In the paper, we propose a novel approach for solving Bayesian inverse problems with physics-informed invertible neural networks (PI-INN). The architecture of PI-INN consists of two sub-networks: an invertible neural network (INN) and a neural basis network (NB-Net). The invertible map between the parametric input and the INN output with the aid of NB-Net is constructed to provide a tractable estimation of the posterior distribution, which enables efficient sampling and accurate density evaluation. Furthermore, the loss function of PI-INN includes two components: a residual-based physics-informed loss term and a new independence loss term. The presented independence loss term can Gaussianize the random latent variables and ensure statistical independence between two parts of INN output by effectively utilizing the estimated density function. Several numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed PI-INN, including inverse kinematics, inverse problems of the 1-d and 2-d diffusion equations, and seismic traveltime tomography.

翻译：本文提出了一种利用物理信息可逆神经网络（PI-INN）求解贝叶斯反问题的新方法。PI-INN架构由两个子网络组成：可逆神经网络（INN）和神经基础网络（NB-Net）。通过NB-Net的辅助，构建了参数输入与INN输出之间的可逆映射，从而提供后验分布的可处理估计，实现高效采样与精确密度评估。此外，PI-INN的损失函数包含两个组成部分：基于残差的物理信息损失项和新的独立性损失项。所提出的独立性损失项通过有效利用估计的密度函数，能够使随机潜变量服从高斯分布，并确保INN输出两部分之间的统计独立性。通过逆运动学、一维及二维扩散方程反问题、地震走时层析成像等数值实验，验证了所提出的PI-INN方法的效率与准确性。