Optimal experimental design via gradient flow
CoRR(2024)
摘要
Optimal experimental design (OED) has far-reaching impacts in many scientific
domains. We study OED over a continuous-valued design space, a setting that
occurs often in practice. Optimization of a distributional function over an
infinite-dimensional probability measure space is conceptually distinct from
the discrete OED tasks that are conventionally tackled. We propose techniques
based on optimal transport and Wasserstein gradient flow. A practical
computational approach is derived from the Monte Carlo simulation, which
transforms the infinite-dimensional optimization problem to a
finite-dimensional problem over Euclidean space, to which gradient descent can
be applied. We discuss first-order criticality and study the convexity
properties of the OED objective. We apply our algorithm to the tomography
inverse problem, where the solution reveals optimal sensor placements for
imaging.
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