We present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an inference network for parameter estimation. The summary network encodes raw observations into a fixed-size vector of summary features, while the inference network generates samples of the approximate posterior distribution of the model parameters based on these summary features. The posterior samples are produced in a deep generative fashion by sampling from a latent Gaussian distribution and passing these samples through an invertible transformation. We construct this invertible transformation by sequentially alternating conditional invertible neural network and conditional neural spline flow layers. The summary and inference networks are trained simultaneously.

中文翻译：

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使用具有噪声和不完整数据的摊销无似然推理解决高维逆问题

我们提出了一种基于高维逆问题归一化流的无似然性反演方法。所提出的方法由两个互补网络组成：用于数据压缩的汇总网络和用于参数估计的推理网络。摘要网络将原始观测值编码为固定大小的摘要特征向量，而推理网络则根据这些摘要特征生成模型参数的近似后验分布样本。后验样本是通过从潜在高斯分布中采样并通过可逆变换传递这些样本，以深度生成方式生成的。我们通过依次交替条件可逆神经网络和条件神经样条流层来构建这种可逆变换。摘要网络和推理网络是同时训练的。