Ab initio uncertainty quantification in scattering analysis of microscopy
arXiv (Cornell University)(2023)
摘要
Estimating parameters from data is a fundamental problem in physics,
customarily done by minimizing a loss function between a model and observed
statistics. In scattering-based analysis, researchers often employ their domain
expertise to select a specific range of wavevectors for analysis, a choice that
can vary depending on the specific case. We introduce another paradigm that
defines a probabilistic generative model from the beginning of data processing
and propagates the uncertainty for parameter estimation, termed ab initio
uncertainty quantification (AIUQ). As an illustrative example, we demonstrate
this approach with differential dynamic microscopy (DDM) that extracts
dynamical information through Fourier analysis at a selected range of
wavevectors. We first show that DDM is equivalent to fitting a temporal
variogram in the reciprocal space using a latent factor model as the generative
model. Then we derive the maximum marginal likelihood estimator, which
optimally weighs information at all wavevectors, therefore eliminating the need
to select the range of wavevectors. Furthermore, we substantially reduce the
computational cost by utilizing the generalized Schur algorithm for Toeplitz
covariances without approximation. Simulated studies validate that AIUQ
significantly improves estimation accuracy and enables model selection with
automated analysis. The utility of AIUQ is also demonstrated by three distinct
sets of experiments: first in an isotropic Newtonian fluid, pushing limits of
optically dense systems compared to multiple particle tracking; next in a
system undergoing a sol-gel transition, automating the determination of gelling
points and critical exponent; and lastly, in discerning anisotropic diffusive
behavior of colloids in a liquid crystal. These outcomes collectively
underscore AIUQ's versatility to capture system dynamics in an efficient and
automated manner.
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关键词
initio uncertainty quantification
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