Related papers: Neural Hamiltonian Operator

Neural networks have been applied to control problems, typically by combining data, differential equation residuals, and objective costs in the training loss or by incorporating auxiliary architectural components. Instead, we propose a…

Fourier neural operators (FNOs) are a recently introduced neural network architecture for learning solution operators of partial differential equations (PDEs), which have been shown to perform significantly better than comparable deep…

Time-periodic quantum systems exhibit a rich variety of far-from-equilibrium phenomena and serve as ideal platforms for quantum engineering and control. However, simulating their dynamics with conventional numerical methods remains…

In this paper, we propose a martingale-based neural network, SOC-MartNet, for solving high-dimensional Hamilton-Jacobi-Bellman (HJB) equations where no explicit expression is needed for the infimum of the Hamiltonian, $\inf_{u \in U}…

Solving constrained nonlinear optimization problems (CNLPs) is a longstanding problem that arises in various fields, e.g., economics, computer science, and engineering. We propose optimization-informed neural networks (OINN), a deep…

We show that the problem of finding an optimal stochastic 'blind' controller in a Markov decision process is an NP-hard problem. The corresponding decision problem is NP-hard, in PSPACE, and SQRT-SUM-hard, hence placing it in NP would imply…

Solving cell problems in homogenization is hard, and available deep-learning frameworks fail to match the speed and generality of traditional computational frameworks. More to the point, it is generally unclear what to expect of…

Bayesian Optimization (BO) is a widely used approach for blackbox optimization that leverages a Gaussian process (GP) model and an acquisition function to guide future sampling. While effective in low-dimensional settings, BO faces…

We are interested in optimally driving a dynamical system that can be influenced by exogenous noises. This is generally called a Stochastic Optimal Control (SOC) problem and the Dynamic Programming (DP) principle is the natural way of…

The Koopman operator has emerged as a powerful tool for the analysis of nonlinear dynamical systems as it provides coordinate transformations to globally linearize the dynamics. While recent deep learning approaches have been useful in…

Mathematical solvers use parametrized Optimization Problems (OPs) as inputs to yield optimal decisions. In many real-world settings, some of these parameters are unknown or uncertain. Recent research focuses on predicting the value of these…

Neural operators have emerged as powerful deep learning frameworks for approximating solution operators of parameterized partial differential equations (PDE). However, current methods predominantly rely on multilayer perceptrons (MLPs) for…

Although there is a substantial body of literature on control and optimization problems for parabolic and hyperbolic systems, the specific problem of controlling and optimizing the coefficients of the associated operators within such…

A challenging problem in decentralized optimization is to develop algorithms with fast convergence on random and time varying topologies under unreliable and bandwidth-constrained communication network. This paper studies a stochastic…

This paper extends the Model Predictive Static Programming (MPSP) framework for nonlinear systems evolving on Euclidean spaces to simple mechanical systems evolving on Lie groups. Classical optimal control approaches based on Pontryagin's…

Efficient algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the curse of dimensionality. We extend the forward-backward stochastic neural networks…

This paper addresses the problem of robust stabilization for linear hyperbolic Partial Differential Equations (PDEs) with Markov-jumping parameter uncertainty. We consider a 2 x 2 heterogeneous hyperbolic PDE and propose a control law using…

Solving Singularly Perturbed Differential Equations (SPDEs) poses computational challenges arising from the rapid transitions in their solutions within thin regions. The effectiveness of deep learning in addressing differential equations…

Neural operator learning directly constructs the mapping relationship from the equation parameter space to the solution space, enabling efficient direct inference in practical applications without the need for repeated solution of partial…

General-sum differential games can approximate values solved by Hamilton-Jacobi-Isaacs (HJI) equations for efficient inference when information is incomplete. However, solving such games through conventional methods encounters the curse of…