MUQ: The MIT Uncertainty Quantification Library

Parno, Matthew; Davis, A. D.; Seelinger, Linus

doi:10.21105/joss.03076

Cited by 19 publications

(15 citation statements)

References 15 publications

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“…To generate samples of the posterior distributions of the eigenvalues using Markov Chain Monte Carlo (MCMC), the Delayed Rejection Adaptive Metropolis (DRAM) algorithm [4], implemented in Version 1 of the MIT UQ Library (MUQ1) [13], is used. The starting point of the Markov chain is determined by performing two deterministic optimizations, also using MUQ.…”

Section: Inference Implementationmentioning

confidence: 99%

Bayesian inference of an uncertain generalized diffusion operator

Portone,

Moser

2021

Preprint

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This paper defines a novel Bayesian inverse problem to infer an infinite-dimensional uncertain operator appearing in a differential equation, whose action on an observable state variable affects its dynamics. The operator is parametrized using its eigendecomposition, which enables prior information to be incorporated into its formulation. The Bayesian inverse problem is defined in terms of an uncertain, generalized diffusion operator appearing in an evolution equation for a contaminant's transport through a heterogeneous porous medium. Limited observations of the state variable's evolution are used as data for inference, and the dependence on the solution of the inverse problem is studied as a function of the frequency of observations, as well as on whether or not the data is collected as a spatial or time series.

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Section: Inference Implementationmentioning

confidence: 99%

Bayesian inference of an uncertain generalized diffusion operator

Portone,

Moser

2021

Preprint

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“…Among the most prominent we mention QUESO [52,58], DAKOTA [30,1], PSUADE [70], All of these libraries provide Bayesian inversion capabilities, but the underlying methods do not fully exploit the structure of the problem or make use of derivatives and as such are not intended for high-dimensional problems. Finally, MUQ [54] provides powerful Bayesian inversion models and algorithms, but expects forward models to come equipped with gradients/Hessians to permit largescale solution.…”

Section: Algorithmic Contributionsmentioning

confidence: 99%

hIPPYlib: An Extensible Software Framework for Large-Scale Inverse Problems Governed by PDEs; Part I: Deterministic Inversion and Linearized Bayesian Inference

Villa¹,

Petra²,

Ghattas³

2019

Preprint

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We present an extensible software framework, hIPPYlib, for solution of large-scale deterministic and Bayesian inverse problems governed by partial differential equations (PDEs) with (possibly) infinite-dimensional parameter fields (which are high-dimensional after discretization). hIPPYlib overcomes the prohibitive nature of Bayesian inversion for this class of problems by implementing state-of-the-art scalable algorithms for PDE-based inverse problems that exploit the structure of the underlying operators, notably the Hessian of the log-posterior. The key property of the algorithms implemented in hIPPYlib is that the solution of the deterministic and linearized Bayesian inverse problem is computed at a cost, measured in linearized forward PDE solves, that is independent of the parameter dimension. The mean of the posterior is approximated by the MAP point, which is found by minimizing the negative log-posterior. This deterministic nonlinear least-squares optimization problem is solved with an inexact matrix-free Newton-CG method. The posterior covariance is approximated by the inverse of the Hessian of the negative log posterior evaluated at the MAP point. This Gaussian approximation is exact when the parameter-to-observable map is linear; otherwise, its logarithm agrees to two derivatives with the log-posterior at the MAP point, and thus it can serve as a proposal for Hessian-based MCMC methods. The construction of the posterior covariance is made tractable by invoking a low-rank approximation of the Hessian of the log-likelihood. Scalable tools for sample generation are also implemented. hIPPYlib makes all of these advanced algorithms easily accessible to domain scientists and provides an environment that expedites the development of new algorithms. hIPPYlib is also a teaching tool that can be used to educate researchers and practitioners who are new to inverse problems and the Bayesian inference framework.

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“…In this paper, we present a software framework to tackle large-scale Bayesian inverse problems with PDE-based forward models, which has applications across a wide range of science and engineering fields. The software integrates two open-source software packages, an Inverse Problems Python library (hIPPYlib) [65] and the MIT Uncertainty Quantification Library (MUQ) [46], respecting their attractive complementary capabilities.…”

Section: Introductionmentioning

confidence: 99%

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

Kim

Villa

Parno

et al. 2021

Preprint

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Bayesian inference provides a systematic framework for integration of data with mathematical models to quantify the 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. These algorithms accelerate MCMC sampling by exploiting the geometry and intrinsic low-dimensionality of parameter space via derivative information and low rank approximation. The software integrates two complementary opensource software packages, hIPPYlib and MUQ. hIPPYlib solves PDE-constrained inverse problems using automatically-generated adjoint-based derivatives, but it lacks full Bayesian capabilities. MUQ provides a spectrum of powerful Bayesian inversion models and algorithms, but expects forward models to come equipped with gradients and Hessians to permit large-scale solution. By combining these two complementary libraries, we created a robust, scalable, and efficient software framework that realizes the benefits of each and allows us 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 present a comparison of a number of MCMC methods available in the integrated software on several high-dimensional Bayesian inverse problems. These include problems characterized by both linear and nonlinear PDEs, low and high levels of data noise, and different parameter dimensions. The results demonstrate that large (∼ 50×) 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.

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MUQ: The MIT Uncertainty Quantification Library

Cited by 19 publications

References 15 publications

Bayesian inference of an uncertain generalized diffusion operator

Bayesian inference of an uncertain generalized diffusion operator

hIPPYlib: An Extensible Software Framework for Large-Scale Inverse Problems Governed by PDEs; Part I: Deterministic Inversion and Linearized Bayesian Inference

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

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