Related papers: Multi-Objective Loss Balancing in Physics-Informed…
Neural networks can be trained to solve partial differential equations (PDEs) by using the PDE residual as the loss function. This strategy is called "physics-informed neural networks" (PINNs), but it currently cannot produce high-accuracy…
Recent studies have demonstrated the success of deep learning in solving forward and inverse problems in engineering and scientific computing domains, such as physics-informed neural networks (PINNs). Source inversion problems under sparse…
Physics-Informed Neural Networks (PINNs) provide a powerful and general framework for solving Partial Differential Equations (PDEs) by embedding physical laws into loss functions. However, training PINNs is notoriously difficult due to the…
In machine learning and statistical modeling, the mean square or absolute error is commonly used as an error metric, also called a "loss function." While effective in reducing the average error, this approach may fail to address localized…
One of the biggest challenges in the optimization of micro-scale fluid transport phenomena is the prediction of unsteady fluid flow in the presence of rough channel walls. Even though the accuracy of available computational fluid dynamics…
Physics-Informed Neural Networks (PINNs) have been recognized as a mesh-free alternative to solve partial differential equations where physics information is incorporated. However, in dealing with problems characterized by high stiffness or…
This study introduces a computational approach leveraging Physics-Informed Neural Networks (PINNs) for the efficient computation of arterial blood flows, particularly focusing on solving the incompressible Navier-Stokes equations by using…
Physics-informed neural networks (PINNs) and their variants have been very popular in recent years as algorithms for the numerical simulation of both forward and inverse problems for partial differential equations. This article aims to…
Physics-informed neural networks (PINNs) provide a framework to build surrogate models for dynamical systems governed by differential equations. During the learning process, PINNs incorporate a physics-based regularization term within the…
Deep learning has been highly successful in some applications. Nevertheless, its use for solving partial differential equations (PDEs) has only been of recent interest with current state-of-the-art machine learning libraries, e.g.,…
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…
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…
Physics-informed neural networks (PINNs) are a newly emerging research frontier in machine learning, which incorporate certain physical laws that govern a given data set, e.g., those described by partial differential equations (PDEs), into…
Recent work in scientific machine learning has developed so-called physics-informed neural network (PINN) models. The typical approach is to incorporate physical domain knowledge as soft constraints on an empirical loss function and use…
Physics-informed neural networks (PINNs) offer a promising avenue for tackling both forward and inverse problems in partial differential equations (PDEs) by incorporating deep learning with fundamental physics principles. Despite their…
For multi-scale problems, the conventional physics-informed neural networks (PINNs) face some challenges in obtaining available predictions. In this paper, based on PINNs, we propose a practical deep learning framework for multi-scale…
Physics-informed neural networks (PINNs) are numerical solvers that embed all the physical information of a system into the loss function of a neural network. In this way the learned solution accounts for data (if available), the governing…
Solving partial differential equations (PDEs) with discontinuous solutions , such as shock waves in multiphase viscous flow in porous media , is critical for a wide range of scientific and engineering applications, as they represent sudden…
As an emerging technology in deep learning, physics-informed neural networks (PINNs) have been widely used to solve various partial differential equations (PDEs) in engineering. However, PDEs based on practical considerations contain…
Physics-informed neural networks (PINNs) can be used to solve partial differential equations (PDEs) and identify hidden variables by incorporating the governing equations into neural network training. In this study, we apply PINNs to the…