We propose a novel modular inference approach combining two different generative models -- generative adversarial networks (GAN) and normalizing flows -- to approximate the posterior distribution of physics-based Bayesian inverse problems framed in high-dimensional ambient spaces. We dub the proposed framework GAN-Flow. The proposed method leverages the intrinsic dimension reduction and superior sample generation capabilities of GANs to define a low-dimensional data-driven prior distribution. Once a trained GAN-prior is available, the inverse problem is solved entirely in the latent space of the GAN using variational Bayesian inference with normalizing flow-based variational distribution, which approximates low-dimensional posterior distribution by transforming realizations from the low-dimensional latent prior (Gaussian) to corresponding realizations of a low-dimensional variational posterior distribution. The trained GAN generator then maps realizations from this approximate posterior distribution in the latent space back to the high-dimensional ambient space. We also propose a two-stage training strategy for GAN-Flow wherein we train the two generative models sequentially. Thereafter, GAN-Flow can estimate the statistics of posterior-predictive quantities of interest at virtually no additional computational cost. The synergy between the two types of generative models allows us to overcome many challenges associated with the application of Bayesian inference to large-scale inverse problems, chief among which are describing an informative prior and sampling from the high-dimensional posterior. We demonstrate the efficacy and flexibility of GAN-Flow on various physics-based inverse problems of varying ambient dimensionality and prior knowledge using different types of GANs and normalizing flows.

翻译：我们提出了一种新颖的模块化推理方法，该方法融合两种不同的生成模型——生成对抗网络（GAN）与归一化流——以逼近定义在高维环境空间中的物理贝叶斯反问题的后验分布。我们将所提框架命名为GAN-Flow。该方法利用GAN的内在降维能力和优质样本生成能力来定义低维数据驱动先验分布。在获得训练好的GAN先验后，整个反问题在GAN的潜在空间中通过变分贝叶斯推理求解，使用基于归一化流的变分分布，该分布通过将低维潜在先验（高斯分布）的样本变换为低维变分后验分布的对应样本来逼近低维后验分布。训练好的GAN生成器再将潜在空间中该近似后验分布的样本映射回高维环境空间。我们还为GAN-Flow提出了一种两阶段训练策略，其中依次训练这两个生成模型。此后，GAN-Flow几乎无需额外计算成本即可估计后验预测感兴趣量的统计特性。两类生成模型之间的协同作用使我们能够克服贝叶斯推理应用于大规模反问题时的诸多挑战，其主要挑战包括描述信息性先验以及对高维后验分布进行采样。我们通过不同环境维度和先验知识水平的多类物理反问题，使用不同类型的GAN与归一化流，验证了GAN-Flow的有效性和灵活性。