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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…

Physics-informed neural networks (PINNs) are a promising approach for solving partial differential equations (PDEs). Their training, however, is often difficult because multiple loss terms induced by PDE residuals and boundary or initial…

Motivated by recent research on Physics-Informed Neural Networks (PINNs), we make the first attempt to introduce the PINNs for numerical simulation of the elliptic Partial Differential Equations (PDEs) on 3D manifolds. PINNs are one of the…

Recent works have shown that deep neural networks can be employed to solve partial differential equations, giving rise to the framework of physics informed neural networks. We introduce a generalization for these methods that manifests as a…

The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…

In this paper, we introduce cell-average based neural network (CANN) method to solve high-dimensional parabolic partial differential equations. The method is based on the integral or weak formulation of partial differential equations. A…

Neural networks can be trained to solve partial differential equations (PDEs) by using the PDE residual as the loss function. This strategy is called "physics-informed neural networks" (PINNs), but it currently cannot produce high-accuracy…

The neural network method of solving differential equations is used to approximate the electric potential and corresponding electric field in the slit-well microfluidic device. The device's geometry is non-convex, making this a challenging…

In this paper, a new deep-learning architecture for solving the non-linear Falkner-Skan equation is proposed. Using Legendre and Chebyshev neural blocks, this approach shows how orthogonal polynomials can be used in neural networks to…

We introduce a new approach for solving forward systems of differential equations using a combination of splitting methods and physics-informed neural networks (PINNs). The proposed method, splitting PINN, effectively addresses the…

We propose a new semi-analytic physics informed neural network (PINN) to solve singularly perturbed boundary value problems. The PINN is a scientific machine learning framework that offers a promising perspective for finding numerical…

Ordinary and partial differential equations (DE) are used extensively in scientific and mathematical domains to model physical systems. Current literature has focused primarily on deep neural network (DNN) based methods for solving a…

Neural operators have emerged as powerful deep learning frameworks for approximating solution operators of parameterized partial differential equations (PDE). However, current methods predominantly rely on multilayer perceptrons (MLPs) for…

Nonlinear differential equations are challenging to solve numerically and are important to understanding the dynamics of many physical systems. Deep neural networks have been applied to help alleviate the computational cost that is…

Solving differential equations efficiently and accurately sits at the heart of progress in many areas of scientific research, from classical dynamical systems to quantum mechanics. There is a surge of interest in using Physics-Informed…

Solving Singularly Perturbed Differential Equations (SPDEs) presents challenges due to the rapid change of their solutions at the boundary layer. In this manuscript, We propose Asymptotic Physics-Informed Neural Networks (ASPINN), a…

We propose a method combining boundary integral equations and neural networks (BINet) to solve partial differential equations (PDEs) in both bounded and unbounded domains. Unlike existing solutions that directly operate over original PDEs,…

In this work, we propose a learning method for solving the linear transport equation under the diffusive scaling. Due to the multiscale nature of our model equation, the model is challenging to solve by using conventional methods. We employ…

Partial Differential Equations (PDEs) are integral to modeling many scientific and engineering problems. Physics-informed Neural Networks (PINNs) have emerged as promising tools for solving PDEs by embedding governing equations into the…

We propose a two-scale neural network method for solving partial differential equations (PDEs) with small parameters using physics-informed neural networks (PINNs). We directly incorporate the small parameters into the architecture of…