An Uncertainty-Weighted Asynchronous ADMM Method for Parallel PDE Parameter Estimation
An Uncertainty-Weighted Asynchronous ADMM Method for Parallel PDE Parameter Estimation
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DOI：
10.1137/18m119166x
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发表时间：
2018-06
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通讯作者：
Samy Wu Fung;Lars Ruthotto
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文献类型：
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作者：
Samy Wu Fung;Lars Ruthotto
我们考虑了一个全局变量一致ADMM算法，用于异步并行地求解大规模PDE参数估计问题。为此，我们将数据分区，并将产生的子问题分发给可用的工作人员。由于每个子问题可以与不同的正演模型和右手边，这提供了足够的选择，定制的方法，包括多源和多物理PDE参数估计问题的不同应用。我们还考虑了共识ADMM的异步变体，以减少通信和延迟。我们的主要贡献是一个新的加权方案，经验增加了共识ADMM计划的早期迭代取得的进展，并在使用大量的子问题时是有吸引力的。这使得共识ADMM在解决PDE参数估计方面具有竞争力，这会导致每次迭代的巨大成本。在我们的计划中的权重有关的不确定性与每个子问题的解决方案。我们举例说明，加权方案结合异步实现提高了时间的解决方案的3D单物理场和多物理场PDE参数估计问题。
We consider a global variable consensus ADMM algorithm for solving large-scale PDE parameter estimation problems asynchronously and in parallel. To this end, we partition the data and distribute the resulting subproblems among the available workers. Since each subproblem can be associated with different forward models and right-hand-sides, this provides ample options for tailoring the method to different applications including multi-source and multi-physics PDE parameter estimation problems. We also consider an asynchronous variant of consensus ADMM to reduce communication and latency. Our key contribution is a novel weighting scheme that empirically increases the progress made in early iterations of the consensus ADMM scheme and is attractive when using a large number of subproblems. This makes consensus ADMM competitive for solving PDE parameter estimation, which incurs immense costs per iteration. The weights in our scheme are related to the uncertainty associated with the solutions of each subproblem. We exemplarily show that the weighting scheme combined with the asynchronous implementation improves the time-to-solution for a 3D single-physics and multiphysics PDE parameter estimation problems.