Related papers: BINN: A deep learning approach for computational m…

Since their advent nearly a decade ago, physics-informed neural networks (PINNs) have been studied extensively as a novel technique for solving forward and inverse problems in physics and engineering. The neural network discretization of…

We propose characteristics-informed neural networks (CINN), a simple and efficient machine learning approach for solving forward and inverse problems involving hyperbolic PDEs. Like physics-informed neural networks (PINN), CINN is a…

Over the past years, inverse problems in partial differential equations have garnered increasing interest among scientists and engineers. However, due to the lack of conventional stability, nonlinearity and non-convexity, these problems are…

A Physics-Informed Neural Network (PINN) provides a distinct advantage by synergizing neural networks' capabilities with the problem's governing physical laws. In this study, we introduce an innovative approach for solving seepage problems…

Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical…

Reconstructing unknown external source functions is an important perception capability for a large range of robotics domains including manipulation, aerial, and underwater robotics. In this work, we propose a Physics-Informed Neural Network…

Data-driven modeling of spatiotemporal physical processes with general deep learning methods is a highly challenging task. It is further exacerbated by the limited availability of data, leading to poor generalizations in standard neural…

A method is presented that allows to reduce a problem described by differential equations with initial and boundary conditions to the problem described only by differential equations. The advantage of using the modified problem for…

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 (PINNs) show great advantages in solving partial differential equations. In this paper, we for the first time propose to study conformable time fractional diffusion equations by using PINNs. By solving the…

In this work, we have applied physics-informed neural networks (PINN) for solving mesh deformation problems. We used the collocation PINN method to capture the new positions of the vertex nodes while preserving the connectivity information.…

Recently, physics-informed neural networks (PINNs) have offered a powerful new paradigm for solving problems relating to differential equations. Compared to classical numerical methods PINNs have several advantages, for example their…

Physics-informed neural networks have attracted significant attention in scientific machine learning for their capability to solve forward and inverse problems governed by partial differential equations. However, the accuracy of PINN…

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…

In this study, we propose a new numerical scheme for physics-informed neural networks (PINNs) that enables precise and inexpensive solution for partial differential equations (PDEs) in case of arbitrary geometries while strictly enforcing…

Variational inequalities are widely applied in mechanical engineering, fluid penetration, transportation, and other fields. In this paper, a Deep Ritz method based on Physics-Informed Neural Networks (PINNs) is proposed to enhance the…

We introduce conditional PINNs (physics informed neural networks) for estimating the solution of classes of eigenvalue problems. The concept of PINNs is expanded to learn not only the solution of one particular differential equation but the…

This paper proposes a novel neural network framework, denoted as spectral integrated neural networks (SINNs), for resolving three-dimensional forward and inverse dynamic problems. In the SINNs, the spectral integration method is applied to…

Physics-Informed Neural Networks (PINNs) have been widely used to obtain solutions to various physical phenomena modeled as Differential Equations. As PINNs are not naturally equipped with mechanisms for Uncertainty Quantification, some…

Physically informed neural networks (PINNs) are a promising emerging method for solving differential equations. As in many other deep learning approaches, the choice of PINN design and training protocol requires careful craftsmanship. Here,…