Through examples of coordinate and probability transformation between
different distributions, the basic principle of normalizing flow is introduced
in a simple and concise manner. From the perspective of the distribution of
random variable function, the essence of probability transformation is
explained, and the scaling factor Jacobian determinant of probability
transformation is introduced. Treating the dataset as a sample from the
population, obtaining normalizing flow is essentially through sampling surveys
to statistically infer the numerical features of the population, and then the
loss function is established by using the maximum likelihood estimation method.
This article introduces how normalizing flow cleverly solves the two major
application challenges of high-dimensional matrix determinant calculation and
neural network reversible transformation. Using symmetric structured image
dataset of three-span beam bridge, arch bridge, cable-stayed bridge and
suspension bridge, constructing and training normalizing flow based on the Glow
API in the TensorFlow Probability library. The model can smoothly transform the
complex distribution of the bridge dataset into a standard normal distribution,
and from the obtained latent space sampling, it can generate new bridge types
that are different from the training dataset.

本文介绍了归一化流在高维矩阵行列式计算和神经网络可逆变换这两个应用挑战中的巧妙应用，并使用三孔梁桥、拱桥、斜拉桥和悬索桥的对称结构图像数据集构建和训练了基于 TensorFlow Probability 库中的 Glow API 的归一化流模型，使其能够将桥梁数据集的复杂分布平滑地转换为标准正态分布，并通过对获得的潜在空间进行采样，生成与训练数据集不同的新桥梁类型。