Calibration of POD reduced-order models using Tikhonov regularization

Calibration of POD reduced-order models using Tikhonov regularization

Reduced-Order Subscales for POD models

In this work the Reduced-Order Subscales for Proper Orthogonal Decomposition models are presented. The basic idea consists in splitting the full-order solution into the part which can be captured by the reduced-order model and the part which cannot, the subscales, for which a model is required. The proposed model for the subscales is defined as a linear function of the solution of the reduced-o...

Tikhonov Regularization Using Sobolev Metrics

Given an ill-posed linear operator equation Au = f in a Hilbert space, we formulate a variational problem using Tikhonov regularization with a Sobolev norm of u, and we treat the variational problem by a Sobolev gradient flow. We show that the gradient system has a unique global solution for which the asymptotic limit exists with convergence in the strong sense using the Sobolev norm, and that ...

Reduced order models based on local POD plus Galerkin projection

A method is presented to accelerate numerical simulations on parabolic problems using a numerical code and a Galerkin system (obtained vía POD plus Galerkin projection) on a sequence of interspersed intervals. The lengths of these intervals are chosen according to several basic ideas that include an a priori estímate of the error of the Galerkin approximation. Several improvements are introduce...

Tikhonov Regularization

An important issue in quantitative nance is model calibration. The calibration problem is the inverse of the pricing problem. Instead of computing prices in a model with given values for its parameters, one wishes to compute the values of the model parameters that are consistent with observed prices. Now, it is well-known by physicists that such inverse problems are typically ill-posed. So, if ...