一种通过深度神经网络进行随机化然后优化采样的加速策略
An acceleration strategy for randomize-then-optimize sampling via deep neural networks
摘要：
随机化后优化（RTO）是贝叶斯反问题中广泛使用的后验分布抽样方法。然而，RTO可能是计算密集的复杂性问题，由于昂贵的前向模型及其梯度的重复评估。在这项工作中，我们提出了一种新的策略，通过使用面向目标的深度神经网络（DNN）代理方法来大大减少RTO的计算负担。特别是，从局部近似的后验分布中提取DNN代理的训练点，并且结果表明，所得到的算法可以提供灵活且高效的采样算法，其收敛于直接RTO方法。我们提出了一个由基准椭圆偏微分方程控制的贝叶斯逆问题，以证明我们的新算法的计算精度和效率（即，DNN-RTO）。结果表明，我们的算法，可以显着优于传统的RTO。
英文摘要：
Randomize-then-optimize (RTO) is widely used for sampling from posterior distributions in Bayesian inverse problems. However, RTO may be computationally intensive for complexity problems due to repetitive evaluations of the expensive forward model and its gradient. In this work, we present a novel strategy to substantially reduce the computation burden of RTO by using a goal-oriented deep neural networks (DNN) surrogate approach. In particular, the training points for the DNN-surrogate are drawn from a local approximated posterior distribution, and it is shown that the resulting algorithm can provide a flexible and efficient sampling algorithm, which converges to the direct RTO approach. We present a Bayesian inverse problem governed by a benchmark elliptic PDE to demonstrate the computational accuracy and efficiency of our new algorithm (i.e., DNN-RTO). It is shown that with our algorithm, one can significantly outperform the traditional RTO.
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