相关论文: A Physics-Informed Learning Framework to Solve the…

Physics-informed neural networks (PINNs) have emerged as a promising numerical method based on deep learning for modeling boundary value problems, showcasing promising results in various fields. In this work, we use PINNs to discretize…

This paper introduces the Hamilton-Jacobi-Bellman Proximal Policy Optimization (HJBPPO) algorithm into reinforcement learning. The Hamilton-Jacobi-Bellman (HJB) equation is used in control theory to evaluate the optimality of the value…

This paper introduces a framework based on physics-informed neural networks (PINNs) for addressing key challenges in nonlinear lattices, including solution approximation, bifurcation diagram construction, and linear stability analysis. We…

Physics-Informed Neural Networks (PINNs) have revolutionized solving differential equations by integrating physical laws into neural networks training. This paper explores PINNs for open-loop optimal control problems (OCPs) with incomplete…

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…

Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing…

We show that the physics-informed neural networks (PINNs), in combination with some recently developed discontinuity capturing neural networks, can be applied to solve optimal control problems subject to partial differential equations…

Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…

Computing optimal feedback controls for nonlinear systems generally requires solving Hamilton-Jacobi-Bellman (HJB) equations, which are notoriously difficult when the state dimension is large. Existing strategies for high-dimensional…

A physics informed neural network (PINN) incorporates the physics of a system by satisfying its boundary value problem through a neural network's loss function. The PINN approach has shown great success in approximating the map between the…

Physics-informed neural networks (PINNs) are an influential method of solving differential equations and estimating their parameters given data. However, since they make use of neural networks, they provide only a point estimate of…

A large number of magnetohydrodynamic (MHD) equilibrium calculations are often required for uncertainty quantification, optimization, and real-time diagnostic information, making MHD equilibrium codes vital to the field of plasma physics.…

Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding physical laws directly into neural network training. However, solving high-fidelity PDEs remains…

In this article, we propose a novel Stabilized Physics Informed Neural Networks method (SPINNs) for solving wave equations. In general, this method not only demonstrates theoretical convergence but also exhibits higher efficiency compared…

We implement physics-informed neural networks (PINNs) to solve the time-independent Schr\"odinger equation for three canonical one-dimensional quantum potentials: an infinite square well, a finite square well, and a finite barrier. The PINN…

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.…

We study physics-informed neural networks (PINNs) as numerical tools for the optimal control of semilinear partial differential equations. We first recall the classical direct and indirect viewpoints for optimal control of PDEs, and then…

Physics-informed neural networks (PINNs) impose known physical laws into the learning of deep neural networks, making sure they respect the physics of the process while decreasing the demand of labeled data. For systems represented by…

We use Physics-Informed Neural Networks (PINNs) to solve the discrete-time nonlinear observer state estimation problem. Integrated within a single-step exact observer linearization framework, the proposed PINN approach aims at learning a…

Physics-Informed Neural Networks (PINNs) have been widely used to obtain solutions to various physical phenomena modeled as Differential Equations. As PINNs are not naturally equipped with mechanisms for Uncertainty Quantification, some…