2

A novel autoencoder architecture is proposed to construct efficient reduced order models for advection-dominated PDEs. Numerical results are presented for parametric, linear and nonlinear advection-dominated problems.

A Python-based software package for constructing purely data-driven reduced order models of time-dependent PDEs.

A novel reduced order model for time-dependent PDEs using proper orthogonal decomposition and radial basis function interpolation. A new greedy algorithm for optimal selection of interpolation points is also proposed. Real world examples are presented using 2D shallow water equations.

Convergence analysis is performed in 1D for a hybrid numerical method that combines a discontinuous finite element method with a finite difference method to solve tow-phase, two-component flow and transport in porous media.

A novel hybrid numerical method for multiphase multicomponent flows in porous media using a combination of a discontinuous finite element method and a modified method of characteristics-based finite difference method. Real world numerical examples are presented for chemical enhanced oil recovery using surfactant-polymer flooding.