This paper presents a review of proper orthogonal decomposition (POD) methods for order
reduction in a variety of research areas. The historical development and basic mathematical …

Real-time state estimation and forecasting are critical for the efficient operation of power
grids. In this paper, a physics-informed Gaussian process regression (PhI-GPR) method is …

Equations governing flow and transport in randomly heterogeneous porous media are
stochastic and scale dependent. In the moment equation (ME) method, exact deterministic …

We present a probability density function (PDF) method for a system of nonlinear stochastic
ordinary differential equations driven by colored noise. The method provides an …

A method is described to solve the nonlinear Langevin equations arising from quadratic
interactions in quantum mechanics. While the zeroth order linearization approximation to the …

We present a physics-informed Gaussian Process Regression (GPR) model to predict the
phase angle, angular speed, and wind mechanical power from a limited number of …

We present a physics-informed Gaussian Process Regression (GPR) model to predict the
phase angle, angular speed, and wind mechanical power from a limited number of …

Real-time state estimation and forecasting is critical for efficient operation of power grids. In
this paper, a physics-informed Gaussian process regression (PhI-GPR) method is presented …

The polynomial dimensional decomposition (PDD) method is applied to study the amplitude-
frequency response behaviors of dynamical system model in this paper. The first two order …

We present a numerical approach for estimating the probability density function (PDF) of
quantities of interest (QoIs) of power grid systems subject to uncertain power generation and …