Related papers: Initialization-enhanced Physics-Informed Neural Ne…

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…

Ultrafast optics is driven by a myriad of complex nonlinear dynamics. The ubiquitous presence of governing equations in the form of partial integro-differential equations (PIDE) necessitates the need for advanced computational tools to…

The strongly-constrained physics-informed neural network (SCPINN) is proposed by adding the information of compound derivative embedded into the soft-constraint of physics-informed neural network(PINN). It is used to predict nonlinear…

This study explores the potential of physics-informed neural networks (PINNs) for the realization of digital twins (DT) from various perspectives. First, various adaptive sampling approaches for collocation points are investigated to verify…

This paper proposes a meshless deep learning algorithm, enriched physics-informed neural networks (EPINNs), to solve dynamic Poisson-Nernst-Planck (PNP) equations with strong coupling and nonlinear characteristics. The EPINNs takes the…

In this work, we develop interface-gated physics-informed neural networks (IG-PINNs) to solve elliptic interface equations. In IG-PINNs, we use a fully connected neural network to capture the smooth behavior across the entire domain. In…

In this paper, we develop a physics-informed neural network (PINN) model for parabolic problems with a sharply perturbed initial condition. As an example of a parabolic problem, we consider the advection-dispersion equation (ADE) with a…

Recently, there has been growing interest in using physics-informed neural networks (PINNs) to solve differential equations. However, the preservation of structure, such as energy and stability, in a suitable manner has yet to be…

Physics-informed neural networks (PINNs) are effective in solving integer-order partial differential equations (PDEs) based on scattered and noisy data. PINNs employ standard feedforward neural networks (NNs) with the PDEs explicitly…

Physics-informed neural networks (PINNs) have recently received much attention due to their capabilities in solving both forward and inverse problems. For training a deep neural network associated with a PINN, one typically constructs a…

Physics-informed neural networks have gained growing interest. Specifically, they are used to solve partial differential equations governing several physical phenomena. However, physics-informed neural network models suffer from several…

Physics-Informed Neural Networks (PINNs) often suffer from slow convergence, training instability, and reduced accuracy on challenging partial differential equations due to the anisotropic and rapidly varying geometry of their loss…

For decades, solutions to regional scale landslide prediction have mostly relied on data-driven models, by definition, disconnected from the physics of the failure mechanism. The success and spread of such tools came from the ability to…

We present an application of Physics-Informed Neural Networks to handle MultiPhase-Field simulations of microstructure evolution. It has been showcased that a combination of optimization techniques extended and adapted from the PINNs…

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…

With growing investigations into solving partial differential equations by physics-informed neural networks (PINNs), more accurate and efficient PINNs are required to meet the practical demands of scientific computing. One bottleneck of…

We introduce Physics Informed Symbolic Networks (PISN) which utilize physics-informed loss to obtain a symbolic solution for a system of Partial Differential Equations (PDE). Given a context-free grammar to describe the language of symbolic…

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…

The present study investigates the dynamics of nonlocal beams by establishing a consistent stress-driven integral elastic using the Physics-Informed Neural Network (PINN) approach. Specifically, a PINN is developed to compute the first…

The integration of physics-based knowledge with machine learning models is increasingly shaping the monitoring, diagnostics, and prognostics of electrical transformers. In this two-part series, the first paper introduced the foundations of…