15 citations · 46 across the 8 of their papers we have counts for
8 papers
Sequential bi-level regularized inversion with application to hidden reaction law discovery
Tram Thi Ngoc Nguyen
In this article, we develop and present a novel regularization scheme for ill-posed inverse problems governed by nonlinear time-dependent partial differential equations (PDEs). In…
Bi-level iterative regularization for inverse problems in nonlinear PDEs
Tram Thi Ngoc Nguyen
We investigate the ill-posed inverse problem of recovering unknown spatially dependent parameters in nonlinear evolution PDEs. We propose a bi-level Landweber scheme, where the upp…
Learning-informed parameter identification in nonlinear time-dependent PDEs
Christian Aarset, Martin Holler, Tram Thi Ngoc Nguyen
We introduce and analyze a method of learning-informed parameter identification for partial differential equations (PDEs) in an all-at-once framework. The underlying PDE model is f…
Discretization of parameter identification in PDEs using Neural Networks
Barbara Kaltenbacher, Tram Thi Ngoc Nguyen
We consider the ill-posed inverse problem of identifying a nonlinearity in a time-dependent PDE model. The nonlinearity is approximated by a neural network, and needs to be determi…
On numerical aspects of parameter identification for the Landau-Lifshitz-Gilbert equation in Magnetic Particle Imaging
Tram Thi Ngoc Nguyen, Anne Wald
The Landau-Lifshitz-Gilbert equation yields a mathematical model to describe the evolution of the magnetization of a magnetic material, particularly in response to an external appl…
Parameter identification for the Landau-Lifshitz-Gilbert equation in Magnetic Particle Imaging
Barbara Kaltenbacher, Tram Thi Ngoc Nguyen, Anne Wald +1
Magnetic particle imaging (MPI) is a tracer-based technique for medical imaging where the tracer consists of ironoxide nanoparticles. The key idea is to measure the particle respon…
The tangential cone condition for some coefficient identification model problems in parabolic PDEs
Barbara Kaltenbacher, Tram Thi Ngoc Nguyen, Otmar Scherzer
The tangential condition was introduced in [Hanke et al., 95] as a sufficient condition for convergence of the Landweber iteration for solving ill-posed problems. In this paper we…
Landweber-Kaczmarz for parameter identification in time-dependent inverse problems: All-at-once versus Reduced version
Tram Thi Ngoc Nguyen
In this study, we consider a general time-space system, whose model operator and observation operator are locally Lipschitz continuous, over a finite time horizon and parameter ide…