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Ab initio uncertainty quantification in scattering analysis of microscopy.

Mengyang Gu1, Yue He1, Xubo Liu1

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We introduce ab initio uncertainty quantification (AIUQ), a new method for parameter estimation that removes the need to manually select wave vectors in scattering-based analysis. AIUQ improves accuracy and enables automated analysis across diverse physical systems.

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Area of Science:

  • Physics
  • Data Analysis
  • Materials Science

Background:

  • Parameter estimation in physics often involves minimizing loss functions in reciprocal space, requiring manual selection of wave vector ranges.
  • Conventional methods in differential dynamic microscopy (DDM) are equivalent to fitting a temporal variogram, limiting analysis to chosen wave vectors.

Purpose of the Study:

  • Introduce a new paradigm, ab initio uncertainty quantification (AIUQ), for probabilistic parameter estimation from data.
  • Demonstrate AIUQ's effectiveness in differential dynamic microscopy (DDM) for improved accuracy and automated analysis.

Main Methods:

  • Developed a probabilistic generative model for AIUQ, propagating uncertainty from data processing.
  • Derived a maximum marginal likelihood estimator that optimally utilizes all wave vector information.
  • Utilized the generalized Schur algorithm for efficient computation of the likelihood function.

Main Results:

  • AIUQ eliminates the need for manual wave vector selection, improving estimation accuracy.
  • Significantly reduced computational cost for likelihood function computation.
  • Validated AIUQ through simulations of various dynamical systems and experimental studies.

Conclusions:

  • AIUQ offers a robust and automated approach to parameter estimation in scattering-based analyses.
  • Demonstrated AIUQ's utility in diverse systems, including Newtonian fluids, sol-gel transitions, and anisotropic colloids.
  • The method enables automated analysis and model selection without manual intervention.