Related papers: Solving the wave equation with physics-informed de…
Deep learning models trained on finite data lack a complete understanding of the physical world. On the other hand, physics-informed neural networks (PINNs) are infused with such knowledge through the incorporation of mathematically…
Physics-informed neural networks (PINN) have achieved notable success in solving partial differential equations (PDE), yet solving the Navier-Stokes equations (NSE) with complex boundary conditions remains a challenging task. In this paper,…
We put forth two physics-informed neural network (PINN) schemes based on Miura transformations and the novelty of this research is the incorporation of Miura transformation constraints into neural networks to solve nonlinear PDEs. The most…
Machine learning and neural networks have advanced numerous research domains, but challenges such as large training data requirements and inconsistent model performance hinder their application in certain scientific problems. To overcome…
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 introduce an optimized physics-informed neural network (PINN) trained to solve the problem of identifying and characterizing a surface breaking crack in a metal plate. PINNs are neural networks that can combine data and physics in the…
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…
Recent developments in acoustic signal processing have seen the integration of deep learning methodologies, alongside the continued prominence of classical wave expansion-based approaches, particularly in sound field reconstruction.…
Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding physical laws into neural network training. However, traditional PINN models are typically designed…
In this study, we present and validate the predictive capability of the Physics-Informed Neural Networks (PINNs) methodology for solving a variety of engineering and biological dynamical systems governed by ordinary differential equations…
The concepts and techniques of physics-informed neural networks (PINNs) is studied and limitations are identified to make it efficient to approximate dynamical equations. Potential working research domains are explored for increasing the…
Numerical solutions to the equation for advection are determined using different finite-difference approximations and physics-informed neural networks (PINNs) under conditions that allow an analytical solution. Their accuracy is examined by…
The Vlasov-Poisson system is employed in its reduced form version (1D1V) as a test bed for the applicability of Physics Informed Neural Network (PINN) to the wave-particle resonance. Two examples are explored: the Landau damping and the…
Physics-informed neural networks (PINNs) provide a flexible and effective alternative for estimating seismic wavefield solutions due to their typical mesh-free and unsupervised features. However, their accuracy and training cost restrict…
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…
In recent years the study of deep learning for solving differential equations has grown substantially. The use of physics-informed neural networks (PINNs) and deep operator networks (DeepONets) have emerged as two of the most useful…
This paper employs physics-informed neural networks (PINNs) to solve Fisher's equation, a fundamental reaction-diffusion system with both simplicity and significance. The focus is on investigating Fisher's equation under conditions of large…
A physics-informed neural network (PINN) that combines deep learning with physics is studied to solve the nonlinear Schr\"odinger equation for learning nonlinear dynamics in fiber optics. We carry out a systematic investigation and…
Physics-Informed Neural Networks (PINNs) recast PDE solving as an optimisation problem in function space by minimising a residual-based objective, yet many applications require additional derivative-based relations that are just as…
The aim of this paper is to introduce a Mapping-based Hard-constrained Physics-Informed Neural Network (MH-PINN) for efficiently and accurately solving unbounded wave problems. First, we propose a coordinate mapping technique that…