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This the text of a proceeding accepted for the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014). We present some results of an ongoing research on the controllability problem of an abstract bilinear…
In this paper, we introduce a model-based deep-learning approach to solve finite-horizon continuous-time stochastic control problems with jumps. We iteratively train two neural networks: one to represent the optimal policy and the other to…
The problem of quantum state preparation is one of the main challenges in achieving the quantum advantage. Furthermore, classically, for multi-level problems, our ability to solve the corresponding quantum optimal control problems is rather…
In this paper, we intend to present some already known results about the internal controllability of the linear and nonlinear Schr\"odinger equation. After presenting the basic properties of the equation, we give a self contained proof of…
Neural networks (NNs) can achieved high performance in various fields such as computer vision, and natural language processing. However, deploying NNs in resource-constrained safety-critical systems has challenges due to uncertainty in the…
Solving the time-dependent Schr\"odinger equation is an important application area for quantum algorithms. We consider Schr\"odinger's equation in the semi-classical regime. Here the solutions exhibit strong multiple-scale behavior due to a…
Model predictive control (MPC) provides a useful means for controlling systems with constraints, but suffers from the computational burden of repeatedly solving an optimization problem in real time. Offline (explicit) solutions for MPC…
Emerging reinforcement learning techniques using deep neural networks have shown great promise in control optimization. They harness non-local regularities of noisy control trajectories and facilitate transfer learning between tasks. To…
A promising approach to optimal control of nonlinear systems involves iteratively linearizing the system and solving an optimization problem at each time instant to determine the optimal control input. Since this approach relies on online…
In many areas, such as the physical sciences, life sciences, and finance, control approaches are used to achieve a desired goal in complex dynamical systems governed by differential equations. In this work we formulate the problem of…
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…
This paper develops algorithms for high-dimensional stochastic control problems based on deep learning and dynamic programming. Unlike classical approximate dynamic programming approaches, we first approximate the optimal policy by means of…
The configuration interaction approach provides a conceptually simple and powerful approach to solve the Schr\"odinger equation for realistic molecules and materials but is characterized by an unfavourable scaling, which strongly limits its…
We introduce the Schrodinger Neural Network (SNN), a principled architecture for conditional density estimation and uncertainty quantification inspired by quantum mechanics. The SNN maps each input to a normalized wave function on the…
In this paper, we propose a deep learning based approach to design online power control policies for large EH networks, which are often intractable stochastic control problems. In the proposed approach, for a given EH network, the optimal…
We propose a novel approach to solving input- and state-constrained parametric mixed-integer optimal control problems using Differentiable Predictive Control (DPC). Our approach follows the differentiable programming paradigm by learning an…
The manpower scheduling problem is a kind of critical combinational optimization problem. Researching solutions to scheduling problems can improve the efficiency of companies, hospitals, and other work units. This paper proposes a new model…
Controlling network systems has become a problem of paramount importance. In this paper, we consider a distributed linear-quadratic problem and propose the use of graph neural networks (GNNs) to parametrize and design a distributed…
Social science studies dealing with control in networks typically resort to heuristics or describing the static control distribution. Optimal policies, however, require interventions that optimize control over a socioeconomic network…
This paper introduces a novel deep-learning-based approach for numerical simulation of a time-evolving Schr\"odinger equation inspired by stochastic mechanics and generative diffusion models. Unlike existing approaches, which exhibit…