Related papers: A novel model reduction method to solve inverse pr…
We propose a new approach to generate a reliable reduced model for a parametric elliptic problem, in the presence of noisy data. The reference model reduction procedure is the directional HiPOD method, which combines Hierarchical Model…
We propose and analyze an inexact gradient method based on incremental proper orthogonal decomposition (iPOD) to address the data storage difficulty in time-dependent PDE-constrained optimization, particularly for a data assimilation…
We propose a globally convergent computational technique for the nonlinear inverse problem of reconstructing the zero-order coefficient in a parabolic equation using partial boundary data. This technique is called the "reduced dimensional…
In this contribution we investigate in mathematical modeling and efficient simulation of biological cells with a particular emphasis on effective modeling of structural properties that originate from active forces generated from…
Proper orthogonal decomposition (POD) is often employed in developing reduced-order models (ROM) in fluid flows for design, control, and optimization. Contrary to the usual practice where velocity field is the focus, we apply the POD…
This paper deals with the development of a Reduced-Order Model (ROM) to investigate haemodynamics in cardiovascular applications. It employs the use of Proper Orthogonal Decomposition (POD) for the computation of the basis functions and the…
We show that Boundary Control method, a method for hyperbolic inverse problems, is also capable of dealing directly with certain classes of elliptic and parabolic Inverse Boundary Value Problems; thus pointing towards Boundary Control…
In our earlier work [Fareed et al., Comput. Math. Appl. 75 (2018), no. 6, 1942-1960], we proposed an incremental SVD algorithm with respect to a weighted inner product to compute the proper orthogonal decomposition (POD) of a set of…
In this paper, we address the challenging problem of optimal experimental design (OED) of constrained inverse problems. We consider two OED formulations that allow reducing the experimental costs by minimizing the number of measurements.…
Proper orthogonal decomposition methods for model reduction utilize information about the solution at certain time and parameter points to generate a reduced space basis. In this paper, we compare two proper orthogonal decomposition methods…
This paper investigates the solution of a parabolic inverse problem based upon the convection-diffusion-reaction equation, which can be used to estimate both water and air pollution. We will consider both known and unknown source location:…
Data-driven decompositions of Particle Image Velocimetry (PIV) measurements are widely used for a variety of purposes, including the detection of coherent features (e.g., vortical structures), filtering operations (e.g., outlier removal or…
In this paper, we propose a multiscale method for heterogeneous Stokes problems. The method is based on the Localized Orthogonal Decomposition (LOD) methodology and has approximation properties independent of the regularity of the…
Model Predictive Control (MPC) is a well-established approach to solve infinite horizon optimal control problems. Since optimization over an infinite time horizon is generally infeasible, MPC determines a suboptimal feedback control by…
In the context of simulation-based methods, multiple challenges arise, two of which are considered in this work. As a first challenge, problems including time-dependent phenomena with complex domain deformations, potentially even with…
In this work, we propose an observation system based on the available data which solution is one-be-one mapping to the forward problem(with the unknown initial function) solution. It implies their solutions share the same linear structure…
We present a method to construct reduced-order models for duct flows of Bingham media. Our method is based on proper orthogonal decomposition (POD) to find a low-dimensional approximation to the velocity and artificial neural network to…
In this paper, a new alternating direction trust region method based on conic model is used to solve unconstrained optimization problems. By use of the alternating direction method, the new conic model trust region subproblem is solved by…
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
The work provides an integrated pipeline for the model order reduction of turbulent flows around parametrised geometries in aerodynamics. In particular, Free-Form Deformation is applied for geometry parametrisation, whereas two different…