Proper orthogonal decomposition for parameter estimation in oscillating biological networks

Proper orthogonal decomposition for parameter estimation in oscillating biological networks

Galerkin Proper Orthogonal Decomposition Methods for Parameter Dependent Elliptic Systems

Proper orthogonal decomposition (POD) is a powerful technique for model reduction of linear and non-linear systems. It is based on a Galerkin type discretization with basis elements created from the system itself. In this work, error estimates for Galerkin POD methods for linear elliptic, parameter-dependent systems are proved. The resulting error bounds depend on the number of POD basis functi...

Parameter Identification in Cardiac Electrophysiology Using Proper Orthogonal Decomposition Method

We consider the problem of estimating some parameters (like ionic models or parameters involved in the initial stimulation) of a model of electrocardiograms (ECG) from the data of the Einthoven leads. This problem can be viewed as a first attempt to identify or to locate a pathology. The direct model is based on the bidomain equations in the heart and a Poisson equation in the torso and. To kee...

Dimensionality reduction of parameter-dependent problems through proper orthogonal decomposition

The numerical solution of partial differential equations (PDEs) depending on parametrized or random input data is computationally intensive. Reduced order modeling techniques, such as the reduced basis methods, have been developed to alleviate this computational burden, and are nowadays exploited to accelerate real-time analysis, as well as the solution of PDE-constrained optimization and inver...

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...