Mengyang Gu
Title: Fast ab initio uncertainty quantification
Abstract: Estimating parameters from data is a fundamental problem in physics and mathematics, customarily done by minimizing a loss function between a model and observed statistics. We discuss 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) method. We introduce a two-step approach to improve the estimation from loss minimization by an AIUQ approach. As an illustrative example, we show that differential dynamic microscopy (DDM), a scattering-based analysis tool that extracts dynamical information from Fourier decomposition is equivalent to fitting a temporal variogram at a selected range of wavevectors using a probabilistic latent factor 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 reduce the computational cost of computing the likelihood function by more than a hundred thousand times, without approximation, by utilizing the generalized Schur algorithm for Toeplitz covariances. This advantage of our approach is validated by a wide range of simulated and real experiments of complex dynamics. Finally, we will apply the principle of converting loss minimization to generative models for a wide range of models, such as dynamic mode decomposition (DMD) and its extensions, allowing for better understanding of the model assumptions from these approaches, deriving nonlinear estimators, such as parallel partial Gaussian processes, for forecasting complex dynamical systems, and accelerating the computation by fast algorithms such as Kalman filter, without approximating the likelihood.
Bio: Mengyang Gu is an assistant professor from the Department of Statistics and Applied Probability at UC Santa Barbara. He focuses on developing fast and accurate statistical learning methods to estimate high-dimensional dynamical systems from experimental or field observations, and to emulate expensive computer simulations with high-dimensional inputs and massive outcomes. He has expertise in Bayesian analysis and uncertainty quantification. He received the SIAM activity group on uncertainty quantification (SIAG/UQ) early career prize in 2022. His collaborative work received Soft Matter Editor board’s highlights of 2022 and Best Long Paper Award in ACM IMC in 2022.
Joyce Cummings Center, Room 260
Meeting ID: 923 7689 4365
Passcode: 186580