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：本文提出一种基于物理信息可逆神经网络（PI-INN）求解贝叶斯逆问题的新方法。PI-INN架构包含两个子网络：可逆神经网络（INN）与神经基网络（NB-Net）。通过NB-Net辅助构建参数输入与INN输出之间的可逆映射，实现对后验分布的可处理估计，从而支持高效采样与精确密度评估。此外，PI-INN的损失函数包含两项：基于残差的物理信息损失项与新的独立性损失项。所提出的独立性损失项通过有效利用估计密度函数，能够使随机潜变量高斯化，并确保INN输出两部分的统计独立性。通过逆运动学、一维及二维扩散方程逆问题、地震走时层析成像等数值实验，验证了所提PI-INN方法的效率与精度。