Related papers: Solving Inverse Parametrized Problems via Finite E…
In this paper, we consider a class of time-optimal control problems governed by linear parabolic equations with mixed control-state constraints and end-point constraints, and without Tikhonov regularization term in the objective function.…
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 determined alongside other unknown physical parameters and the…
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
In this work, we propose a model order reduction framework to deal with inverse problems in a non-intrusive setting. Inverse problems, especially in a partial differential equation context, require a huge computational load due to the…
Empirical interpolation method (EIM) is a well-known technique to efficiently approximate parameterized functions. This paper proposes to use EIM algorithm to efficiently reduce the dimension of the training data within supervised machine…
In this paper we present a finite element method for the direct transcription of constrained non-linear optimal control problems. We prove that our method converges of high order under mild assumptions. Our analysis uses a regularized…
Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…
In this work we analyze the inverse problem of recovering the space-dependent potential coefficient in an elliptic / parabolic problem from distributed observation. We establish novel (weighted) conditional stability estimates under very…
Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and…
Based on the work of Xu and Zhou [Math.Comput., 69(2000), pp.881-909], we establish new three-level and multilevel finite element discretizations by local defect-correction technique. Theoretical analysis and numerical experiments show that…
We develop error estimates for the finite element approximation of elliptic partial differential equations on perturbed domains, i.e. when the computational domain does not match the real geometry. The result shows that the error related to…
Recent efforts on solving inverse problems in imaging via deep neural networks use architectures inspired by a fixed number of iterations of an optimization method. The number of iterations is typically quite small due to difficulties in…
When using the finite element method (FEM) in inverse problems, its discretization error can produce parameter estimates that are inaccurate and overconfident. The Bayesian finite element method (BFEM) provides a probabilistic model for the…
One fundamental problem when solving inverse problems is how to find regularization parameters. This article considers solving this problem using data-driven bilevel optimization, i.e. we consider the adaptive learning of the regularization…
Variational regularization methods are commonly used to approximate solutions of inverse problems. In recent years, model-based variational regularization methods have often been replaced with data-driven ones such as the fields-of-expert…
In this work, we investigate the performance CutFEM as a high fidelity solver as well as we construct a competent and economical reduced order solver for PDE-constrained optimization problems in parametrized domains that live in a fixed…
Reduced-order modeling is an efficient approach for solving parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space and an online step…
In this paper, we demonstrate a computationally efficient new approach based on deep learning (DL) techniques for analysis, design, and optimization of electromagnetic (EM) nanostructures. We use the strong correlation among features of a…
The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…