Spline-Based Bayesian Emulators for Large Scale Spatial Inverse Problems

TL;DR

This paper introduces a spline-based Bayesian emulator approach for large-scale nonlinear spatial inverse problems, effectively reducing computational costs and enabling efficient posterior sampling in complex models.

Contribution

It develops a novel emulator methodology using BMARS and DCT for dimension reduction, combined with trans-dimensional MCMC for Bayesian inference in spatial inverse problems.

Findings

Effective dimension reduction with DCT improves computational efficiency.

BMARS successfully models complex nonlinear input-output relationships.

Method applied to hydrocarbon reservoir data demonstrates practical utility.

Abstract

A Bayesian approach to nonlinear inverse problems is considered where the unknown quantity (input) is a random spatial field. The forward model is complex and non-linear, therefore computationally expensive. An emulator-based methodology is developed, where the Bayesian multivariate adaptive regression splines (BMARS) are used to model the function that maps the inputs to the outputs. Discrete cosine transformation (DCT) is used for dimension reduction of the input spatial field. The posterior sampling is carried out using trans-dimensional Markov Chain Monte Carlo (MCMC) methods. Numerical results are presented by analyzing simulated as well as real data on hydrocarbon reservoir characterization.