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hIPPYlib
ACM Transactions on Mathematical Software ( IF 2.7 ) Pub Date : 2021-04-01 , DOI: 10.1145/3428447
Umberto Villa 1 , Noemi Petra 2 , Omar Ghattas 3
Affiliation  

We present an extensible software framework, hIPPYlib, for solution of large-scale deterministic and Bayesian inverse problems governed by partial differential equations (PDEs) with (possibly) infinite-dimensional parameter fields (which are high-dimensional after discretization). hIPPYlib overcomes the prohibitively expensive nature of Bayesian inversion for this class of problems by implementing state-of-the-art scalable algorithms for PDE-based inverse problems that exploit the structure of the underlying operators, notably the Hessian of the log-posterior. The key property of the algorithms implemented in hIPPYlib is that the solution of the inverse problem is computed at a cost, measured in linearized forward PDE solves, that is independent of the parameter dimension. The mean of the posterior is approximated by the MAP point, which is found by minimizing the negative log-posterior with an inexact matrix-free Newton-CG method. The posterior covariance is approximated by the inverse of the Hessian of the negative log posterior evaluated at the MAP point. The construction of the posterior covariance is made tractable by invoking a low-rank approximation of the Hessian of the log-likelihood. Scalable tools for sample generation are also discussed. hIPPYlib makes all of these advanced algorithms easily accessible to domain scientists and provides an environment that expedites the development of new algorithms.

中文翻译:

hIPPYlib

我们提出了一个可扩展的软件框架 hIPPYlib,用于解决由具有(可能)无限维参数场(离散化后为高维)的偏微分方程 (PDE) 控制的大规模确定性和贝叶斯逆问题。hIPPYlib 通过为基于 PDE 的逆问题实现最先进的可扩展算法,利用底层算子的结构,特别是对数后验的 Hessian,克服了此类问题的贝叶斯反演过于昂贵的性质。在 hIPPYlib 中实现的算法的关键属性是,逆问题的解决方案是以线性化正向 PDE 解决方案衡量的成本计算的,该成本与参数维度无关。后验的平均值由 MAP 点近似,这是通过使用不精确的无矩阵 Newton-CG 方法最小化负对数后验来发现的。后验协方差近似为在 MAP 点评估的负对数后验的 Hessian 矩阵的倒数。通过调用对数似然的 Hessian 的低秩近似,后协方差的构建变得易于处理。还讨论了用于样本生成的可扩展工具。hIPPYlib 使领域科学家可以轻松访问所有这些高级算法,并提供一个加速新算法开发的环境。通过调用对数似然的 Hessian 的低秩近似,后协方差的构建变得易于处理。还讨论了用于样本生成的可扩展工具。hIPPYlib 使领域科学家可以轻松访问所有这些高级算法,并提供一个加速新算法开发的环境。通过调用对数似然的 Hessian 的低秩近似,后协方差的构建变得易于处理。还讨论了用于样本生成的可扩展工具。hIPPYlib 使领域科学家可以轻松访问所有这些高级算法,并提供一个加速新算法开发的环境。
更新日期:2021-04-01
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