Related papers: PINNIES: An Efficient Physics-Informed Neural Netw…
In this paper, we explore the acceleration of tensor product operations in finite element methods, leveraging the computational power of the NVIDIA A100 GPU Tensor Cores. We provide an accessible overview of the necessary mathematical…
With growing investigations into solving partial differential equations by physics-informed neural networks (PINNs), more accurate and efficient PINNs are required to meet the practical demands of scientific computing. One bottleneck of…
Modern power systems require fast and accurate dynamic simulations for stability assessment, digital twins, and real-time control, but classical ODE solvers are often too slow for large-scale or online applications. We propose a…
Neural operators improve conventional neural networks by expanding their capabilities of functional mappings between different function spaces to solve partial differential equations (PDEs). One of the most notable methods is the Fourier…
Physics-informed neural networks (PINNs) have been widely applied to solve partial differential equations (PDEs) by enforcing outputs and gradients of deep models to satisfy target equations. Due to the limitation of numerical computation,…
We present the partial evolutionary tensor neural networks (pETNNs), a novel framework for solving time-dependent partial differential equations with high accuracy and capable of handling high-dimensional problems. Our architecture…
Physics-Informed Neural Networks (PINN) are a machine learning tool that can be used to solve direct and inverse problems related to models described by Partial Differential Equations. This paper proposes an adaptive inverse PINN applied to…
Initial boundary value problems arise commonly in applications with engineering and natural systems governed by nonlinear partial differential equations (PDEs). Operator learning is an emerging field for solving these equations by using a…
Neural Operators offer a powerful, data-driven tool for solving parametric PDEs as they can represent maps between infinite-dimensional function spaces. In this work, we employ physics-informed Neural Operators in the context of…
Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently. Here, we present an overview of physics-informed neural networks (PINNs),…
We present a method to solve fractional optimal control problems, where the dynamic depends on integer and Caputo fractional derivatives. Our approach consists to approximate the initial fractional order problem with a new one that involves…
This article introduces a general purpose framework and software to approximate partial differential equations (PDEs). The sparsity patterns of finite element discretized operators is identified automatically using the tools from…
Physics-informed neural networks (PINNs) are capable of finding the solution for a given boundary value problem. We employ several ideas from the finite element method (FEM) to enhance the performance of existing PINNs in engineering…
In this article, we propose an algorithm for approximating the action of $\varphi-$functions of matrices against vectors, which is a key operation in exponential time integrators. In particular, we consider matrices with Kronecker sum…
This work presents a new framework for approximating Caputo fractional derivatives (FDs) of any positive order using a shifted Gegenbauer pseudospectral (SGPS) method. By transforming the Caputo FD into a scaled integral of the…
Physics informed neural networks (PINNs) are nowadays used as efficient machine learning methods for solving differential equations. However, vanilla-PINNs fail to learn complex problems as ones involving stiff ordinary differential…
Physics-informed neural networks (PINNs) constitute a flexible deep learning approach for solving partial differential equations (PDEs), which model phenomena ranging from heat conduction to quantum mechanical systems. Despite their…
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…
There has been rapid progress recently on the application of deep networks to the solution of partial differential equations, collectively labelled as Physics Informed Neural Networks (PINNs). In this paper, we develop Physics Informed…
We enhance machine learning algorithms for learning model parameters in complex systems represented by ordinary differential equations (ODEs) with domain decomposition methods. The study evaluates the performance of two approaches, namely…