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.
14:00
Goal-Oriented Optimal Experimental Design Framework for Sensor Placement and Acquisition of Highly-Correlated Data
Ahmed Attia | Argonne National Laboratory | United States
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Authors:
Ahmed Attia | Argonne National Laboratory | United States
Emil Constantinescu | Argonne National Laboratory | United States
Optimal design of experiments is the general formalism of sensor placement and decisions on the data collection strategy for engineered or natural experiments. This problem is prevalent in many critical fields such as battery design, geosciences, environmental and urban studies. State-of-the-art computational methods for experimental design do not account for correlations in observations produced by many expensive-to-operate devices such as X-ray machines, radars, and satellites. Discarding the evidence of such data correlations leads to biased results, computational inefficiencies of sub-optimal results. In this talk, we discuss a new goal-oriented optimal experimental design framework, where measurement errors are generally correlated. This framework follows a Shur-product approach to formulate the weighted-likelihood, which is then used in the optimality criterion. Preliminary results using a standard advection-diffusion model will be presented.
14:30
Majorization-minimization algorithm for D-optimal sensor selection in the presence of correlated measurement noise
Dariusz Uciński | Institute of Control and Computation Engineering, University of Zielona Góra | Poland
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Dariusz Uciński | Institute of Control and Computation Engineering, University of Zielona Góra | Poland
The problem of sensor selection for parameter estimation of spatiotemporal systems with correlated measurement noise is considered. Since in the examined setting the correlation structure of the noise is not known exactly, the ordinary least squares method is supposed to be used for estimation and the determinant of the covariance matrix of the resulting estimator is adopted as the measure of estimation accuracy. This design criterion is to be minimized by choosing a set of spatiotemporal measurement locations from among a given finite set of candidate locations. To make the problem computationally tractable for large sensor networks, its relaxed formulation is first considered. As the resulting problem is nonconvex, a majorization-minimization algorithmic framework is employed. Thus, at each iteration, a convex tangent surrogate function that majorizes the original nonconvex design criterion is minimized using simplicial decomposition. This results in a sequence of iterates which monotonically reduce the value of the original nonconvex design criterion. The settings with and without prior information on parameters are considered. As the relaxed solution is a measure on the set of candidate measurements and not a specific subset, a branch-and-bound algorithm is used to convert it to a nearly-optimal subset of selected sensors.The approximate design produced in this manner then forms a basis for computation of the appropriate exact design using the branch-and-bound technique.
15:00
Computing A-optimal design of experiments for large-scale inverse problems using randomized methods and reweighted $\ell_1$ minimization
Elizabeth Herman | Department of Mathematics, North Carolina State University | United States
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Authors:
Elizabeth Herman | Department of Mathematics, North Carolina State University | United States
Alen Alexanderian | Department of Mathematics, North Carolina State University | United States
Arvind K. Saibaba | Department of Mathematics, North Carolina State University | United States
An optimal experimental design (OED) problem seeks to optimize certain design criteria over the design variables for an experiment. The experiment we consider is collecting data for a large-scale Bayesian linear inverse problem and our design variables consist of the placement of data-gathering sensors. We consider the A-optimal design criterion, which is defined as the trace of the posterior covariance operator. For large-scale problems, computing the trace of the posterior covariance operator is challenging. Our algorithm exploits problem structure, applying efficient randomized methods for the computation of the posterior covariance operator (and its gradient) along with reweighted $\ell_1$ minimization to enforce sparsity. These techniques allow the design criteria to computed efficiently and in a matrix-free way. We illustrate the success of this method through a contaminant source identification problem.
15:30
- MOVED from MS012 - A Stein Variational Newton Method for Optimal Experimental Design Problems
Keyi Wu | University of Texas at Austin | United States
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Keyi Wu | University of Texas at Austin | United States
Peng Chen | ICES - UT Austin | United States
In this talk, we present an efficient, accurate, and scalable method based on Stein variational Newton method to solve Bayesian OED problems. A critical challenge arises when we use the the double-loop Monte Carlo method to evaluate the expected information gain -- the inner loop involves computation of a normalization constant as an integral of the likelihood function with respect to the prior distribution, which is typically intractable especially in high dimensions. To tackle this challenge, we propose an adaptive Stein variational Newton importance sampling method that once we construct the kernel-based transport map that push the prior distribution to a surrogate distribution close to the posterior, we could cheaply generate samples that from that surrogate distribution in every step of the optimization and derive the formula to compute the densities of the generated samples to facilitate the computation of the normalized constant. The computation for the map construction, sample generation, density evaluation, and resulted optimization is scalable with respect to the parameter dimension, i.e., the total number of function evaluations depend only on the intrinsic dimension of the problem informed by the effective rank of the Hessian of the potential (log likelihood function). We use several numerical examples ranging from low-dimensional analytic models to high-dimensional PDE models, to demonstrate the efficiency, accuracy, and scalability of our proposed method.