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Physics-informed Neural Networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be…
This paper considers an insurance surplus process modeled by a spectrally negative L\'{e}vy process. Instead of the time of ruin in the traditional setting, we apply the time of drawdown as the risk indicator in this paper. We study the…
Differential equations are involved in modeling many engineering problems. Many efforts have been devoted to solving differential equations. Due to the flexibility of neural networks, Physics Informed Neural Networks (PINNs) have recently…
In this paper, we numerically examine the precision challenges that emerge in automatic differentiation and numerical integration in various tasks now tackled by physics-informed neural networks (PINNs). Specifically, we illustrate how…
The use of neural networks to solve differential equations, as an alternative to traditional numerical solvers, has increased recently. However, error bounds for the obtained solutions have only been developed for certain equations. In this…
Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…
Physics-Informed Neural Networks (PINNs) are a class of deep learning models aiming to approximate solutions of PDEs by training neural networks to minimize the residual of the equation. Focusing on non-equilibrium fluctuating systems, we…
This paper investigates a numerical solution of Allen-Cahn equation with constant and degenerate mobility, with polynomial and logarithmic energy functionals, with deterministic and random initial functions, and with advective term in one,…
The simulation of power system dynamics poses a computationally expensive task. Considering the growing uncertainty of generation and demand patterns, thousands of scenarios need to be continuously assessed to ensure the safety of power…
Although physics-informed neural networks (PINNs) have shown great potential in dealing with nonlinear partial differential equations (PDEs), it is common that PINNs will suffer from the problem of insufficient precision or obtaining…
Fractional physics-informed neural networks (fPINNs) have been successfully introduced in [Pang, Lu and Karniadakis, SIAM J. Sci. Comput. 41 (2019) A2603-A2626], which observe relative errors of $10^{-3} \, \sim \, 10^{-4}$ for 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) represent a groundbreaking paradigm in scientific computing, seamlessly integrating the robust framework of deep learning with fundamental physical laws. This paper meticulously applies the standard…
Addressing high-dimensional partial differential equations to derive effective actions within the functional renormalization group is formidable, especially when considering various field configurations, including inhomogeneous states, even…
In this paper, we developed a new PINN-based model to predict the potential of point-charged particles surrounded by conductive walls. As a result of the proposed physics-informed neural network model, the mean square error and R2 score are…
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…
Physics-Informed Neural Networks (PINNs) have become a promising research direction in the field of solving Partial Differential Equations (PDEs). Dealing with singular perturbation problems continues to be a difficult challenge in the…
The physics-informed neural network (PINN) is effective in solving the partial differential equation (PDE) by capturing the physics constraints as a part of the training loss function through the Automatic Differentiation (AD). This study…
We propose Gradient Informed Neural Networks (GradINNs), a methodology inspired by Physics Informed Neural Networks (PINNs) that can be used to efficiently approximate a wide range of physical systems for which the underlying governing…
This paper employs physics-informed neural networks (PINNs) to solve Fisher's equation, a fundamental reaction-diffusion system with both simplicity and significance. The focus is on investigating Fisher's equation under conditions of large…