Title: VIP -- Variational Inversion Package with example implementations of Bayesian tomographic imaging Show Chinese title

Title: VIP -- 变分反演包，包含贝叶斯断层成像的示例实现

Abstract: Bayesian inference has become an important tool to solve inverse problems and to quantify uncertainties in their solutions. Variational inference is a method that provides probabilistic, Bayesian solutions efficiently by using optimization. In this study we present a Python Variational Inversion Package (VIP), to solve inverse problems using variational inference methods. The package includes automatic differential variational inference (ADVI), Stein variational gradient descent (SVGD) and stochastic SVGD (sSVGD), and provides implementations of 2D travel time tomography and 2D full waveform inversion including test examples and solutions. Users can solve their own problems by supplying an appropriate forward function and a gradient calculation code. In addition, the package provides a scalable implementation which can be deployed easily on a desktop machine or using modern high performance computational facilities. The examples demonstrate that VIP is an efficient, scalable, extensible and user-friendly package, and can be used to solve a wide range of low or high dimensional inverse problems in practice. Show Chinese abstract

Abstract: 贝叶斯推断已成为解决反问题和量化其解不确定性的一个重要工具。 变分推断是一种通过使用优化来高效提供概率性贝叶斯解的方法。 在本研究中，我们提出一个Python变分反演包（VIP），用于使用变分推断方法解决反问题。 该包包括自动微分变分推断（ADVI）、Stein变分梯度下降（SVGD）和随机SVGD（sSVGD），并提供了二维旅行时间层析成像和二维全波形反演的实现，包括测试示例和解决方案。 用户可以通过提供适当的前向函数和梯度计算代码来解决自己的问题。 此外，该包提供了一个可扩展的实现，可以在台式机上轻松部署或使用现代高性能计算设施。 这些示例表明，VIP是一个高效、可扩展、可扩展且用户友好的包，可以用于实际解决各种低维或高维反问题。