An Offline-Online Decomposition Method for Efficient Linear Bayesian Goal-Oriented Optimal Experimental Design: Application to Optimal Sensor Placement

Wu, Keyi; Chen, Peng; Ghattas, Omar

doi:10.1137/21m1466542

Cited by 4 publications

(2 citation statements)

References 49 publications

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“…They can therefore be applied for any general interrogation problem, for which T or T −1 is computable. Only if the mapping T is linear is it possible to use linear (bayesian) experimental design methods (Curtis, 1999b;Wu et al, 2021;Attia et al, 2018)…”

Section: Designing Experiments For Interrogation Problemsmentioning

confidence: 99%

Variational Experimental Design Methods for Geophysical Applications

Strutz

Curtis

2023

Preprint

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<div> <p><span data-contrast="auto">The design of geophysical surveys or experiments (henceforth, the experimental design) significantly influences the uncertainty in scientific results that can be inferred from recorded data. Typical aspects of experimental designs that can be varied are locations of sensors, sensor types, and the modelling or data processing methods to be applied to recorded data. To tighten constraints on the solution to any inverse or inference problem, and thus to rule out as many false possibilities as possible, the design should be optimised such that it is practically achievable within cost and logistical constraints, and such that it maximises expected post-experimental information about the solution.</span><span data-ccp-props="{">&#160;</span></p> </div> <div> <p><span data-contrast="auto">Bayesian experimental design refers to a class of methods that use uncertainty estimation methods to quantify the expected gain in information about target parameters provided by an experiment, and to optimise the design of the experiment to maximise that gain. Information gain quantifies the decrease in uncertainty caused by observing data. Expected information gain is an estimate of the gain in information that will be offered by any particular design post-experiment. Bayesian experimental design methods vary the design so as to maximise the expected information gain, subject to practical constraints.</span><span data-ccp-props="{">&#160;</span></p> </div> <div> <p><span data-contrast="auto">We introduce variational experimental design methods that are novel to geophysics, and discuss their benefits and limitations in the context of geophysical applications. The family of variational methods relies on functional approximations of probability distributions, and in some cases, of the model-data relationships. They can be used to design experiments that best resolve either all model parameters, or the answer to a specific question about the system studied. Their potential advantage over some other design methods is that finding the functional approximations used by variational methods tends to rely more on optimisation theory than the more common stochastic uncertainty analysis used to approximate Bayesian uncertainties. This allows the wealth of understanding of optimisation methods to be applied to the full Bayesian design problem.</span><span data-ccp-props="{">&#160;</span></p> </div> <div> <p><span data-contrast="auto">Variational design methods are demonstrated by optimising the design of an experiment consisting of seismometer locations on the Earth&#8217;s surface, so as to best estimate seismic source parameters given arrival time data obtained at seismometers. By designing separate experiments to constrain the hypocentres and epicentres of events, we show that optimal designs may change substantially depending on which questions about the subsurface we wish the experiment to help us to answer.</span><span data-ccp-props="{">&#160;</span></p> </div> <div> <p><span data-contrast="auto">By accounting for differing expected uncertainties in travel time picks depending on the picking method used, we demonstrate that the data processing method can be optimised as part of the design process, provided that expected uncertainties are available from each method.</span></p> </div>

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Section: Designing Experiments For Interrogation Problemsmentioning

confidence: 99%

Variational Experimental Design Methods for Geophysical Applications

Strutz

Curtis

2023

Preprint

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“…As mentioned above, the motivation for the linearization is to allow explicit integration of (1). However, there exist approaches to tackling Bayesian OED without such a simplifying assumption; see, e.g., [4,9,27,28,38,54,55]. Moreover, one can also aim to avoid discretizing the problem setting before employing OED; see, e.g., the series of papers on Bayesian OED in the framework of infinite-dimensional inverse problems [2,3,4,5].…”

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confidence: 99%

Bayesian experimental design for linear elasticity

Eberle-Blick,

Hyvönen

2024

IPI

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This work considers Bayesian experimental design for the inverse boundary value problem of linear elasticity in a two-dimensional setting. The aim is to optimize the positions of compactly supported pressure activations on the boundary of the examined body in order to maximize the value of the resulting boundary deformations as data for the inverse problem of reconstructing the Lamé parameters inside the object. We resort to a linearized measurement model and adopt the framework of Bayesian experimental design, under the assumption that the prior and measurement noise distributions are mutually independent Gaussians. This enables the use of the standard Bayesian A-optimality criterion for deducing optimal positions for the pressure activations. The (second) derivatives of the boundary measurements with respect to the Lamé parameters and the positions of the boundary pressure activations are deduced to allow minimizing the corresponding objective function, i.e., the trace of the covariance matrix of the posterior distribution, by gradient-based optimization algorithms. Two-dimensional numerical experiments are performed to test the functionality of our approach: all introduced algorithms are able to improve experimental designs, but only exhaustive search reliably finds a global minimizer.

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