Inverse medium scattering solvers generally reconstruct a single solution without an associated measure of uncertainty. This is true both for the classical iterative solvers and for the emerging deep learning methods. But ill-posedness and noise can make this single estimate inaccurate or misleading. While deep networks such as conditional normalizing flows can be used to sample posteriors in inverse problems, they often yield low-quality samples and uncertainty estimates. In this paper, we propose U-Flow, a Bayesian U-Net based on conditional normalizing flows, which generates high-quality posterior samples and estimates physically-meaningful uncertainty. We show that the proposed model significantly outperforms the recent normalizing flows in terms of posterior sample quality while having comparable performance with the U-Net in point estimation.
翻译:反向分散的中度中位数求解器一般会重建单一的解决方案,而没有相关的不确定性度。古典迭代求解器和新兴的深层学习方法都是如此。但是,错误和噪音可以使这一单一的估计不准确或误导。虽然有条件的正常流等深层网络可以用来对反向问题中的后端生物进行抽样,但它们往往产生低质量的样本和不确定性估计。 在本文中,我们提议基于有条件的正常流的巴耶斯的U-Flow,即基于有条件的正常流的Bayesian U-Net,产生高质量的后端样品,并估计具有物理意义的不确定性。我们表明,拟议的模型在后端样本质量方面大大超过最近的正常流,同时与点估计的U-Net具有可比性。