Related papers: On a PDE-based material parameter identification p…
We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct boundary data, we are provided with a large dataset of…
We address the problem to infer physical material parameters and boundary conditions from the observed motion of a homogeneous deformable object via the solution of an inverse problem. Parameters are estimated from potentially unreliable…
This paper pertains to the analysis and design of decentralized estimation schemes that make use of limited communication. Briefly, these schemes equip the sensors with scalar states that iteratively merge the measurements and the state of…
To study the nonlinear properties of complex natural phenomena, the evolution of the quantity of interest can be often represented by systems of coupled nonlinear stochastic differential equations (SDEs). These SDEs typically contain…
Models with interacting dark energy can alleviate the cosmic coincidence problem by allowing dark matter and dark energy to evolve in a similar fashion. At a fundamental level, these models are specified by choosing a functional form for…
Barrier potentials gained popularity as a means for robust contact handling in physical modeling and for modeling self-avoiding shapes. The key to the success of these approaches is adherence to geometric constraints, i.e., avoiding…
In this paper, we propose and study several inverse problems of identifying/determining unknown coefficients for a class of coupled PDE systems by measuring the average flux data on part of the underlying boundary. In these coupled systems,…
A special aspect of parameter identification in finite-strain elasto-plasticity is considered. Namely, we analyze the impact of the measurement errors on the resulting set of material parameters. In order to define the sensitivity of…
In this paper we prove uniqueness for some parameter identification problems for the JMGT equation, a third order in time quasilinear PDE in nonlinear acoustics. The coefficients to be recovered are the space dependent nonlinearity…
This paper explores the reconstruction of a space-dependent parameter in inverse diffusion problems, proposing a shape-optimization-based approach. We consider a Robin boundary condition, physically motivated in diffuse optical tomography…
Physics-informed neural networks have emerged as a powerful tool in the scientific machine learning community, with applications to both forward and inverse problems. While they have shown considerable empirical success, significant…
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…
Identifiability of parameters is a fundamental prerequisite for model identification. It concerns uniqueness of the model parameters determined from experimental or simulated observations. This dissertation specifically deals with…
Computational approaches to PDE-constrained optimization under uncertainty may involve finite-dimensional approximations of control and state spaces, sample average approximations of measures of risk and reliability, smooth approximations…
The purpose of this paper is twofold. First, we rigorously justify Koiter's model for linearly elastic elliptic membrane shells in the case where the shell is subject to a geometrical constraint modelled via a normal compliance contact…
Identifying unique parameters for mathematical models describing biological data can be challenging and often impossible. Parameter identifiability for partial differential equations models in cell biology is especially difficult given that…
We introduce a general differentiable solver for time-dependent deformation problems with contact and friction. Our approach uses a finite element discretization with a high-order time integrator coupled with the recently proposed…
Regularization robust preconditioners for PDE-constrained optimization problems have been successfully developed. These methods, however, typically assume that observation data is available throughout the entire domain of the state…
Parameter estimation is of foundational importance for various model-based battery management tasks, including charging control, state-of-charge estimation and aging assessment. However, it remains a challenging issue as the existing…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…