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In this article we consider the widely used immersed finite element method (IFEM), in both explicit and implicit form, and its relationship to our more recent one-field fictitious domain method (FDM). We review and extend the formulation of…

This study introduces the concept of finite element network analysis (FENA) which is a physics-informed, machine-learning-based, computational framework for the simulation of complex physical systems. The framework leverages the extreme…

This paper focuses on the study of the Filament Based Lamellipodium Model (FBLM) and the corresponding Finite Element Method (FEM) from a numerical point of view. We study fundamental numerical properties of the FEM and justify the further…

We propose a neural network model to estimate the current frame from two reference frames, using affine transformation and adaptive spatially-varying filters. The estimated affine transformation allows for using shorter filters compared to…

In this work, the Immersed Boundary Method (IBM) with feedback forcing introduced by Goldstein et al. (1993) and often referred in the literature as the Virtual Boundary Method (VBM), is addressed. The VBM has been extensively applied both…

Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…

The aim of this study was to check how efficient can be smoothed finite element method (FEM) for solution of the linear fracture mechanics problems. Accuracy of stress intensity factor (SIF) computation were investigated using three types…

Graph neural networks (GNNs) naturally align with sparse operators and unstructured discretizations, making them a promising paradigm for physics-informed machine learning in computational mechanics. Motivated by discrete physics losses and…

The Matrix Element Method (MEM) is a powerful method to extract information from measured events at collider experiments. Compared to multivariate techniques built on large sets of experimental data, the MEM does not rely on an…

Traditional image segmentation methods, such as variational models based on partial differential equations (PDEs), offer strong mathematical interpretability and precise boundary modeling, but often suffer from sensitivity to parameter…

Numerical homogenization for mechanical multiscale modeling by means of the finite element method (FEM) is an elegant way of obtaining structure-property relations, if the behavior of the constituents of the lower scale is well understood.…

The kernel embedding algorithm is an important component for adapting kernel methods to large datasets. Since the algorithm consumes a major computation cost in the testing phase, we propose a novel teacher-learner framework of learning…

In this paper, we introduce the Deep Finite Volume Method (DFVM), an innovative deep learning framework tailored for solving high-order (order \(\geq 2\)) partial differential equations (PDEs). Our approach centers on a novel loss function…

Although large-scale visual foundation models (VFMs) achieve remarkable performance in semantic understanding, they still underperform in instance-aware dense prediction tasks. They exhibit different biases in representation: for instance,…

Finite element method (FEM) suffers from a serious mesh distortion problem when used for high velocity impact analyses. The smooth particle hydrodynamics (SPH) method is appropriate for this class of problems involving severe damages but at…

Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and design of nanostructured optical components. A vectorial finite element method (FEM) is a good choice for an…

This work introduces a new method for selecting the number of components in finite mixture models (FMMs) using variational Bayes, inspired by the large-sample properties of the Evidence Lower Bound (ELBO) derived from mean-field (MF)…

We introduce a method that combines neural operators, physics-informed machine learning, and standard numerical methods for solving PDEs. The proposed approach extends each of the aforementioned methods and unifies them within a single…

In this paper, we propose a way to solve partial differential equations (PDEs) by combining machine learning techniques and the finite element method called Phi-FEM. For that, we use the Fourier Neural Operator (FNO), a learning mapping…

Recommending items to users has long been a fundamental task, and studies have tried to improve it ever since. Most well-known models commonly employ representation learning to map users and items into a unified embedding space for matching…