VIP -- Variational Inversion Package with example implementations of Bayesian tomographic imaging

TL;DR

VIP is a Python package that enables efficient Bayesian inverse problem solving using variational inference methods, with implementations for tomography and waveform inversion, suitable for various computational environments.

Contribution

The paper introduces VIP, a versatile Python package implementing multiple variational inference algorithms for inverse problems, with practical examples and scalable solutions.

Findings

VIP is efficient and scalable for inverse problems.

The package supports automatic differentiation and custom forward models.

Examples demonstrate practical applicability in tomography and waveform inversion.

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.