A machine learning based plasticity model using proper orthogonal decomposition

Model Reduction via Proper Orthogonal Decomposition

Model Reduction by Proper Orthogonal Decomposition (POD)

Mathematical models for human tissue and blood flow both represent time dependent nonlinear partial differential equations in three space dimensions. Their numerical solution based on appropriate space/time discretizations requires computational times that even when using state-of-the-art algorithmic solvers are far from being acceptable for real time OR scenarios. A way to overcome this diffic...

Model Reduction for fluids, Using Balanced Proper Orthogonal Decomposition

Many of the tools of dynamical systems and control theory have gone largely unused for fluids, because the governing equations are so dynamically complex, both high-dimensional and nonlinear. Model reduction involves finding low-dimensional models that approximate the full high-dimensional dynamics. This paper compares three different methods of model reduction: proper orthogonal decomposition ...

Artificial viscosity proper orthogonal decomposition

We introduce improved reduced-order models for turbulent flows. These models are inspired from successful methodologies used in large eddy simulation, such as artificial viscosity, applied to standardmodels created by proper orthogonal decomposition of flows coupled with Galerkin projection. As a first step in the analysis and testing of our new methodology, we use the Burgers equation with a s...

A New Look at Proper Orthogonal Decomposition

We investigate some basic properties of the proper orthogonal decomposition (POD) method as it is applied to data compression and model reduction of finite dimensional nonlinear systems. First we provide an analysis of the errors involved in solving a nonlinear ODE initial value problem using a POD reduced order model. Then we study the effects of small perturbations in the ensemble of data fro...