Related papers: On a neural network approach for solving potential…
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…
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…
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…
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,…
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…
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…
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…
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…
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,…
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…
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…
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…
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…
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…
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…
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…
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…