Related papers: Physics-Informed Neural Networks for Parametric Co…

Data assimilation for parameter and state estimation in subsurface transport problems remains a significant challenge due to the sparsity of measurements, the heterogeneity of porous media, and the high computational cost of forward…

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…

We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…

Fluid flows are governed by the nonlinear Navier-Stokes equations, which can manifest multiscale dynamics even from predictable initial conditions. Predicting such phenomena remains a formidable challenge in scientific machine learning,…

Solving partial differential equations (PDEs) is an important yet challenging task in fluid mechanics. In this study, we embed an improved Fourier series into neural networks and propose a physics-informed Fourier basis neural network…

Simulating discontinuities is a long standing problem especially for shock waves with strong nonlinear feather. Despite being a promising method, the recently developed physics-informed neural network (PINN) is still weak for calculating…

In this paper, we train turbulence models based on convolutional neural networks. These learned turbulence models improve under-resolved low resolution solutions to the incompressible Navier-Stokes equations at simulation time. Our study…

We introduce a novel artificial compressibility technique to approximate the incompressible Navier-Stokes equations with variable fluid properties such as density and dynamical viscosity. The proposed scheme used the couple pressure and…

Multi-scale, multi-fidelity numerical simulations form the pillar of scientific applications related to numerically modeling fluids. However, simulating the fluid behavior characterized by the non-linear Navier Stokes equations are often…

We propose Gauss-Newton's method in function space for the solution of the Navier-Stokes equations in the physics-informed neural network (PINN) framework. Upon discretization, this yields a natural gradient method that provably mimics the…

Volume-resolving imaging techniques are rapidly advancing progress in experimental fluid mechanics. However, reconstructing the full and structured Eulerian velocity and pressure fields from sparse and noisy particle tracks obtained…

Physics-Informed Neural Networks (PINNs) offer a powerful paradigm for flow reconstruction, seamlessly integrating sparse velocity measurements with the governing Navier-Stokes equations to recover complete velocity and latent pressure…

Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…

Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…

In many computational problems in engineering and science, function or model differentiation is essential, but also integration is needed. An important class of computational problems include so-called integro-differential equations which…

A constructive numerical approximation of the two-dimensional unsteady stochastic Navier-Stokes equations of an incompressible fluid is proposed via a pseudo-compressibility technique involving a parameter $\epsilon$. Space and time are…

This work proposes a wavelet-based physics-informed quantum neural network framework to efficiently address multiscale partial differential equations that involve sharp gradients, stiffness, rapid local variations, and highly oscillatory…

We describe a Physics-Informed Neural Network (PINN) that simulates the flow induced by the astronomical tide in a synthetic port channel, with dimensions based on the Santos - S\~ao Vicente - Bertioga Estuarine System. PINN models aim to…

Physics-informed neural networks (NN) are an emerging technique to improve spatial resolution and enforce physical consistency of data from physics models or satellite observations. A super-resolution (SR) technique is explored to…

Recently, physics-informed neural networks (PINNs) have emerged as a flexible and promising application of deep learning to partial differential equations in the physical sciences. While offering strong performance and competitive inference…