Related papers: T-IFISS: a toolbox for adaptive FEM computation

\textbf{FlexBox} is a flexible MATLAB toolbox for finite dimensional convex variational problems in image processing and beyond. Such problems often consist of non-differentiable parts and involve linear operators. The toolbox uses a…

We present an efficient deterministic hypothesis generation algorithm for robust fitting of multiple structures based on the maximum feasible subsystem (MaxFS) framework. Despite its advantage, a global optimization method such as MaxFS has…

This paper develops and implements an algorithm to compute sequences of polytopic Robust Forward Invariant Sets (RFIS) that can parametrically vary in size between the maximal and minimal RFIS of a nonlinear dynamical system. This is done…

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…

The prediction accuracy of machine learning methods is steadily increasing, but the calibration of their uncertainty predictions poses a significant challenge. Numerous works focus on obtaining well-calibrated predictive models, but less is…

We propose a novel finite element-based physics-informed operator learning framework that allows for predicting spatiotemporal dynamics governed by partial differential equations (PDEs). The proposed framework employs a loss function…

fixest is an R package for fast and flexible econometric estimation. It provides a unified framework for applied research, with comprehensive support for a diverse class of models: ordinary least squares, instrumental variables, generalized…

We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in…

This article aims to demonstrate and discuss the applications of automatic differentiation (AD) for finding derivatives in PDE-constrained optimization problems and Jacobians in non-linear finite element analysis. The main idea is to…

This paper presents a MATLAB toolbox for implementing robust-to-early termination model predictive control, abbreviated as REAP, which is designed to ensure a sub-optimal yet feasible solution when MPC computations are prematurely…

Commercially available Noisy Intermediate-Scale Quantum (NISQ) devices now make small hybrid quantum-classical experiments practical, but many tools hide configuration or demand ad-hoc scripting. We introduce the Quantum Experiment…

Accurate time series forecasting is a highly valuable endeavour with applications across many industries. Despite recent deep learning advancements, increased model complexity, and larger model sizes, many state-of-the-art models often…

Machine learning is a powerful tool for extracting valuable information and making various predictions from diverse datasets. Traditional machine learning algorithms rely on well-defined input and output variables; however, there are…

In recent years, with the advancements in machine learning and neural networks, algorithms using physics-informed neural networks (PINNs) to solve PDEs have gained widespread applications. While these algorithms are well-suited for a wide…

The new software FEniCS-preCICE is a middle software layer, sitting in between the existing finite-element library FEniCS and the coupling library preCICE. The middle layer simplifies coupling (existing) FEniCS application codes to other…

Recently, deep learning has driven significant advancements in multivariate time series forecasting (MTSF) tasks. However, much of the current research in MTSF tends to evaluate models from a holistic perspective, which obscures the…

This paper proposes a novel optimization framework for discrete phase shifts of a reconfigurable intelligent surface (RIS) using a coherent Ising machine (CIM). Unlike conventional methods based on iterative convex approximation or…

This work is a user guide to the FEMPAR scientific software library. FEMPAR is an open-source object-oriented framework for the simulation of partial differential equations (PDEs) using finite element methods on distributed-memory…

We present a multiscale mixed finite element method for solving second order elliptic equations with general $L^{\infty}$-coefficients arising from flow in highly heterogeneous porous media. Our approach is based on a multiscale spectral…

An adaptive refinement strategy, based on an equilibrated flux a posteriori error estimator, is proposed in the context of defeaturing problems. Defeaturing consists of removing features from complex domains to simplify mesh generation and…