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In this letter, motivated by the question that whether the empirical fitting of data by neural network can yield the same structure of physical laws, we apply the neural network to a simple quantum mechanical two-body scattering problem…

Computational Physics · Physics 2018-08-08 Yadong Wu , Pengfei Zhang , Huitao Shen , Hui Zhai

In this work, we use an explainable convolutional neural network (NLS-Net) to solve an inverse problem of the nonlinear Schr\"odinger equation, which is widely used in fiber-optic communications. The landscape and minimizers of the…

Numerical Analysis · Mathematics 2021-07-20 Yiran Wang , Zhen Li

Robust and high-precision quantum control is extremely important but challenging for the functionization of scalable quantum computation. In this paper, we show that this hard problem can be translated to a supervised machine learning task…

Quantum Physics · Physics 2019-04-24 Re-Bing Wu , Haijin Ding , Daoyi Dong , Xiaoting Wang

We address the problem of reshaping light in the Schr\"odinger optics regime from the perspective of optimal control theory. In technological applications, Schr\"odinger optics is often used to model a slowly-varying amplitude of a…

Optimization and Control · Mathematics 2022-05-04 Jimmie Adriazola , Roy H. Goodman

Stochastic control problems with delay are challenging due to the path-dependent feature of the system and thus its intrinsic high dimensions. In this paper, we propose and systematically study deep neural networks-based algorithms to solve…

Optimization and Control · Mathematics 2021-06-18 Jiequn Han , Ruimeng Hu

In the paper we study a deep learning based method to solve the multicell power control problem for sum rate maximization subject to per-user rate constraints and per-base station (BS) power constraints. The core difficulty of this problem…

Signal Processing · Electrical Eng. & Systems 2020-12-09 Yinghan Li , Shengqian Han , Chenyang Yang

In this thesis, we consider two simple but typical control problems and apply deep reinforcement learning to them, i.e., to cool and control a particle which is subject to continuous position measurement in a one-dimensional quadratic…

Quantum Physics · Physics 2022-12-15 Zhikang Wang

Control of a dynamical system without the knowledge of dynamics is an important and challenging task. Modern machine learning approaches, such as deep neural networks (DNNs), allow for the estimation of a dynamics model from control inputs…

Systems and Control · Electrical Eng. & Systems 2023-11-14 Suruchi Sharma , Volodymyr Makarenko , Gautam Kumar , Stas Tiomkin

Learning-based methods could provide solutions to many of the long-standing challenges in control. However, the neural networks (NNs) commonly used in modern learning approaches present substantial challenges for analyzing the resulting…

Machine Learning · Computer Science 2022-02-03 Michael Everett

The article sets and solves the task to control an error of the artificial neural network with variable signal conductivity. This kind of neural networks was especially developed to construct timetables. Behavior of such a neural network…

Optimization and Control · Mathematics 2016-08-17 Alexander Ignatenkov , Alexey Olshansky

Quantum control is a ubiquitous research field that has enabled physicists to delve into the dynamics and features of quantum systems, delivering powerful applications for various atomic, optical, mechanical, and solid-state systems. In…

Quantum Physics · Physics 2023-12-11 Ariel Norambuena , Marios Mattheakis , Francisco J. González , Raúl Coto

In recent years, deep learning has been connected with optimal control as a way to define a notion of a continuous underlying learning problem. In this view, neural networks can be interpreted as a discretization of a parametric Ordinary…

Optimization and Control · Mathematics 2020-07-07 Joubine Aghili , Olga Mula

Deep learning is formulated as a discrete-time optimal control problem. This allows one to characterize necessary conditions for optimality and develop training algorithms that do not rely on gradients with respect to the trainable…

Machine Learning · Computer Science 2018-06-05 Qianxiao Li , Shuji Hao

Strichartz estimates, well-posedness theory and long time behavior for (nonlinear) Schr\"odinger equations on waveguide manifolds $\mathbb{R}^m \times \mathbb{T}^n$ are intensively studied in recent decades while the corresponding control…

Analysis of PDEs · Mathematics 2025-02-20 Jingrui Niu , Zehua Zhao

The development of quantum technologies relies on creating and manipulating quantum systems of increasing complexity, with key applications in computation, simulation, and sensing. This poses severe challenges in efficient control,…

Quantum Physics · Physics 2025-09-09 Hailan Ma , Bo Qi , Ian R. Petersen , Re-Bing Wu , Herschel Rabitz , Daoyi Dong

We consider recent work of Haber and Ruthotto 2017 and Chang et al. 2018, where deep learning neural networks have been interpreted as discretisations of an optimal control problem subject to an ordinary differential equation constraint. We…

Optimization and Control · Mathematics 2019-10-02 Martin Benning , Elena Celledoni , Matthias J. Ehrhardt , Brynjulf Owren , Carola-Bibiane Schönlieb

We develop a spacetime neural network method with second order optimization for solving quantum dynamics from the high dimensional Schr\"{o}dinger equation. In contrast to the standard iterative first order optimization and the…

Disordered Systems and Neural Networks · Physics 2021-08-05 Jiangran Wang , Zhuo Chen , Di Luo , Zhizhen Zhao , Vera Mikyoung Hur , Bryan K. Clark

Given enough data, Deep Neural Networks (DNNs) are capable of learning complex input-output relations with high accuracy. In several domains, however, data is scarce or expensive to retrieve, while a substantial amount of expert knowledge…

Artificial Intelligence · Computer Science 2020-02-26 Mattia Silvestri , Michele Lombardi , Michela Milano

We have trained a deep (convolutional) neural network to predict the ground-state energy of an electron in four classes of confining two-dimensional electrostatic potentials. On randomly generated potentials, for which there is no analytic…

Materials Science · Physics 2017-11-06 Kyle Mills , Michael Spanner , Isaac Tamblyn

We present a neural network approach for approximating the value function of high-dimensional stochastic control problems. Our training process simultaneously updates our value function estimate and identifies the part of the state space…

Optimization and Control · Mathematics 2024-05-08 Xingjian Li , Deepanshu Verma , Lars Ruthotto