In recent years Bayesian inference has emerged as the most comprehensive and systematic framework for formulating and solving inverse problems with quantified uncertainties. However, the solution of Bayesian inverse problems governed by PDEs is extremely challenging; complex forward models or large parameter dimensions can make Bayesian inversion prohibitive with standard methods. In addition, often one has to solve a PDE-constrained optimization subproblem several times. Recent years have seen intensive efforts to develop advanced algorithms aimed at this class of problems; however, due to the complexity of the algorithms and potential dependencies on derivative information, they have remained buried in the literature and out of the reach of a broad community of scientists and engineers who solve inverse problems. The goal of this minisymposium is to present software frameworks that make advanced algorithms more accessible to domain scientists and provide an environment that expedites the development of new algorithms. These software frameworks can also be used as teaching tools that can be used to educate researchers and practitioners who are new to inverse problems, PDE-constrained optimization, the Bayesian inference framework and UQ in general.
16:30
dolfin-adjoint: A Python framework for automated adjoints of PDEs
Sebastian Mitusch | Simula Research Laboratory | Norway
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Authors:
Sebastian Mitusch | Simula Research Laboratory | Norway
Simon Funke | Simula Research Laboratory | Norway
Jørgen Dokken | University of Cambridge | United Kingdom
Using gradient based optimization methods to solve large-scale PDE-constrained optimization problems requires a way to efficiently compute gradients. The adjoint method enables the computation of the full gradient at a cost proportional to the forward model. However, the derivation and implementation of adjoint models can be challenging, especially for models governed by non-linear or time-dependent partial differential equations. We present dolphin adjoint, a Python framework that automatically derives discrete adjoint models for models implemented in the finite element framework FEniCS. Through the use of automatic differentiation, dolfin-adjoint is able to compute derivatives with respect to PDE coefficients, Dirichlet boundary conditions and mesh coordinates, and can easily be extended to support new operations.
17:00
Bayesian Inference Tools in the UQTk UQ Toolkit
Katherine Johnston | Sandia National Laboratories | United States
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Katherine Johnston | Sandia National Laboratories | United States
Ellen Stechel | Arizona State University | United States
Bert Debusschere | Sandia National Laboratories | United States
The Uncertainty Quantification Toolkit (UQTk) is a collection of tools and libraries for the quantification of uncertainty in numerical model predictions. This talk will specifically focus on the UQTk Bayesian Inference capabilities including MCMC samplers in a variety of flavors, tools for Bayesian model comparison and selection, and tools for model error assessment and propagation into derived quantities. Most of these tools are available through a C++, Python, or command line interface. In addition to a high level overview of these tools, we will illustrate typical workflows and show results on the inference of thermodynamic models of redox active metal oxide materials, used for example to facilitate water splitting to produce hydrogen. The development of UQTk has been funded as part of the DOE SciDAC FASTMath Institute.
17:30
Using the MIT Uncertainty Quantification (MUQ) library for high-dimensional inverse problems
Matthew Parno | US Army Cold Regions Research and Engineering Laboratory (CRREL) | United States
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Matthew Parno | US Army Cold Regions Research and Engineering Laboratory (CRREL) | United States
Andrew Davis | US Army Cold Regions Research and Engineering Laboratory (CRREL) | United States
Youssef Marzouk | Massachusets Institute of Technology (MIT) | United States
Recent algorithmic advancements have made it possible to efficiently solve some high-dimensional Bayesian inference problems by exploiting low dimensional structure in either the posterior distribution itself or in the prior-to-posterior update. While these techniques have incredible potential, they are nontrivial to implement and require first, and possibly second, order derivative information, which can be difficult to calculate for complex models with many subcomponents. This talk will focus on the efficient implementation of high-dimensional sampling algorithms and the use of the MIT Uncertainty Quantification (MUQ) library for efficiently computing derivative information of models that can be represented as the combination of several sub-components in a high level computational graph. Example inference problems with coupled partial differential equation models and hierarchical prior models will be used to highlight salient features of our software and our ongoing collaboration with the hIPPYlib team. MUQ is an open source libraryin c++ and Python released under the BSD license.
18:00
End-to-end Uncertainty Quantification with hIPPYlib
Umberto Villa | Washington University in St. Louis | United States
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Umberto Villa | Washington University in St. Louis | United States
Noemi Petra | University of California, Merced | United States
Omar Ghattas | The University of Texas at Austin | United States
hIPPYlib is an extensible software framework for the solution of large-scale deterministic and Bayesian inverse problems governed by partial differential equations 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 fast and scalable (with respect to both parameter and data dimensions) algorithms in hIPPYlib allow to address critical questions in applying numerical simulations to real-world problems: 1) How does uncertainty propagate from the inputs to the outputs of a mathematical model (forward UQ)? 2) How to infer model parameters from data with quantified uncertainties (Inference)? 3) How/Where/When to collect data to further reduce uncertainty (Optimal design of experiments)? 4) How to mitigate uncertainties in the final outcome (Decision making under uncertainty)? In summary, not only hIPPYlib makes advanced algorithms easily accessible to domain scientists, but it 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.