Cyberinfrastructure for forward prediction and inversion estimation with uncertainty quantification

• Mengyang Gu (UC Santa Barbara)

**Abstract**: In this talk, we introduce four useful tools for forward prediction and inversion estimation. The first tool is the parallel partial Gaussian process surrogate model for emulating expensive computer simulations with massive coordinates. The tool is implemented in the RobustGaSP package available in R, MATLAB, and Python, for predicting both scalar- and vector-valued outputs with uncertainty assessment. The second tool is implemented in the RobustCalibration package, which handles Bayesian data inversion or model calibration by one or multiple types of experimental observations. A unique feature of the package is the inclusion of fast surrogate models of both scalar- and vector-valued computer simulations that bypass the expensive simulation in one line of code. The third tool is implemented in the AIUQ package, available in both R and MATLAB. In this approach, we show that differential dynamic microscopy, a scattering-based analysis tool that extracts dynamical information from microscopy videos, is equivalent to fitting the temporal auto-covariance in Fourier space, based on a latent factor model we construct. We develop a more efficient estimator and reduce the computational cost to pseudolinear order with respect to the number of observations without approximation, by utilizing the generalized Schur algorithm for the Toeplitz covariance. In the last tool, we developed a new method called the inverse Kalman filter, which enables fast 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 that include emulating expensive simulation at molecular-, meso- and macro-scales, active learning with error control, nonparametric estimation of particle interaction functions, and data inversion from microscopy and velocity fields. **Speaker Biography**: Mengyang Gu is an assistant professor in the Department of Statistics and Applied Probability at UC Santa Barbara. He obtained a PhD in Statistical Science from Duke University. 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.