相关论文: Deep neural network solution of the electronic Sch…
Neutral molecules with sufficiently large dipole moments can bind electrons in diffuse nonvalence orbitals with most of their charge density far from the nuclei, forming so-called dipole-bound anions. Because long-range correlation effects…
A new, open source, parallel, stand-alone software package (Fortnet) has been developed, which implements Behler-Parrinello neural networks. It covers the entire workflow from feature generation to the evaluation of generated potentials,…
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…
Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large…
A robust and general solver for the radial Schr\"odinger, Dirac, and Kohn--Sham equations is presented. The formulation admits general potentials and meshes: uniform, exponential, or other defined by nodal distribution and derivative…
We discuss differences and similarities between variational Monte Carlo approaches that use conventional and artificial neural network parameterizations of the ground-state wave function for systems of fermions. We focus on a relatively…
Inspired by the universal approximation theorem and widespread adoption of artificial neural network techniques in a diversity of fields, we propose feed-forward neural networks as a general purpose trial wave function for quantum Monte…
The stationary 1D Schr\"odinger equation with a polynomial potential $V(q)$ of degree N is reduced to a system of exact quantization conditions of Bohr-Sommerfeld form. They arise from bilinear (Wronskian) functional relations pairing…
Many approaches, which have been developed to express the potential energy of large systems, exploit the locality of the atomic interactions. A prominent example are fragmentation methods, in which quantum chemical calculations are carried…
We discuss stationary solutions of the discrete nonlinear Schr\"odinger equation (DNSE) with a potential of the $\phi^{4}$ type which is generically applicable to several quantum spin, electron and classical lattice systems. We show that…
In this paper we provide a quantum Monte Carlo algorithm to solve multidimensional Black-Scholes PDEs with correlation for option pricing. The payoff function of the option is of general form and is only required to be continuous and…
We formulate a smoothed-particle hydrodynamics numerical method, traditionally used for the Euler equations for fluid dynamics in the context of astrophysical simulations, to solve the non-linear Schrodinger equation in the Madelung…
We study the homogenization of a stochastic Schr\"odinger equation with a large periodic potential in solid state physics. Denoting by $\varepsilon$ the period, the potential is scaled as $\varepsilon^{-2}$. Under a generic assumption on…
An important problem in fiber-optic communications is to invert the nonlinear Schr\"odinger equation in real time to reverse the deterministic effects of the channel. Interestingly, the popular split-step Fourier method (SSFM) leads to a…
A benchmark-quality potential energy curve is reported for the H$_3$ system in collinear nuclear configurations. The electronic Schr\"odinger equation is solved using explicitly correlated Gaussian (ECG) basis functions using an optimized…
It was recently shown that the exact factorization of the electron-nuclear wavefunction allows the construction of a Schr\"odinger equation for the electronic system, in which the potential contains exactly the effect of coupling to the…
Fast and accurate simulation of complex chemical systems in environments such as solutions is a long standing challenge in theoretical chemistry. In recent years, machine learning has extended the boundaries of quantum chemistry by…
Modern laboratory techniques like ultrafast laser excitation and shock compression can bring matter into highly nonequilibrium states with complex structural transformation, metallization and dissociation dynamics. To understand and model…
In a recent paper, Lucco Castello et al. [arXiv:2107.03537] provided an accurate parametrization of classical one-component plasma bridge functions that was embedded in a novel dielectric scheme for strongly coupled electron liquids. Here,…
We develop a quantum algorithm for solving high-dimensional fractional Poisson equations. By applying the Caffarelli-Silvestre extension, the $d$-dimensional fractional equation is reformulated as a local partial differential equation in…