Use of Machine Learning to Estimate Statistics of the Posterior Distribution in Probabilistic Inverse Problems—An Application to Airborne EM Data
Thomas Mejer Hansen, Christopher C. Finlay
Abstract
Abstract The solution to a probabilistic inverse problem is the posterior probability distribution for which a full analytic expression is rarely possible. Sampling methods are therefore often used to generate a sample from the posterior. Decision‐makers may be interested in the probability of features related to model parameters (e.g., existence of pollution or the cumulative clay thickness) rather than the individual realizations themselves. Such features and their associated uncertainty, are simple to compute once a sample from the posterior distribution has been generated. However, sampling methods are often associated with high computational costs, especially when the prior and posterior distribution is non‐trivial (non‐Gaussian), and when the inverse problem is non‐linear. Here we demonstrate how to use a neural network to directly estimate posterior statistics of continuous or discrete features of the posterior distribution. The method is illustrated on a probabilistic inversion of airborne EM data from Morrill Nebraska, where the forward problem is nonlinear and the prior information is non‐Gaussian. Once trained the application of the network is fast, with results similar to those obtained using much slower sampling methods.