An introduction to variational inference in Geophysical inverse problems

Abstract

In a variety of scientific applications we wish to characterize a physical system using measurements or observations. This often requires us to solve an inverse problem, which usually has non-unique solutions so uncertainty must be quantified in order to define the family of all possible solutions. Bayesian inference provides a powerful theoretical framework which defines the set of solutions to inverse problems, and variational inference is a method to solve Bayesian inference problems using optimization while still producing fully probabilistic solutions. This chapter provides an introduction to variational inference, and reviews its applications to a range of geophysical problems, including petrophysical inversion, travel time tomography and full-waveform inversion. We demonstrate that variational inference is an efficient and scalable method which can be deployed in many practical scenarios.

References in corpus (10)

• Expectation Propagation for approximate Bayesian inference
• NICE: Non-linear Independent Components Estimation
• Markov Chain Monte Carlo and Variational Inference: Bridging the Gap
• Inversion using a new low-dimensional representation of complex binary geological media based on a deep neural network
• Stein Variational Gradient Descent With Matrix-Valued Kernels
• Block Neural Autoregressive Flow
• Faster Uncertainty Quantification for Inverse Problems with Conditional Normalizing Flows
• A trust-region method for stochastic variational inference with applications to streaming data
• Perturbative Black Box Variational Inference
• Population Empirical Bayes