms themselves. The main scalability challenge presents itself in the form of strong data dependencies introduced by the MLMCMC method, prohibiting trivial parallelization. Our software is released as part of the modular and open-source MIT UQ Library (MUQ), and can easily be coupled with arbitrary user codes. We demonstrate it using the DUNE and the ExaHyPE Engine. The latter provides a realistic, large-scale tsunami model in which identify the source of a tsunami from buoy-elevation data.
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