Related papers: On a neural network approach for solving potential…
Numerical solving the Schr\"odinger equation with incommensurate potentials presents a great challenge since its solutions could be space-filling quasiperiodic structures without translational symmetry nor decay. In this paper, we propose…
Reinforcement Learning algorithms have recently been proposed to learn time-sequential control policies in the field of autonomous driving. Direct applications of Reinforcement Learning algorithms with discrete action space will yield…
Control of quantum systems via lasers has numerous applications that require fast and accurate numerical solution of the Schr\"odinger equation. In this paper we present three strategies for extending any sixth-order scheme for…
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…
The description of electron current through a splitting is a mathematical problem of electron transport in quantum networks. For quantum networks constructed on the interface of narrow-gap semiconductors the relevant scattering problem for…
We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…
The classical limit of quantum mechanics, formally investigated through frameworks like strict deformation quantization, remains a profound area of inquiry in the philosophy of physics. This paper explores a computational approach employing…
Machine learning has made important headway in helping to improve the treatment of quantum many-body systems. A domain of particular relevance are correlated inhomogeneous systems. What has been missing so far is a general, scalable…
Objective. Precise control of neural systems is essential to experimental investigations of how the brain controls behavior and holds the potential for therapeutic manipulations to correct aberrant network states. Model predictive control,…
Multi-dimensional direct numerical simulation (DNS) of the Schr\"odinger equation is needed for design and analysis of quantum nanostructures that offer numerous applications in biology, medicine, materials, electronic/photonic devices,…
In this paper, we aim to solve the high dimensional stochastic optimal control problem from the view of the stochastic maximum principle via deep learning. By introducing the extended Hamiltonian system which is essentially an FBSDE with a…
We present a neural network based calibration method that performs the calibration task within a few milliseconds for the full implied volatility surface. The framework is consistently applicable throughout a range of volatility models…
Machine learning techniques based on artificial neural networks have been successfully applied to solve many problems in science. One of the most interesting domains of machine learning, reinforcement learning, has natural applicability for…
In this study, we solved Schr\"odinger equation with Cornell potential (Coulomb-plus-linear potential) by using neural network approach. Four different types of Cornell potential were used without a physical relevance. Besides that…
Neural networks are a promising tool for characterizing intermediate-scale quantum devices from limited amounts of measurement data. A challenging problem in this area is to learn the action of an unknown quantum process on an ensemble of…
In this paper, we propose a dynamical low-rank (DLR) approximation framework for solving the semiclassical Schrodinger equation with uncertainties. The primary numerical challenges arise from the dual nature of the oscillations: the spatial…
We study an inverse scattering problem associated with a Schr\"odinger system where both the potential and source terms are random and unknown. The well-posedness of the forward scattering problem is first established in a proper sense. We…
In this work we propose an extension of physics informed supervised learning strategies to parametric partial differential equations. Indeed, even if the latter are indisputably useful in many applications, they can be computationally…
We develop a probabilistic machine learning method, which formulates a class of stochastic neural networks by a stochastic optimal control problem. An efficient stochastic gradient descent algorithm is introduced under the stochastic…
Deep neural networks provide flexible frameworks for learning data representations and functions relating data to other properties and are often claimed to achieve 'super-human' performance in inferring relationships between input data and…