Related papers: Singular Layer Physics-Informed Neural Network Met…
We present our progress on the application of physics informed deep learning to reservoir simulation problems. The model is a neural network that is jointly trained to respect governing physical laws and match boundary conditions. The…
In this paper, we numerically examine the precision challenges that emerge in automatic differentiation and numerical integration in various tasks now tackled by physics-informed neural networks (PINNs). Specifically, we illustrate how…
We revisit the original approach of using deep learning and neural networks to solve differential equations by incorporating the knowledge of the equation. This is done by adding a dedicated term to the loss function during the optimization…
A method for solving elasticity problems based on separable physics-informed neural networks (SPINN) in conjunction with the deep energy method (DEM) is presented. Numerical experiments have been carried out for a number of problems showing…
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…
The prohibitive cost and low fidelity of experimental data in industry scale thermofluid systems limit the usefulness of pure data-driven machine learning methods. Physics-informed neural networks (PINN) strive to overcome this by embedding…
Form-finding of unilateral membrane structures is commonly addressed by solving equilibrium equations with Finite Element Methods (FEMs). This paper investigates Physics-Informed Neural Networks (PINNs) as an alternative, where the…
Physics-informed neural networks (PINNs) represent a significant advancement in scientific machine learning by integrating fundamental physical laws into their architecture through loss functions. PINNs have been successfully applied to…
In this work, we present the physics-informed neural network (PINN) model applied particularly to dynamic problems in solid mechanics. We focus on forward and inverse problems. Particularly, we show how a PINN model can be used efficiently…
Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current state-of-the-art machine learning libraries, e.g.,…
Recently, physics informed neural networks (PINNs) have been explored extensively for solving various forward and inverse problems and facilitating querying applications in fluid mechanics applications. However, work on PINNs for unsteady…
Physics-informed neural networks (PINNs) employed in fluid mechanics deal primarily with stationary boundaries. This hinders the capability to address a wide range of flow problems involving moving bodies. To this end, we propose a novel…
In recent years, Physics-Informed Neural Networks (PINNs) have become a representative method for solving partial differential equations (PDEs) with neural networks. PINNs provide a novel approach to solving PDEs through optimization…
Physics-informed neural networks (PINNs) have recently emerged as promising data-driven PDE solvers showing encouraging results on various PDEs. However, there is a fundamental limitation of training PINNs to solve multi-dimensional PDEs…
Mathematical models in neural networks are powerful tools for solving complex differential equations and optimizing their parameters; that is, solving the forward and inverse problems, respectively. A forward problem predicts the output of…
We investigate the use of Physics-Informed Neural Networks (PINNs) for solving the wave equation. Whilst PINNs have been successfully applied across many physical systems, the wave equation presents unique challenges due to the multi-scale,…
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…
Physics-informed neural networks (PINNs) are an influential method of solving differential equations and estimating their parameters given data. However, since they make use of neural networks, they provide only a point estimate of…
In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a powerful and robust framework for solving nonlinear differential equations across a wide range of scientific and engineering disciplines, including biology,…
Physics-informed neural networks (PINNs) have attracted attention as an alternative approach to solve partial differential equations using a deep neural network (DNN). Their simplicity and capability allow them to solve inverse problems for…