Related papers: Improved convergence of forward and inverse finite…

Electrical machines employing superconductors are attractive solutions in a variety of application domains. Numerical models are powerful and necessary tools to optimize their design and predict their performance. The electromagnetic…

We propose and show the efficacy of a new method to address generic inverse problems. Inverse modeling is the task whereby one seeks to determine the control parameters of a natural system that produce a given set of observed measurements.…

In this paper, we aim at developing new methods to join machine learning techniques and macroscopic differential models for vehicular traffic estimation and forecast. It is well known that data-driven and model-driven approaches have…

In this article we study adaptive finite element methods (AFEM) with inexact solvers for a class of semilinear elliptic interface problems. We are particularly interested in nonlinear problems with discontinuous diffusion coefficients, such…

As inelastic structures are ubiquitous in many engineering fields, a central task in computational mechanics is to develop accurate, robust and efficient tools for their analysis. Motivated by the poor performances exhibited by standard…

Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…

The Finite Element Method (FEM) is a powerful modeling tool for predicting soft robots' behavior, but its computation time can limit practical applications. In this paper, a learning-based approach based on condensation of the FEM model is…

We perform a systematic comparison of various numerical schemes for the approximation of interface problems. We consider unfitted approaches in view of their application to possibly moving configurations. Particular attention is paid to the…

Finding model parameters from data is an essential task in science and engineering, from weather and climate forecasts to plasma control. Previous works have employed neural networks to greatly accelerate finding solutions to inverse…

As global energy systems transit to clean energy, accurate renewable generation and renewable demand forecasting is imperative for effective grid management. Foundation Models (FMs) can help improve forecasting of renewable generation and…

Engineering and applied sciences use models of increasing complexity to simulate the behaviour of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may…

In the framework of solid mechanics, the task of deriving material parameters from experimental data has recently re-emerged with the progress in full-field measurement capabilities and the renewed advances of machine learning. In this…

Advanced feedforward control methods enable mechatronic systems to perform varying motion tasks with extreme accuracy and throughput. The aim of this paper is to develop a data-driven feedforward controller that addresses input…

We propose a general framework for solving forward and inverse problems constrained by partial differential equations, where we interpolate neural networks onto finite element spaces to represent the (partial) unknowns. The framework…

This paper presents adaptive boundary element methods for positive, negative, as well as zero order operator equations, together with proofs that they converge at certain rates. The convergence rates are quasi-optimal in a certain sense…

In this work, we investigate the regularized solutions and their finite element solutions to the inverse source problems governed by partial differential equations, and establish the stochastic convergence and optimal finite element…

We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows…

Numerous tasks at the core of statistics, learning and vision areas are specific cases of ill-posed inverse problems. Recently, learning-based (e.g., deep) iterative methods have been empirically shown to be useful for these problems.…

In the software development process, model transformation is increasingly assimilated. However, systems being developed with model transformation sometimes grow in size and become complex. Meanwhile, the performance of model transformation…

We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme…