Fast Ab Initio Uncertainty Quantification and Data Inversion for Dynamical Systems

Oregon Convention Center 

Estimating parameters from data is a fundamental problem, which is customarily done by minimizing a loss function between a model and observed statistics. In this talk, we discuss another paradigm termed the ab initio uncertainty quantification (AIUQ) method, for improving loss-minimization estimation in two steps. In step one, we define a probabilistic generative model from the beginning of data processing and show the equivalence between loss-minimization estimation and a statistical estimator. In step two, we develop better models or estimators, such as the maximum marginal likelihood or Bayesian estimators to improve estimation. To illustrate, we introduce two approaches to estimate dynamical systems, one in Fourier analysis of microscopy videos, and the other in inversely estimating the particle interaction kernel from trajectory. In the first approach, we show that differential dynamic microscopy, a scattering-based analysis tool that extracts dynamical information of microscopy videos, is equivalent to fitting Fourier temporal auto-covariance based on a latent factor model we constructed. We derived likelihood-based inference and accelerated the computation thousands of times by utilizing the generalized Schur algorithm for Toeplitz covariances. In the second approach, we developed a new method called the inverse Kalman filter which enables accurate matrix-vector multiplication between a covariance matrix from a dynamic linear model and any real-valued vector with a linear computational cost. These new approaches outline a wide range of applications, such as probing optically dense systems, automated determination of gelation time, and estimating cellular interaction for fibroblasts on liquid crystalline substrates.