We introduce a conditional pseudo-reversible normalizing flow for
constructing surrogate models of a physical model polluted by additive noise to
efficiently quantify forward and inverse uncertainty propagation. Existing
surrogate modeling approaches usually focus on approximating the deterministic
component of physical model. However, this strategy necessitates knowledge of
noise and resorts to auxiliary sampling methods for quantifying inverse
uncertainty propagation. In this work, we develop the conditional
pseudo-reversible normalizing flow model to directly learn and efficiently
generate samples from the conditional probability density functions. The
training process utilizes dataset consisting of input-output pairs without
requiring prior knowledge about the noise and the function. Our model, once
trained, can generate samples from any conditional probability density
functions whose high probability regions are covered by the training set.
Moreover, the pseudo-reversibility feature allows for the use of
fully-connected neural network architectures, which simplifies the
implementation and enables theoretical analysis. We provide a rigorous
convergence analysis of the conditional pseudo-reversible normalizing flow
model, showing its ability to converge to the target conditional probability
density function using the Kullback-Leibler divergence. To demonstrate the
effectiveness of our method, we apply it to several benchmark tests and a
real-world geologic carbon storage problem.

通过引入条件伪可逆归一化流，我们提出了一种构建受加性噪声污染的物理模型的替代模型的方法，以便有效量化前向和反向的不确定传播。我们的模型可以直接学习并高效地从条件概率密度函数中生成样本，并且可以针对任何高概率区域被训练集所覆盖的条件概率密度函数生成样本。此外，伪可逆性特性使得我们可以使用全连接神经网络结构，简化了实现并实现了理论分析。我们的方法经过了严格的收敛性分析，证明了其能够使用 KL 散度收敛于目标条件概率密度函数。为了证明我们方法的有效性，我们将其应用于几个基准测试和一个真实的地质碳储存问题。