Related papers: A Hybrid Virtual Element Method and Deep Learning …

We propose and analyze an $H^2$-conforming Virtual Element Method (VEM) for the simplest linear elliptic PDEs in nondivergence form with Cordes coefficients. The VEM hinges on a hierarchical construction valid for any dimension $d \ge 2$.…

This work begins by establishing a mathematical formalization between different geometrical interpretations of Neural Networks, providing a first contribution. From this starting point, a new interpretation is explored, using the idea of…

Beam prediction is critical for reducing beam-training overhead in millimeter-wave (mmWave) systems, especially in high-mobility vehicular scenarios. This paper presents a BEV-Fusion based framework that unifies camera, LiDAR, radar, and…

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…

Achieving human-like reasoning in deep learning models for complex tasks in unknown environments remains a critical challenge in embodied intelligence. While advanced vision-language models (VLMs) excel in static scene understanding, their…

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…

The Matrix-Element Method (MEM) has long been a cornerstone of data analysis in high-energy physics. It leverages theoretical knowledge of parton-level processes and symmetries to evaluate the likelihood of observed events. In parallel, the…

This paper proposes a new framework using physics-informed neural networks (PINNs) to simulate complex structural systems that consist of single and double beams based on Euler-Bernoulli and Timoshenko theory, where the double beams are…

The aim of this paper is to develop a virtual element method (VEM) for the vibration problem of thin plates on polygonal meshes. We consider a variational formulation relying only on the transverse displacement of the plate and propose an…

We propose two globally continuous neural-based variants of the Neural Approximated Virtual Element Method (NAVEM), termed B-NAVEM and P-NAVEM. Both approaches construct local basis functions using pre-trained fully connected neural…

Uneven light image enhancement is a highly demanded task in many industrial image processing applications. Many existing enhancement methods using physical lighting models or deep-learning techniques often lead to unnatural results. This is…

We present the analytical formulation and the finite element solution of a fractional-order nonlocal continuum model of a Euler-Bernoulli beam. Employing consistent definitions for the fractional-order kinematic relations, the governing…

The performance evaluation of a potentially unstable slope involves two key components: the initiation of the slope failure and the post-failure runout. The Finite Element Method (FEM) excels at modeling the initiation of instability but…

In this paper we construct conforming Virtual Element approximations on domains with curved boundary and/or internal curved interfaces, both in two and three dimensions. Our approach allows to impose both Dirichlet and Neumann…

We introduce the nonconforming Virtual Element Method (VEM) for the approximation of second order elliptic problems. We present the construction of the new element in two and three dimensions, highlighting the main differences with the…

In this work we present a novel bulk-surface virtual element method (BSVEM) for the numerical approximation of elliptic bulk-surface partial differential equations (BSPDEs) in three space dimensions. The BSVEM is based on the discretisation…

We deal with the virtual element method (VEM) for solving the Poisson equation on a domain $\Omega$ with curved boundaries. Given a polygonal approximation $\Omega_h$ of the domain $\Omega$, the standard order $m$ VEM [6], for $m$…

We present a hybrid partitioned deep learning framework for the reduced-order modeling of fluid-structure interaction. Using the discretized Navier-Stokes in the arbitrary Lagrangian-Eulerian reference frame, we generate the full-order flow…

Deep learning methods have played a more and more important role in hyperspectral image classification. However, the general deep learning methods mainly take advantage of the information of sample itself or the pairwise information between…

In this paper, a hybrid video compression framework is proposed that serves as a demonstrative showcase of deep learning-based approaches extending beyond the confines of traditional coding methodologies. The proposed hybrid framework is…