Data Analytics and Machine Learning

Highlights

Periodic time series

Robust learning with implicit networks

Image inpainting

Feature-driven exemplar-based nonlocal image inpainting

Solution in random domain

Numerical methods for PDEs in random domains

Stiff chemical system

Numerical integration of stiff stochastic chemical systems

Conceptual comparison of (a) the standard multi-loop Monte Carlo method for propagating multiple probability models, and (b) the proposed multimodel Monte Carlo method with importance sampling reweighting

Monte Carlo Methods for UQ: A Survey

A diagram of the workflow of our method.

A data-driven approach to study the thermodynamics of high entropy alloys

Probabilistic dependent input models

Uncertainty quantification with copula dependence modeling

CDF of imprecise first-order Sobol’ indices as a function of data set size from 100, 250, 500, 1000, 5000 to 10000.

IGSA: Imprecise global sensitivity analysis

Composite materials applications

Probabilistic modeling of composite materials with sparse data

DNN_RM

Non-intrusive inference reduced order model for fluids using deep multistep neural network

exit-2d

A Feynman-Kac based numerical method for the exit time probability of a class of transport problems

RE_sg

A sparse-grid probabilistic scheme for approximation of the runaway probability of electrons in fusion tokamak simulation

RE_MC

A backward Monte-Carlo method for time-dependent runaway electron simulations

quantum control

A stochastic approximate gradient ascent method for Bayesian experimental design with implicit models

Ackley function

AdaDGS: An adaptive black-box optimization method with a nonlocal directional Gaussian smoothing gradient