Related papers: Comparing Physics-Informed and Neural ODE Approach…
In this paper, we propose a refinement strategy to the well-known Physics-Informed Neural Networks (PINNs) for solving partial differential equations (PDEs) based on the concept of Optimal Transport (OT). Conventional black-box PINNs…
A physics-informed neural network (PINN) is used to produce a variety of self-trapped necklace solutions of the (2+1)-dimensional nonlinear Schr\"{o}dinger/Gross-Pitaevskii equation. We elaborate the analysis for the existence and evolution…
The Neural Tangent Kernel (NTK) viewpoint is widely employed to analyze the training dynamics of overparameterized Physics-Informed Neural Networks (PINNs). However, unlike the case of linear Partial Differential Equations (PDEs), we show…
Physics-informed neural networks (PINNs) have shown promising potential for solving partial differential equations (PDEs) using deep learning. However, PINNs face training difficulties for evolutionary PDEs, particularly for dynamical…
Physics-Informed Neural Networks (PINNs) are a class of deep neural networks that are trained, using automatic differentiation, to compute the response of systems governed by partial differential equations (PDEs). The training of PINNs is…
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…
We present a novel numerical approach aiming at computing equilibria and dynamics structures of magnetized plasmas in coronal environments. A technique based on the use of neural networks that integrates the partial differential equations…
As a typical application of deep learning, physics-informed neural network (PINN) {has been} successfully used to find numerical solutions of partial differential equations (PDEs), but how to improve the limited accuracy is still a great…
The accurate representation of numerous physical, chemical, and biological processes relies heavily on differential equations (DEs), particularly nonlinear differential equations (NDEs). While understanding these complex systems…
Machine learning techniques have proven to be effective in addressing the structure of atomic nuclei. Physics$-$Informed Neural Networks (PINNs) are a promising machine learning technique suitable for solving integro-differential problems…
Physics-Informed Neural Networks have emerged as a promising methodology for solving PDEs, gaining significant attention in computer science and various physics-related fields. Despite being demonstrated the ability to incorporate the…
Model Predictive Control (MPC) is a state-of-the-art (SOTA) control technique which requires solving hard constrained optimization problems iteratively. For uncertain dynamics, analytical model based robust MPC imposes additional…
The research in Artificial Intelligence methods with potential applications in science has become an essential task in the scientific community last years. Physics Informed Neural Networks (PINNs) is one of this methods and represent a…
Physics-informed Neural Networks (PINNs) have recently emerged as a principled way to include prior physical knowledge in form of partial differential equations (PDEs) into neural networks. Although PINNs are generally viewed as mesh-free,…
Several forms for constructing novel physics-informed neural-networks (PINN) for the solution of partial-differential-algebraic equations based on derivative operator splitting are proposed, using the nonlinear Kirchhoff rod as a prototype…
Physics-informed neural networks (PINNs) [4, 10] are an approach for solving boundary value problems based on differential equations (PDEs). The key idea of PINNs is to use a neural network to approximate the solution to the PDE and to…
In the past, we have presented a systematic computational framework for analyzing self-similar and traveling wave dynamics in nonlinear partial differential equations (PDEs) by dynamically factoring out continuous symmetries such as…
Physics-informed neural networks (PINNs) approximate solutions of partial differential equations (PDEs) by embedding physical laws into the loss function. In parameterized PDE families, variations in coefficients or boundary/initial…
The use of deep learning methods in scientific computing represents a potential paradigm shift in engineering problem solving. One of the most prominent developments is Physics-Informed Neural Networks (PINNs), in which neural networks are…
Physics-informed neural networks (PINNs) have received significant attention as a unified framework for forward, inverse, and surrogate modeling of problems governed by partial differential equations (PDEs). Training PINNs for forward…