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Solving the two-dimensional shallow water equations is a fundamental problem in flood simulation technology. In recent years, physics-informed neural networks (PINNs) have emerged as a novel methodology for addressing this problem. Given…
Physics-informed neural networks (PINNs) is an emerging category of neural networks which can be trained to solve supervised learning tasks while taking into consideration given laws of physics described by general nonlinear partial…
Physics-informed neural networks (PINNs) offer a powerful framework for seismic wavefield modeling, yet they typically require time-consuming retraining when applied to different velocity models. Moreover, their training can suffer from…
Given the facts of the extensiveness of multi-material diffusion problems and the inability of the standard PINN(Physics-Informed Neural Networks) method for such problems, in this paper we present a novel PINN method that can accurately…
Singularly perturbed problems are known to have solutions with steep boundary layers that are hard to resolve numerically. Traditional numerical methods, such as Finite Difference Methods (FDMs), require a refined mesh to obtain stable and…
We develop a physics-informed neural networks (PINNs) framework for the inverse scattering problem in nuclear physics and apply it to the $P_{3/2}$ partial wave of neutron-alpha elastic scattering. The radial potential is represented by a…
Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional…
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 machine learning models have recently emerged with some interesting and unique features that can be applied to reservoir engineering. In particular, physics-informed neural networks (PINN) leverage the fact that neural…
Turbulence remains a problem that is yet to be fully understood, with experimental and numerical studies aiming to fully characterise the statistical properties of turbulent flows. Such studies require huge amount of resources to capture,…
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…
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…
The accurate determination of electron properties is fundamental to low-temperature plasma simulations, necessitating precise solutions to the spatially inhomogeneous electron Boltzmann equation (EBE). This work explores the use of…
This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the…
A physics-informed neural network (PINN), which has been recently proposed by Raissi et al [J. Comp. Phys. 378, pp. 686-707 (2019)], is applied to the partial differential equation (PDE) of liquid film flows. The PDE considered is the time…
Large-scale dynamics of the oceans and the atmosphere are governed by primitive equations (PEs). Due to the nonlinearity and nonlocality, the numerical study of the PEs is generally challenging. Neural networks have been shown to be a…
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…
Non-equilibrium chemistry is a key process in the study of the InterStellar Medium (ISM), in particular the formation of molecular clouds and thus stars. However, computationally it is among the most difficult tasks to include in…
A physics informed neural network (PINN) incorporates the physics of a system by satisfying its boundary value problem through a neural network's loss function. The PINN approach has shown great success in approximating the map between the…
Parameter estimation remains a challenging task across many areas of engineering. Because data acquisition can often be costly, limited, or prone to inaccuracies (noise, uncertainty) it is crucial to identify sensor configurations that…