Ab initio uncertainty quantification in scattering analysis of microscopy.

IF 2.2 3区 物理与天体物理 Q2 PHYSICS, FLUIDS & PLASMAS Physical Review E Pub Date : 2024-09-01 DOI:10.1103/PhysRevE.110.034601
Mengyang Gu, Yue He, Xubo Liu, Yimin Luo
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Abstract

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, it is common to work in the reciprocal space. Researchers often employ their domain expertise to select a specific range of wave vectors 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 the ab initio uncertainty quantification (AIUQ). As an illustrative example, we demonstrate this approach with differential dynamic microscopy (DDM) that extracts dynamical information through minimizing a loss function for the squared differences of the Fourier-transformed intensities, at a selected range of wave vectors. We first show that the conventional way of estimation in 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 the information at all wave vectors, therefore eliminating the need to select the range of wave vectors. Furthermore, we substantially reduce the computational cost of computing the likelihood function without approximation, by utilizing the generalized Schur algorithm for Toeplitz covariances. Simulated studies of a wide range of dynamical systems validate that the AIUQ method 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 studies demonstrate that the new approach does not require manually selecting the wave vector range and enables automated analysis.

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显微镜散射分析中的 Ab initio 不确定性量化。
从数据中估算参数是物理学中的一个基本问题,通常是通过最小化模型与观测统计数据之间的损失函数来实现的。在基于散射的分析中,通常是在倒数空间工作。研究人员通常利用自己的领域专长来选择特定范围的波矢进行分析,这种选择可能因具体情况而异。我们引入了另一种范式,即在数据处理之初就定义概率生成模型,并传播参数估计的不确定性,称为 "初始不确定性量化"(AIUQ)。作为示例,我们用差分动态显微镜(DDM)演示了这种方法,它通过最小化选定波矢量范围内傅里叶变换强度平方差的损失函数来提取动态信息。我们首先证明,DDM 的传统估算方法等同于在倒易空间中使用潜在因子模型作为生成模型来拟合时间变异图。然后,我们推导出最大边际似然估计器,该估计器可对所有波向量的信息进行最佳权衡,因此无需选择波向量的范围。此外,我们还利用针对托普利兹协方差的广义舒尔算法,大大降低了计算似然函数的计算成本。对各种动力系统的模拟研究证实,AIUQ 方法提高了估计精度,并能通过自动分析进行模型选择。AIUQ 的实用性还体现在三组不同的实验中:首先是在各向同性牛顿流体中,与多粒子跟踪相比,AIUQ 突破了光学致密系统的极限;其次是在发生溶胶-凝胶转变的系统中,自动确定胶凝点和临界指数;最后是在液晶中判别胶体的各向异性扩散行为。这些研究表明,新方法无需手动选择波矢量范围,即可实现自动分析。
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来源期刊
Physical Review E
Physical Review E PHYSICS, FLUIDS & PLASMASPHYSICS, MATHEMAT-PHYSICS, MATHEMATICAL
CiteScore
4.50
自引率
16.70%
发文量
2110
期刊介绍: Physical Review E (PRE), broad and interdisciplinary in scope, focuses on collective phenomena of many-body systems, with statistical physics and nonlinear dynamics as the central themes of the journal. Physical Review E publishes recent developments in biological and soft matter physics including granular materials, colloids, complex fluids, liquid crystals, and polymers. The journal covers fluid dynamics and plasma physics and includes sections on computational and interdisciplinary physics, for example, complex networks.
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