相关论文: Value Approximation for Two-Player General-Sum Dif…

We propose a novel numerical method for high dimensional Hamilton--Jacobi--Bellman (HJB) type elliptic partial differential equations (PDEs). The HJB PDEs, reformulated as optimal control problems, are tackled by the actor-critic framework…

Hamilton-Jacobi (HJ) reachability analysis is an important formal verification method for guaranteeing performance and safety properties of dynamical control systems. Its advantages include compatibility with general nonlinear system…

Physics-informed neural networks (PINN) have achieved notable success in solving partial differential equations (PDE), yet solving the Navier-Stokes equations (NSE) with complex boundary conditions remains a challenging task. In this paper,…

Physics-informed neural networks (PINNs) have attracted significant attention for solving partial differential equations (PDEs) in recent years because they alleviate the curse of dimensionality that appears in traditional methods. However,…

State-of-the-art methods for solving 2-player zero-sum imperfect information games rely on linear programming or regret minimization, though not on dynamic programming (DP) or heuristic search (HS), while the latter are often at the core of…

The use of deep learning methods in scientific computing represents a potential paradigm shift in engineering problem solving. One of the most prominent developments is Physics-Informed Neural Networks (PINNs), in which neural networks are…

Hamilton-Jacobi partial differential equations (HJ PDEs) have deep connections with a wide range of fields, including optimal control, differential games, and imaging sciences. By considering the time variable to be a higher dimensional…

Hamilton-Jacobi partial differential equations (HJ PDEs) play a central role in many applications such as economics, physics, and engineering. These equations describe the evolution of a value function which encodes valuable information…

Physics-informed neural networks (PINNs) have emerged as a prominent approach for solving partial differential equations (PDEs) by minimizing a combined loss function that incorporates both boundary loss and PDE residual loss. Despite their…

Physics-informed neural solvers offer a promising route to model-based reinforcement learning in continuous time, where optimal feedback synthesis is governed by Hamilton--Jacobi--Bellman (HJB) equations. Practical implementations often…

In the present paper, we study a two-player zero-sum deterministic differential game with both players adopting impulse controls, in infinite time horizon, under rather weak assumptions on the cost functions. We prove by means of the…

The recently developed physics-informed machine learning has made great progress for solving nonlinear partial differential equations (PDEs), however, it may fail to provide reasonable approximations to the PDEs with discontinuous…

Hamilton-Jacobi Reachability (HJR) is a popular method for analyzing the liveness and safety of a dynamical system with bounded control and disturbance. The corresponding HJ value function offers a robust controller and characterizes the…

We consider the problem of planning trajectories for a group of $N$ vehicles, each aiming to reach its own target set while avoiding danger zones of other vehicles. The analysis of problems like this is extremely important practically,…

Hamilton-Jacobi (HJ) reachability analysis is a widely used method for ensuring the safety of robotic systems. Traditional approaches compute reachable sets by numerically solving an HJ Partial Differential Equation (PDE) over a grid, which…

Physics-informed neural networks (PINNs) have emerged as a powerful approach for solving partial differential equations (PDEs) by training neural networks with loss functions that incorporate physical constraints. In this work, we introduce…

Learning the solution of partial differential equations (PDEs) with a neural network is an attractive alternative to traditional solvers due to its elegance, greater flexibility and the ease of incorporating observed data. However, training…

Physics-Informed Neural Networks (PINNs) have proven effective in solving partial differential equations (PDEs), especially when some data are available by seamlessly blending data and physics. However, extending PINNs to high-dimensional…

This paper explores the difficulties in solving partial differential equations (PDEs) using physics-informed neural networks (PINNs). PINNs use physics as a regularization term in the objective function. However, a drawback of this approach…

In this paper, we make the first attempt to apply the boundary integrated neural networks (BINNs) for the numerical solution of two-dimensional (2D) elastostatic and piezoelectric problems. BINNs combine artificial neural networks with the…