相关论文: Deep learning and the Schr\"odinger equation

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…

Neural networks can be used to identify phases and phase transitions in condensed matter systems via supervised machine learning. Readily programmable through modern software libraries, we show that a standard feed-forward neural network…

Accurate ab-initio prediction of electronic energies is very expensive for macromolecules by explicitly solving post-Hartree-Fock equations. We here exploit the physically justified local correlation feature in compact basis of small…

As a key property of hadrons, the total width is quite difficult to obtain in theory due to the extreme complexity of the strong and electroweak interactions. In this work, a deep neural network model with the Transformer architecture is…

We present a new dimensional scaling transformation of the Schrodinger equation for the two electron bond. This yields, for the first time, a good description of the two electron bond via D-scaling. There also emerges, in the large-D limit,…

We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\"odinger operator which describes the quantum mechanics of an…

Molecular modeling is an important topic in drug discovery. Decades of research have led to the development of high quality scalable molecular force fields. In this paper, we show that neural networks can be used to train a universal…

Over the past several years, there have been many studies demonstrating the ability of deep neural networks to identify phase transitions in many physical systems, notably in classical statistical physics systems. One often finds that the…

We study analytically the existence and uniqueness of the ground state of the nonlinear Schr\"{o}dinger equation (NLSE) with a general power nonlinearity described by the power index $\sigma\ge0$. For the NLSE under a box or a harmonic…

Machine-learned regression models represent a promising tool to implement accurate and computationally affordable energy-density functionals to solve quantum many-body problems via density functional theory. However, while they can easily…

The density of states for the Schroedinger equation with a Gaussian random potential is calculated in a space of dimension d=4-epsilon in the entire energy range including the vicinity of a mobility edge. Leading terms in 1/epsilon are…

Graph neural network architectures are advantageous for predicting core-electron binding energies which depend on local bond environment effects, as the number of message passing layers defines the topological (bond) radius of the model's…

An infinite sequence of potential well functions is considered. A trial wavefunction is used with the Schr$\ddot{\text{o}}$dinger equation to obtain an approximate ground state energy for each potential well function. We obtain an…

In this paper, we study 1-d random Schr\"odinger operators on a finite interval with Dirichlet boundary conditions. We are interested in the approximation of the ground state energy using the minimum of the effective potential. For the 1-d…

We show the existence of a deep neural network capable of approximating a wide class of high-dimensional approximations. The construction of the proposed neural network is based on a quasi-optimal polynomial approximation. We show that this…

Extensive variational computations are reported for the ground state energy of the non-relativistic two-electron atom. Several different sets of basis functions were systematically explored, starting with the original scheme of Hylleraas.…

Deep neural networks have rightfully won the place of one of the most accurate analysis tools in high energy physics. In this paper we will cover several methods of improving the performance of a deep neural network in a classification task…

We propose here a new model termed as the Differential Equation Model for the ground to first 2+ state excitation energy E2 of a given even-even nucleus, according to which the energy E2 is expressed in terms of its derivatives with respect…

Deep energy-based models are powerful, but pose challenges for learning and inference (Belanger and McCallum, 2016). Tu and Gimpel (2018) developed an efficient framework for energy-based models by training "inference networks" to…

Accurately solving the Schr\"odinger equation for intricate systems remains a prominent challenge in physical sciences. A paradigm-shifting approach to address this challenge involves the application of artificial intelligence techniques.…