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Despite the remarkable progress of physics-informed neural networks (PINNs) in scientific computing, they continue to face challenges when solving hydrodynamic problems with multiple discontinuities. In this work, we propose…
Physics-informed neural networks (PINNs) leverage neural-networks to find the solutions of partial differential equation (PDE)-constrained optimization problems with initial conditions and boundary conditions as soft constraints. These soft…
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…
Physics-informed neural networks (PINNs) have demonstrated promise as a framework for solving forward and inverse problems involving partial differential equations. Despite recent progress in the field, it remains challenging to quantify…
The solution of partial differential equations (PDES) on irregular domains has long been a subject of significant research interest. In this work, we present an approach utilizing physics-informed neural networks (PINNs) to achieve…
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…
This research explores neural network-based numerical approximation of two-dimensional convection-dominated singularly perturbed problems on square, circular, and elliptic domains. Singularly perturbed boundary value problems pose…
The simulation of power system dynamics poses a computationally expensive task. Considering the growing uncertainty of generation and demand patterns, thousands of scenarios need to be continuously assessed to ensure the safety of power…
Physics-informed neural networks (PINNs) hold the potential for supplementing the existing set of techniques for solving differential equations that emerge in the study of black hole quasinormal modes. The present research investigated them…
Physics-Informed Neural Networks (PINNs) serve as a flexible alternative for tackling forward and inverse problems in differential equations, displaying impressive advancements in diverse areas of applied mathematics. Despite integrating…
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…
Complex physical systems are often described by partial differential equations (PDEs) that depend on parameters such as the Reynolds number in fluid mechanics. In applications such as design optimization or uncertainty quantification,…
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 effective in solving integer-order partial differential equations (PDEs) based on scattered and noisy data. PINNs employ standard feedforward neural networks (NNs) with the PDEs explicitly…
Physics-Informed Neural Networks (PINNs) have recently emerged as a novel approach to simulate complex physical systems on the basis of both data observations and physical models. In this work, we investigate the use of PINNs for various…
The present work investigates the use of physics-informed neural networks (PINNs) for the 3D reconstruction of unsteady gravity currents from limited data. In the PINN context, the flow fields are reconstructed by training a neural network…
Physics informed neural networks (PINNs) require regularity of solutions of the underlying PDE to guarantee accurate approximation. Consequently, they may fail at approximating discontinuous solutions of PDEs such as nonlinear hyperbolic…
In this paper, a physics-informed multiresolution wavelet neural network (PIMWNN) method is proposed for solving partial differential equations (PDEs). This method uses the multiresolution wavelet neural network (MWNN) to approximate…
This paper proposes a new framework using physics-informed neural networks (PINNs) to simulate complex structural systems that consist of single and double beams based on Euler-Bernoulli and Timoshenko theory, where the double beams are…
Physics-Informed Neural Networks (PINNs) solve forward PDEs by minimizing residual losses from the governing equations with initial and boundary conditions, but they often struggle with discontinuities such as shocks. In contrast, finite…