Related papers: Spacetime Neural Network for High Dimensional Quan…
This paper provides a new avenue for exploiting deep neural networks to improve physics-based simulation. Specifically, we integrate the classic Lagrangian mechanics with a deep autoencoder to accelerate elastic simulation of deformable…
A matrix inverse free method to solve time-dependent Schrodinger equation is presented. The method is not subject to form of Hamiltonian and adopting real space grid system such as structured and unstructured grid, and achieves the order N…
This paper investigates a reverse space-time higher-order modified self-steepening nonlinear Schr\"odinger equation, which distinguishes its standard local counterparts through the reverse space-time symmetry. The integrability of this…
First-order optimization methods, such as SGD and Adam, are widely used for training large-scale deep neural networks due to their computational efficiency and robust performance. However, relying solely on gradient information, these…
Gradient descent methods have long been the de facto standard for training deep neural networks. Millions of training samples are fed into models with billions of parameters, which are slowly updated over hundreds of epochs. Recently, it's…
Neural networks have achieved impressive breakthroughs in both industry and academia. How to effectively develop neural networks on quantum computing devices is a challenging open problem. Here, we propose a new quantum neural network model…
Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…
A particle confined to an impassable box is a paradigmatic and exactly solvable one-dimensional quantum system modeled by an infinite square well potential. Here we explore some of its infinitely many generalizations to two dimensions,…
Quantum machine learning techniques have been proposed as a way to potentially enhance performance in machine learning applications. In this paper, we introduce two new quantum methods for neural networks. The first one is a quantum…
In recent years, an increasing attention has been paid to quantum heterostructures with tailored functionalities, such as heterojunctions and quantum matematerials, in which quantum dynamics of electrons can be described by the…
We exhibit an alternative method for solving inhomogeneous second--order linear ordinary dynamic equations on time scales, based on reduction of order rather than variation of parameters. Our form extends recent (and long-standing) analysis…
We design and compute first-order implicit-in-time variational schemes with high-order spatial discretization for initial value gradient flows in generalized optimal transport metric spaces. We first review some examples of gradient flows…
Utilization of a quantum system whose time-development is described by the nonlinear Schrodinger equation in the transformation of qubits would make it possible to construct quantum algorithms which would be useful in a large class of…
Hedging exotic options in presence of market frictions is an important risk management task. Deep hedging can solve such hedging problems by training neural network policies in realistic simulated markets. Training these neural networks may…
Higher-order accurate solution to electromagnetic scattering problems are obtained at reduced computational cost in a {\it p}-variable finite volume time domain method. Spatial operators of lower, including first-order accuracy, are…
The time-dependent Schr\"odinger equation (TDSE) in real space is fundamental to understanding the dynamics of many-electron quantum systems, with applications ranging from quantum chemistry to condensed matter physics and materials…
In this note, we generalize the nonlinearity-recovery result in [7] for classical cubic nonlinear Schr\"odinger equations to higher-order Schr\"odinger equations with a more general nonlinearity. More precisely, we consider a…
This paper introduces weighted finite difference methods for numerically solving dispersive evolution equations with solutions that are highly oscillatory in both space and time. We consider a semiclassically scaled cubic nonlinear…
In this paper, we investigate the forward problems on the data-driven rational solitons for the (2+1)-dimensional KP-I equation and spin-nonlinear Schr\"odinger (spin-NLS) equation via the deep neural networks leaning. Moreover, the inverse…
Neural quantum states are a promising framework for simulating many-body quantum dynamics, as they can represent states with volume-law entanglement. As time evolves, the neural network parameters are typically optimized at discrete time…