hIPPYlib-MUQ: A Bayesian Inference Software Framework for Integration of Data with Complex Predictive Models under Uncertainty.

Bayesian inference provides a systematic means of quantifying uncertainty in the solution of the inverse problem. However, solution of Bayesian inverse problems governed by complex forward models described by partial differential equations (PDEs) remains prohibitive with black-box Markov chain Monte Carlo (MCMC) methods. We present hIPPYlib-MUQ, an extensible and scalable software framework that contains implementations of state-of-the art algorithms aimed to overcome the challenges of high-dimensional, PDE-constrained Bayesian inverse problems. hIPPYlib-MUQ integrates two complementary open-source software packages. hIPPYlib solves PDE-constrained inverse problems using automatically-generated adjoint-based derivatives, but it lacks full Bayesian capabilities. MUQ provides numerous powerful Bayesian inversion algorithms, but expects forward models to come equipped with derivatives to permit large-scale solution. By combining these two libraries, we created a robust, scalable, and efficient software framework that can be used to tackle complex large-scale Bayesian inverse problems across a broad spectrum of scientific and engineering disciplines. To illustrate the capabilities of hIPPYlib-MUQ, we compare a number of MCMC methods on several high-dimensional Bayesian inverse problems. The results demonstrate that large ($\sim 50\times$) speedups over conventional black box and gradient-based MCMC algorithms can be obtained by exploiting Hessian information (from the log-posterior), underscoring the power of the integrated hIPPYlib-MUQ framework.