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Efficient Deconvolution in Populational Inverse Problems

delete2026-05-04
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OA
AI
A
Arnaud Vadeboncoeur *
M
Mark Girolami
A
Andrew M. Stuart
DOI：10.1002/nme.70335delete
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摘要

摘要

En 中文
本工作专注于推断感兴趣参数分布的反演任务，该任务会导致多组观测数据。解决此类分布反演问题的潜力得益于数据的日益丰富，但主要障碍是盲去卷积，这源于观测噪声分布未知。然而，当数据源自物理系统集合（即种群）时，可以利用此信息进行去卷积。为此，我们提出一种方法，利用来自同一物理过程不同实现的观测大数据集，同时去卷积数据污染噪声分布，并识别定义物理过程的模型参数分布。采用了一个依赖于参数的物理过程数学模型。定义了一个损失函数，用于表征观测数据与数学模型输出之间的匹配度；该损失函数被最小化，作为模型物理参数输入和参数化观测噪声的函数。该耦合问题通过一种改进的梯度下降算法解决，该算法利用了噪声模型中的特定结构。此外，提出了一种基于自适应经验测度的新型主动学习方案，用于训练代理模型，使其在感兴趣参数区域内准确；这种方法加速了计算，并实现了对计算参数-解映射的黑箱（可能不可微）代码进行自动微分。所提出的方法在多孔介质流、阻尼弹性动力学和大气动力学简化模型上进行了验证。
Keyword:
deconvolution
inverse problems
populational inference
surrogate models
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期刊

International Journal for Numerical Methods in Engineering 封面图
International Journal for Numerical Methods in Engineering
IF:
2.9
论文数:
478
被引数:
2.2W

机构

U
university of cambridge
学者数:
8.3K
论文数: 3.9K
被引数: 3
C
california institute of technology
学者数:
2.9K
论文数: 1.1K
被引数: 0
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