Related papers: A registration method for reduced basis problems u…
Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…
This work addresses model order reduction for complex moving fronts, which are transported by advection or through a reaction-diffusion process. Such systems are especially challenging for model order reduction since the transport cannot be…
Surface matching usually provides significant deformations that can lead to structural failure due to the lack of physical policy. In this context, partial surface matching of non-linear deformable bodies is crucial in engineering to govern…
We consider entropically regularized, semi-discrete versions of variational problems on the set of probability measures involving optimal transport as well as other terms. We prove that the solutions can be characterized by well-posed…
We develop and analyze a parametric registration procedure for manifolds associated with the solutions to parametric partial differential equations in two-dimensional domains. Given the domain $\Omega \subset \mathbb{R}^2$ and the manifold…
These lecture notes summarize various summer schools that I have given on the topic of solving inverse problems (state and parameter estimation) by combining optimally measurement observations and parametrized PDE models. After defining a…
We study MinMax solution methods for a general class of optimization problems related to (and including) optimal transport. Theoretically, the focus is on fitting a large class of problems into a single MinMax framework and generalizing…
This paper introduces the use of unbalanced optimal transport methods as a similarity measure for diffeomorphic matching of imaging data. The similarity measure is a key object in diffeomorphic registration methods that, together with the…
A methodology grounded in model reduction is presented for accelerating the gradient-based solution of a family of linear or nonlinear constrained optimization problems where the constraints include at least one linear Partial Differential…
We investigate an optimization problem governed by an elliptic partial differential equation with uncertain parameters. We introduce a robust optimization framework that accounts for uncertain model parameters. The resulting non-linear…
We present a general -- i.e., independent of the underlying equation -- registration procedure for parameterized model order reduction. Given the spatial domain $\Omega \subset \mathbb{R}^2$ and the manifold $\mathcal{M}= \{ u_{\mu} : \mu…
The solution of conservation laws with parametrized shock waves presents challenges for both high-order numerical methods and model reduction techniques. We introduce an r-adaptivity scheme based on optimal transport and apply it to develop…
In this work, we aim at efficiently solving a parametrized family of optimal transport problems by using model order reduction methods. We propose a reduced-order model by adding to the primal (respectively dual) version of the…
We propose a model reduction procedure for rapid and reliable solution of parameterized hyperbolic partial differential equations. Due to the presence of parameter-dependent shock waves and contact discontinuities, these problems are…
In many high-frequency simulation workflows, eigenvalue tracking along a parameter variation is necessary. This can become computationally prohibitive when repeated time-consuming eigenvalue problems must be solved. Therefore, we employ a…
This work introduces a new approach to reduce the computational cost of solving partial differential equations (PDEs) with convection-dominated solutions: model reduction with implicit feature tracking. Traditional model reduction…
We consider a class of parameter-dependent optimal control problems of elliptic PDEs with constraints of general type on the control variable. Applying the concept of variational discretization, [4], together with techniques from the…
Image registration has traditionally been done using two distinct approaches: learning based methods, relying on robust deep neural networks, and optimization-based methods, applying complex mathematical transformations to warp images…
In this manuscript, we introduce the tensor-train reduced basis method, a novel projection-based reduced-order model designed for the efficient solution of parameterized partial differential equations. While reduced-order models are widely…
In many scientific fields imaging is used to relate a certain physical quantity to other dependent variables. Therefore, images can be considered as a map from a real-world coordinate system to the non-negative measurements being acquired.…