Related papers: A tutorial-driven introduction to the parallel fin…
The main computing tasks of a finite element code(FE) for solving partial differential equations (PDE's) are the algebraic system assembly and the iterative solver. This work focuses on the first task, in the context of a hybrid MPI+X…
Deep learning approaches for partial differential equations (PDEs) have received much attention in recent years due to their mesh-freeness and computational efficiency. However, most of the works so far have concentrated on time-dependent…
We present Fiend - a simulation package for three-dimensional single-particle time-dependent Schr\"odinger equation for cylindrically symmetric systems. Fiend has been designed for the simulation of electron dynamics under inhomogeneus…
A new concept is introduced for the adaptive finite element discretization of partial differential equations that have a sparsely representable solution. Motivated by recent work on compressed sensing, a recursive mesh refinement procedure…
PDE-to-solver code generation aims to automatically synthesize executable numerical solvers from partial differential equation (PDE) specifications. This task requires not only understanding the mathematical structure of PDEs, but also…
Many physical problems involve spatial and temporal inhomogeneities that require a very fine discretization in order to be accurately simulated. Using an adaptive mesh, a high level of resolution is used in the appropriate areas while…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
Partial differential equations (PDEs) underlie our understanding and prediction of natural phenomena across numerous fields, including physics, engineering, and finance. However, solving parametric PDEs is a complex task that necessitates…
Partial differential equations (PDEs) involving high contrast and oscillating coefficients are common in scientific and industrial applications. Numerical approximation of these PDEs is a challenging task that can be addressed, for example,…
Distributed model fitting refers to the process of fitting a mathematical or statistical model to the data using distributed computing resources, such that computing tasks are divided among multiple interconnected computers or nodes, often…
In this paper, we present PARTIME, a software library written in Python and based on PyTorch, designed specifically to speed up neural networks whenever data is continuously streamed over time, for both learning and inference. Existing…
In this work, we have developed a multiscale computational algorithm to couple finite element method with an open source molecular dynamics code --- the Large scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) --- to perform…
We establish a simple, rigorous, and easy to implement connection between the classical continuous finite element method (FEM) and the discontinuous Galerkin (DG) method for Poisson's problem. The key idea is to insert a vanishing-thickness…
A numerical framework is developed to solve various types of PDEs on complicated domains, including steady and time-dependent, non-linear and non-local PDEs, with different boundary conditions that can also include non-linear and non-local…
Large-scale PDE simulations using high-order finite-element methods on unstructured meshes are an indispensable tool in science and engineering. The widely used open-source PETSc library offers an efficient representation of generic…
We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct boundary data, we are provided with a large dataset of…
Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…
Functional data analysis has become a tool of interest in applied areas such as economics, medicine, and chemistry. Among the techniques developed in recent literature, functional semiparametric regression stands out for its balance between…
Modeling real-world problems with partial differential equations (PDEs) is a prominent topic in scientific machine learning. Classic solvers for this task continue to play a central role, e.g. to generate training data for deep learning…
This work proposes an $r$-adaptive finite element method (FEM) using neural networks (NNs). The method employs the Ritz energy functional as the loss function, currently limiting its applicability to symmetric and coercive problems, such as…