Large-Scale Bayesian Optimal Experimental Design with Derivative-Informed Projected Neural Network
Large-Scale Bayesian Optimal Experimental Design with Derivative-Informed Projected Neural Network
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DOI：
10.1007/s10915-023-02145-1
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发表时间：
2022-01
影响因子：
2.5
通讯作者：
Keyi Wu;Thomas O'Leary-Roseberry;Peng Chen;O. Ghattas
中科院分区：
文献类型：
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作者：
Keyi Wu;Thomas O'Leary-Roseberry;Peng Chen;O. Ghattas
我们解决大规模贝叶斯最优实验设计（OED）问题的解决方案的偏微分方程（PDE）与无限维参数字段。OED问题的目的是找到传感器的位置，最大限度地提高预期的信息增益（EIG）的解决方案的基础贝叶斯逆问题。EIG的计算通常是禁止的偏微分方程为基础的OED问题。为了使评估的EIG易于处理，我们近似（基于PDE的）参数可观察的映射与导数通知投影神经网络（DIPNet）代理，它利用了几何形状，平滑度和内在的低维映射使用一个小的和维度独立的PDE解决方案。代理，然后部署在一个贪婪的基于算法的解决方案的OED问题，这样就没有进一步的PDE解决方案是必需的。我们分析了EIG近似误差的DIPNet的泛化误差，并表明他们是相同的顺序。最后，该方法的效率和准确性证明通过数值实验OED问题的逆散射和逆反应输运多达16,641个不确定参数和100个实验设计变量，在那里我们观察到三个数量级的加速相对于参考双环路蒙特卡罗方法。
We address the solution of large-scale Bayesian optimal experimental design (OED) problems governed by partial differential equations (PDEs) with infinite-dimensional parameter fields. The OED problem seeks to find sensor locations that maximize the expected information gain (EIG) in the solution of the underlying Bayesian inverse problem. Computation of the EIG is usually prohibitive for PDE-based OED problems. To make the evaluation of the EIG tractable, we approximate the (PDE-based) parameter-to-observable map with a derivative-informed projected neural network (DIPNet) surrogate, which exploits the geometry, smoothness, and intrinsic low-dimensionality of the map using a small and dimension-independent number of PDE solves. The surrogate is then deployed within a greedy algorithm-based solution of the OED problem such that no further PDE solves are required. We analyze the EIG approximation error in terms of the generalization error of the DIPNet and show they are of the same order. Finally, the efficiency and accuracy of the method are demonstrated via numerical experiments on OED problems governed by inverse scattering and inverse reactive transport with up to 16,641 uncertain parameters and 100 experimental design variables, where we observe up to three orders of magnitude speedup relative to a reference double loop Monte Carlo method.