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We propose the coarse-grained spectral projection method (CGSP), a deep learning assisted approach for tackling quantum unitary dynamic problems with an emphasis on quench dynamics. We show that CGSP can extract spectral components of many-body quantum states systematically with a sophisticated neural network quantum ansatz. CGSP fully exploits the linear unitary nature of the quantum dynamics and is potentially superior to other quantum Monte Carlo methods for ergodic dynamics. Preliminary numerical results on one-dimensional XXZ models with periodic boundary conditions are carried out to demonstrate the practicality of CGSP.

We introduce a machine-learning-based framework for constructing continuum a non-Newtonian fluid dynamics model directly from a microscale description. Dumbbell polymer solutions are used as examples to demonstrate the essential ideas. To faithfully retain molecular fidelity, we establish a micro-macro correspondence via a set of encoders for the microscale polymer configurations and their macroscale counterparts, a set of nonlinear conformation tensors. The dynamics of these conformation tensors can be derived from the microscale model, and the relevant terms can be parametrized using machine learning. The final model, named the deep non-Newtonian model (DeePN^{2}), takes the form of conventional non-Newtonian fluid dynamics models, with a generalized form of the objective tensor derivative that retains the microscale interpretations. Both the formulation of the dynamic equation and the neural network representation rigorously preserve the rotational invariance, which ensures the admissibility of the constructed model. Numerical results demonstrate the accuracy of DeePN^{2} where models based on empirical closures show limitations.

Fully anharmonic calculations of the dielectric response of insulators require costly $a\phantom{\rule{0}{0ex}}b$ $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ molecular dynamics simulations. Here, the authors show that this electronic response property can be described efficiently by a deep neural network that retains the accuracy of $a\phantom{\rule{0}{0ex}}b$ $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ molecular dynamics. The scheme is demonstrated with calculations of the infrared absorption spectrum of liquid water at standard conditions, and of the evolution of the spectrum of crystalline ice undergoing a pressure-induced structural transformation from molecular ice VII to ionic ice X.

Spatial artificial neural network (SANN) models are developed for subgrid-scale (SGS) forces in the large eddy simulation of turbulence, whose input features are based on the derivatives of the filtered field at different spatial locations. The correlation coefficients of SGS forces predicted by the SANN models can be made larger than 0.99, much higher than that of the traditional gradient model. The SANN models perform better than the dynamic Smagorinsky model and the dynamic mixed model in spectrum prediction and in velocity and instantaneous flow structure statistics.

An active learning procedure called deep potential generator (DP-GEN) is proposed for the construction of accurate and transferable machine learning-based models of the potential energy surface (PES) for the molecular modeling of materials. This procedure consists of three main components: exploration, generation of accurate reference data, and training. Application to the sample systems of Al, Mg, and Al-Mg alloys demonstrates that DP-GEN can produce uniformly accurate PES models with a minimal number of reference data.

Statistical properties of solutions of the random forced Burgers equation have been a subject of intensive studies recently (see Refs. [1–6]). Of particular interest are the asymptotic properties of probability distribution functions associated with velocity gradients and velocity increments. Aside from the fact that such issues are of direct interest to a large number of problems such as the growth of random surfaces [1], it is also hoped that the field-theoretic techniques developed for the Burgers equation will eventually be useful for understanding more complex phenomena such as turbulence. In this paper, we propose a new and direct approach for analyzing the scaling properties of the various distribution functions for the random forced Burgers equation. We will consider the problem

Point defects play a dominant role in determining the wide spectrum of electronic and physical properties of semiconducting materials that have vast technological applications. Using ab initio simulations, a method to calculate equilibrium defect concentrations, Fermi energy and defect stability diagrams as functions of external parameters, such as temperature and pressure, is presented. Using SrTiO${}_{3}$ as a representative material, we report our analysis of the stability of oxygen vacancies and interstitials, in their different charge states, as a function of temperature, oxygen partial pressure and Fermi energy of the system. Further, by analyzing the defect chemistry at experimentally relevant temperatures, we find that at low oxygen partial pressure, neutral oxygen vacancies are most dominant and at intermediate and high oxygen partial pressure, doubly charged oxygen vacancies are dominant.

Analytical solution of Maxwell's equations is obtained for general linear optical materials: lossy and optically active crystals. Explicit expressions are obtained for the dispersion relation and the propagating eigenmodes. In general, four rather than two distinct modes are present. The results are useful in describing light propagation in optically complex media.

We propose a multipole representation of the Fermi-Dirac function and the Fermi operator, and use this representation to develop algorithms for electronic structure analysis of metallic systems. The new algorithm is quite simple and efficient. Its computational cost scales logarithmically with $\beta\Delta\eps$ where $\beta$ is the inverse temperature, and $\Delta \eps$ is the width of the spectrum of the discretized Hamiltonian matrix., Comment: 10 pages, 3 figures, 3 tables

We present a linear-scaling method for electronic structure computations in the context of Kohn-Sham density functional theory (DFT). The method is based on a subspace iteration, and takes advantage of the nonorthogonal formulation of the Kohn-Sham functional, and the improved localization properties of nonorthogonal wave functions. A one-dimensional linear problem is presented as a benchmark for the analysis of linear-scaling algorithms for Kohn-Sham DFT. Using this one-dimensional model, we study the convergence properties of the localized subspace-iteration algorithm presented. We demonstrate the efficiency of the algorithm for practical applications by performing fully three-dimensional computations of the electronic density of alkane chains.

This paper presents a systematic approach for finding efficient boundary conditions for molecular dynamics simulations of crystalline solids. These boundary conditions effectively eliminate phonon reflection at the boundary and at the same time allow the thermal energy from the bath to be introduced to the system. Our starting point is the Mori-Zwanzig formalism [R. Zwanzig, J. Chem. Phys. 32, 1173 (1960); in Systems Far from Equilibrium, edited by L. Garrido (Interscience, New York, 1980); H. Mori, Prog. Theor. Phys. 33, 423 (1965)] for eliminating the thermal bath, but we take the crucial next step that goes beyond this formalism in order to obtain memory kernels that decay faster. An equivalent variational formulation allows us to find the optimal approximate boundary conditions, after specifying the spatial-temporal domain of dependence for the positions of the boundary atoms. Application to a one-dimensional chain, a two-dimensional Lennard-Jones system, and a three-dimensional model of $\ensuremath{\alpha}$-iron with embedded atom potential is presented to demonstrate the effectiveness of this approach.

The accuracy of the quasicontinuum method is studied by reformulating the summation rules in terms of reconstruction schemes for the local atomic environment of the representative atoms. The necessary and sufficient condition for uniform first-order accuracy and, consequently, the elimination of the ``ghost force'' is formulated in terms of the reconstruction schemes. The quasi-nonlocal approach is discussed as a special case of this condition. Examples of reconstruction schemes that satisfy this condition are presented. Transition between atom-based and element-based summation rules are studied.

We present an elementary and systematic discussion on the derivation of continuum theories from atomistic models for studying the elastic deformation of plates, sheets, and rods. The derivation is based on various generalizations of the classical Cauchy-Born rule. In particular, we discuss a so-called local Cauchy-Born rule which is very general and particularly easy to use. As an application, we use the atomistically derived continuum models to study the elastic deformation of carbon nanotubes.

We consider phase separation in multicomponent systems in the limit as the free volume goes to zero. Excluded volume effects are taken into account via a pressure field which implicitly relates currents and forces. The pressure, obtainable from a divergence condition, may give rise to circulating currents. A simple description of the dynamics of phase separation at late times follows. @S1063-651X~97!50504-6#

In heteroepitaxial growth, the mismatch between the lattice constants in the film and the substrate causes misfit strain in the film, making a flat surface unstable to small perturbations. This morphological instability is called Asaro-Tiller-Grinfeld (ATG) instability. In practice, most devices are fabricated on vicinal surfaces which consist of steps and terraces. In this case, the misfit strain causes step bunching and traditional continuum models for the ATG instability do not apply directly. In this paper, we present a continuum model for this elastically driving step bunching. We validate our model by performing linear stability analysis and numerical simulation in the nonlinear regime. We also present a continuum description for the misfit elastic energy on vicinal surface which incorporates the underlying atomic features of the vicinal surface.

The heterogeneous multiscale method, is presented as a general methodology for an efficient numerical computation of problems with multiple scales. The method relies on an efficient coupling between the macroscopic and microscopic models. In case the macroscopic model is not explicitly available or is invalid in part of the domain, the microscopic model is used to supply the necessary data for the macroscopic model. Scale separation is exploited so that coarse-grained variables can be evolved on macroscopic spatial/temporal scales using data that are predicted based on the simulation of the microscopic process on microscale spatial/temporal domains. Applications to homogenization, dislocation dynamics and crack propagation are discussed.

The Doi kinetic theory for flows of homogeneous, rodlike liquid crystalline polymers (LCPs) is extended to model flows of nonhomogeneous, rodlike LCPs through a nonlocal (long-range) intermolecular potential. The theory features (i) a nonlocal, anisotropic, effective intermolecular potential in an integral form that is consistent with the chemical potential, (ii) short-range elasticity as well as long-range isotropic and anisotropic elasticity, (iii) a closed-form stress expression accounting for the nonlocal molecular interaction, and (iv) an extra elastic body force exclusively associated with the integral form of the intermolecular potential. With the effective intermolecular potential, the theory is proven to be well posed in that it warrants a positive entropy production and thereby the second law of thermodynamics. Approximate theories are obtained by gradient expansions of the number density function in the free energy density.