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Physics-informed neural networks (PINN) have been widely used in computational physics to solve partial differential equations (PDEs). In this study, we propose an energy-embedding-based physics-informed neural network method for solving…

Computational Physics · Physics 2025-06-02 Yi-Qiang Wu , Xuan Liu , Hanlin Li , Fuqiang Wang

This paper studies the local exact controllability and the local stabilization of the semilinear Schr\"odinger equation posed on a product of $n$ intervals ($n\ge 1$). Both internal and boundary controls are considered, and the results are…

Analysis of PDEs · Mathematics 2010-02-08 Lionel Rosier , Bing-Yu Zhang

Robust control design for quantum systems has been recognized as a key task in the development of practical quantum technology. In this paper, we present a systematic numerical methodology of sampling-based learning control (SLC) for…

Systems and Control · Computer Science 2016-11-17 Daoyi Dong , Chunlin Chen , Ruixing Long , Bo Qi , Ian R. Petersen

The solution to partial differential equations using deep learning approaches has shown promising results for several classes of initial and boundary-value problems. However, their ability to surpass, particularly in terms of accuracy,…

Numerical Analysis · Mathematics 2023-08-23 Ziad Aldirany , Régis Cottereau , Marc Laforest , Serge Prudhomme

In this paper, we compute the eigenvalue problem (EVP) for the semiclassical random Schr\"odinger operators, where the random potentials are parameterized by an infinite series of random variables. After truncating the series, we introduce…

Numerical Analysis · Mathematics 2025-02-12 Panchi Li , Zhiwen Zhang

We present a hierarchical, control theory inspired method for variational inference (VI) for neural stochastic differential equations (SDEs). While VI for neural SDEs is a promising avenue for uncertainty-aware reasoning in time-series, it…

Machine Learning · Computer Science 2025-05-26 Rembert Daems , Manfred Opper , Guillaume Crevecoeur , Tolga Birdal

This paper is concerned with the efficient numerical computation of solutions to the 1D stationary Schr\"odinger equation in the semiclassical limit in the highly oscillatory regime. A previous approach to this problem based on explicitly…

Numerical Analysis · Mathematics 2019-11-05 A. Arnold , C. Klein. B. Ujvari

Robust control design for quantum systems has been recognized as a key task in the development of practical quantum technology. In this paper, we present a systematic numerical methodology of sampling-based learning control (SLC) for…

Quantum Physics · Physics 2016-03-29 Daoyi Dong , Mohamed A. Mabrok , Ian R. Petersen , Bo Qi , Chunlin Chen , Herschel Rabitz

Results obtained with stochastic methods have an inherent uncertainty due to the finite number of samples that can be achieved in practice. In lattice QCD this problem is particularly salient in some observables like, for instance,…

High Energy Physics - Lattice · Physics 2025-03-13 Paulo F. Bedaque , Hyunwoo Oh

Machine translation systems based on deep neural networks are expensive to train. Curriculum learning aims to address this issue by choosing the order in which samples are presented during training to help train better models faster. We…

Computation and Language · Computer Science 2018-11-05 Xuan Zhang , Gaurav Kumar , Huda Khayrallah , Kenton Murray , Jeremy Gwinnup , Marianna J Martindale , Paul McNamee , Kevin Duh , Marine Carpuat

This paper explores some variations of a hierarchical control framework that has been recently proposed. The framework is dedicated to control a network of interconnected subsystems such as the ones describing cryogenic processes or power…

Systems and Control · Electrical Eng. & Systems 2022-01-07 Xuan-Huy Pham , Mazen Alamir , François Bonne

Nonlinear Model Predictive Control (NMPC) is a general and flexible control approach, used in many industrial contexts, and is based on the online solution of a nonlinear optimization problem. This operation requires in general a high…

Systems and Control · Electrical Eng. & Systems 2024-11-06 Carlo Novara , Mattia Boggio , Deborah Volpe

We study a non-linear Schroedinger equation with a Hartree-type nonlinearity and a localized random time-dependent external potential. Sharp dispersive estimates for the linear Schroedinger equation with a random time-dependent potential…

Analysis of PDEs · Mathematics 2019-03-11 Marius Beceanu , Avy Soffer

Neural networks have emerged as a powerful way to approach many practical problems in quantum physics. In this work, we illustrate the power of deep learning to predict the dynamics of a quantum many-body system, where the training is…

Quantum Neural Networks (QNNs) are a promising variational learning paradigm with applications to near-term quantum processors, however they still face some significant challenges. One such challenge is finding good parameter initialization…

Deep Neural Networks miss a principled model of their operation. A novel framework for supervised learning based on Topological Quantum Field Theory that looks particularly well suited for implementation on quantum processors has been…

Model predictive control (MPC) is a method to formulate the optimal scheduling problem for grid flexibilities in a mathematical manner. The resulting time-constrained optimization problem can be re-solved in each optimization time step…

Systems and Control · Electrical Eng. & Systems 2021-08-20 Steven de Jongh , Sina Steinle , Anna Hlawatsch , Felicitas Mueller , Michael Suriyah , Thomas Leibfried

In this paper, we consider an optimal bilinear control problem for the nonlinear Schr\"{o}dinger equations with singular potentials. We show well-posedness of the problem and existence of an optimal control. In addition, the first order…

Analysis of PDEs · Mathematics 2013-01-21 Binhua Feng , Dun Zhao , Pengyu Chen

In this work, we conduct a comparative study on two deep unfolding mechanisms to efficiently perform power control in the next generation wireless networks. The power control problem is formulated as energy efficiency over multiple…

Networking and Internet Architecture · Computer Science 2024-03-29 Abuzar B. M. Adam , Mohammed A. M. Elhassan , Elhadj Moustapha Diallo

Deep learning of the Artificial Neural Networks (ANN) can be treated as a particular class of interpolation problems. The goal is to find a neural network whose input-output map approximates well the desired map on a finite or an infinite…

Optimization and Control · Mathematics 2021-03-02 Andrei Agrachev , Andrey Sarychev