Related papers: Neural Networks to solve Partial Differential Equa…
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…
We present a novel approach that integrates unfitted finite element methods and neural networks to approximate partial differential equations on complex geometries. Easy-to-generate background meshes (e.g., a simple Cartesian mesh) that cut…
This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document you are assumed to have familiarity with concepts from the…
In nodal based finite element method (FEM), degrees of freedom are associated with the nodes of the element whereas, for edge FEM, degrees of freedom are assigned to the edges of the element. Edge element is constructed based on Whitney…
Information loss in numerical physics simulations can arise from various sources when solving discretized partial differential equations. In particular, errors related to numerical precision ("sub-precision errors") can accumulate in the…
The primary goal of this research is to propose a novel architecture for a deep neural network that can solve fractional differential equations accurately. A Gaussian integration rule and a $L_1$ discretization technique are used in the…
Finite element method (FEM) is one of the most important numerical methods in modern engineering design and analysis. Since traditional serial FEM is difficult to solve large FE problems efficiently and accurately, high-performance parallel…
Studying the peeling behaviour of adhesives on skin is vital for advancing biomedical applications such as medical adhesives and transdermal patches. Traditional methods like experimental testing and finite element method (FEM), though…
In this paper, we present a finite element method (FEM) framework enhanced by an operator-adapted wavelet decomposition algorithm designed for the efficient analysis of multiscale electromagnetic problems. Usual adaptive FEM approaches,…
Verification of Neural Networks (NNs) that approximate the solution of Partial Differential Equations (PDEs) is a major milestone towards enhancing their trustworthiness and accelerating their deployment, especially for safety-critical…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…
Deep neural networks (DNNs) have achieved great success in the area of computer vision. The disparity estimation problem tends to be addressed by DNNs which achieve much better prediction accuracy than traditional hand-crafted feature-based…
In this paper, an innovative Physical Model-driven Neural Network (PMNN) method is proposed to solve time-fractional differential equations. It establishes a temporal iteration scheme based on physical model-driven neural networks which…
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…
In this report, we propose a divergence-free preserving mixed finite element method (FEM) for the system of nonlinear fourth-order thermally driven active fluid equations. By introducing two auxiliary variables, we lower the complexity of…
Much recent research is devoted to exploring tradeoffs between computational accuracy and energy efficiency at different levels of the system stack. Approximation at the floating point unit (FPU) allows saving energy by simply reducing the…
We present a novel parallelization strategy for evaluating Finite Element Method (FEM) variational forms on GPUs, focusing on those that are expressible through the Unified Form Language (UFL) on simplex meshes. We base our approach on code…
The information content of atomic resolution scanning transmission electron microscopy (STEM) images can often be reduced to a handful of parameters describing each atomic column, chief amongst which is the column position. Neural networks…
The Fractional Diffusion Equation (FDE) is a mathematical model that describes anomalous transport phenomena characterized by non-local and long-range dependencies which deviate from the traditional behavior of diffusion. Solving this…