Related papers: Physics-Informed Neural Networks for Transonic Flo…

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…

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…

The widespread use of neural networks across different scientific domains often involves constraining them to satisfy certain symmetries, conservation laws, or other domain knowledge. Such constraints are often imposed as soft penalties…

When modelling turbulent flows, it is often the case that information on the forcing terms or the boundary conditions is either not available or overly complicated and expensive to implement. Instead, some flow features, such as the mean…

We leverage Physics-Informed Neural Networks (PINNs) to learn solution functions of parametric Navier-Stokes Equations (NSE). Our proposed approach results in a feasible optimization problem setup that bypasses PINNs' limitations in…

This work concerns the application of physics-informed neural networks to the modeling and control of complex robotic systems. Achieving this goal required extending Physics Informed Neural Networks to handle non-conservative effects. We…

Physics-informed neural networks (PINNs) demonstrate promising potential in parameterized engineering turbulence optimization problems but face challenges, such as high data requirements and low computational accuracy when applied to…

We establish the existence, stability, and asymptotic behavior of transonic flows with a transonic shock past a curved wedge for the steady full Euler equations in an important physical regime, which form a nonlinear system of…

We propose a new data-driven method to learn the dynamics of an unknown hyperbolic system of conservation laws using deep neural networks. Inspired by classical methods in numerical conservation laws, we develop a new conservative form…

Physics-informed neural networks have emerged as a prominent new method for solving differential equations. While conceptually straightforward, they often suffer training difficulties that lead to relatively large discretization errors or…

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 numerical simulation and optimization of technical systems described by partial differential equations is expensive, especially in multi-query scenarios in which the underlying equations have to be solved for different parameters. A…

In the realm of computational fluid dynamics, traditional numerical methods, which heavily rely on discretization, typically necessitate the formulation of partial differential equations (PDEs) in conservative form to accurately capture…

FourNetFlows, the abbreviation of Fourier Neural Network for Airfoil Flows, is an efficient model that provides quick and accurate predictions of steady airfoil flows. We choose the Fourier Neural Operator (FNO) as the backbone architecture…

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,…

The use of deep learning methods for modeling fluid flow has drawn a lot of attention in the past few years. In situations where conventional numerical approaches can be computationally expensive, these techniques have shown promise in…

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…

Due to the limited accuracy of 4D Magnetic Resonance Imaging (MRI) in identifying hemodynamics in cardiovascular diseases, the challenges in obtaining patient-specific flow boundary conditions, and the computationally demanding and…

In this work, physics-informed neural networks are applied to incompressible two-phase flow problems. We investigate the forward problem, where the governing equations are solved from initial and boundary conditions, as well as the inverse…

Coupling physics with machine learning models has shown great potential for solving fluid dynamics problems governed by partial differential equations. However, conventional methods, such as physics-informed neural networks, often suffer…