Computer models play an essential role in forecasting complicated phenomena such as the atmosphere, ocean dynamics, seismology among others. These models, however, are typically imperfect due to various sources of uncertainty. Measurements are snapshots of reality that are collected as an additional source of information and are used to update and even correct the model-based simulations or forecasts. The accuracy of the overall simulations and model-based forecasts is greatly influenced by the quality of the observational grid design used to collect measurements. Optimal data acquisition can be formulated as an optimal experimental design (OED) problem. The framework of model-based OED has gained wide popularity and attention from researchers in various fields in statistics, engineering, applied math and others. Challenges in model-based OED include high-dimensionality, misrepresentation of prior knowledge, increasing deviation from Gaussianity, high correlations of spatiotemporal observations, among others. This minisymposium aims to showcase the latest developments in tackling the challenges in the field of model-based OED for large-scale inverse problems.
16:30
- CANCELED - Optimal experimental design under model uncertainty, with application to subsurface flow
Karina Koval | Courant Institute of Mathematical Sciences - New York University | United States
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Authors:
Karina Koval | Courant Institute of Mathematical Sciences - New York University | United States
Georg Stadler | Courant Institute of Mathematical Sciences - New York University | United States
Alen Alexanderian | Department of Mathematics - North Carolina State University | United States
We present a method for computing A-optimal sensor placements for Bayesian linear inverse problems governed by PDEs with model uncertainties. Specifically, given a statistical distribution for the model uncertainties we compute the optimal design that minimizes the expected value of the posterior covariance trace. The expected value is discretized using Monte Carlo leading to an objective function consisting of a finite sum of trace operators and a sparsity inducing penalty. Minimization of this objective requires many PDE solves in each step. To make the problem computationally tractable, we construct a composite low-rank basis using a randomized range finder algorithm to eliminate forward and adjoint PDE solves. Additionally, we exploit the problem structure to rewrite the objective in a way which allows us to take the trace of an operator in observation space rather than the parameter space. The sparsity is enforced using a weighted regularized $\ell_0$-sparsification approach. We present numerical results for inference of the initial condition in a subsurface flow problem with inherent uncertainty in the flow fields.
17:00
- CANCELED - Multilevel estimation of the expected information gain
Joakim Beck | King Abdullah University of Science and Technology (KAUST) | Saudi Arabia
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Joakim Beck | King Abdullah University of Science and Technology (KAUST) | Saudi Arabia
Dia Ben Mansour | King Fahd University of Petroleum and Minerals | Saudi Arabia
Luis Espath | RWTH Aachen University | Germany
Raul F. Tempone | RWTH Aachen University and KAUST | Germany
We consider the problem of estimating an expected information criterion used in Bayesian optimal experimental design for nonlinear models. In the case of nonlinear models governed by partial differential equations, we present two multilevel estimators that achieve better computational complexity than their single-level counterparts. The first is a multilevel double loop Monte Carlo estimator, optimized by minimizing the computational work subject to some desired error tolerance. The second is a multilevel double loop stochastic collocation estimator based on high-dimensional integration on sparse grids. We demonstrate the computational efficiency of the multilevel estimators for an electrical impedance tomography design problem where the goal is to infer the fiber orientations in a composite laminate material.
17:30
- MOVED from MS011 - Enhanced Hybrid Projection Methods with Recycling for Large Inverse Problems
Julianne Chung | Virginia Polytechnic Institute and State University | United States
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Julianne Chung | Virginia Polytechnic Institute and State University | United States
In this talk, we describe enhanced Golub-Kahan-based hybrid projection methods that can exploit compression and recycling techniques in order to solve a broad class of inverse problems where memory requirements present a significant computational burden. For example, in streaming data problems or optimal experimental design frameworks for inverse problems, the described methods can be used to efficiently integrate previously computed information in a hybrid framework for faster and better reconstruction. The main benefits of the proposed methods are that various subspace selection and compression techniques can be incorporated, standard techniques for automatic regularization parameter selection can be used, and the methods can be applied in an iterative fashion. Numerical examples from image processing show the potential benefits.
18:00
Optimal Bayesian Experimental Design Using Generalized Laplace Method
Quan Long | United Technology Research Center (UTRC) | United States
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Quan Long | United Technology Research Center (UTRC) | United States
Bayesian experimental design is essential to improve data quality in engineering, particularly when the experiments are expensive. We develop a series of methods to accelerate the computations of the utility function (expected information gain) under rigorous error control. Specifically, we extend the applicable domain of Laplace methods from the asymptotic posterior Gaussianity, to where the shape of the posterior is non-Gaussian. The developed methodologies can be applied to various engineering problems, e.g., impedance tomography, seismic source inversion and parameter inference of combustion kinetics.