论文标题
大规模贝叶斯的最佳实验设计，具有衍生化的投影神经网络
Large-scale Bayesian optimal experimental design with derivative-informed projected neural network
论文作者
论文摘要
我们解决了由偏微分方程（PDE）和无限二维参数字段控制的大规模贝叶斯最佳实验设计（OED）问题的解决方案。 OED问题旨在找到在基础贝叶斯逆问题解决方案中最大化预期信息增益（EIG）的传感器位置。对于基于PDE的OED问题，EIG的计算通常是过时的。为了对EIG进行评估，我们使用衍生性信息的投影神经网络（DIPNET）替代物来近似（基于PDE的）参数到观察的地图，该替代使用了pde solve的小小的和尺寸依赖性数量的pde solve的几何形状，平滑度和内在的低维度。然后将替代物部署在基于OED问题的贪婪算法的解决方案中，因此无需进一步的PDE解决方案。我们根据DIPNET的概括误差分析了EIG近似误差，并表明它们的顺序相同。最后，该方法的效率和准确性通过数值实验证明了由反向散射和反应性逆运输控制的OED问题，最多16,641个不确定的参数和100个实验设计变量，我们观察到相对于参考双环路Monte Carlo方法，我们最多可以观察到三个巨大的速度。
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.
