Physics

To close the moment model deduced from kinetic equations, the canonical approach is to provide an approximation to the flux function not able to be depicted by the moments in the reduced model. In this paper, we propose a brand new closure approach with remarkable advantages than the canonical approach. Instead of approximating the flux function, the new approach close the moment model by approximating the flux gradient. Precisely, we approximate the space derivative of the distribution function by an ansatz which is a weighted polynomial, and the derivative of the closing flux is computed by taking the moments of the ansatz. Consequently, the method provides us an improved framework to derive globally hyperbolic moment models, which preserve all those conservative variables in the low order moments. It is shown that the linearized system at the weight function, which is often the local equilibrium, of the moment model deduced by our new approach is automatically coincided with the system deduced from the classical perturbation theory, which can not be satisfied by previous hyperbolic regularization framework. Taking the Boltzmann equation as example, the linearlization of the moment model gives the correct Navier-Stokes-Fourier law same as that the Chapman-Enskog expansion gives. Most existing globally hyperbolic moment models are re-produced by our new approach, and several new models are proposed based on this framework.

Machine learning has demonstrated great power in materials design, discovery, and property prediction. However, despite the success of machine learning in predicting discrete properties, challenges remain for continuous property prediction. The challenge is aggravated in crystalline solids due to crystallographic symmetry considerations and data scarcity. Here we demonstrate the direct prediction of phonon density of states using only atomic species and positions as input. We apply Euclidean neural networks, which by construction are equivariant to 3D rotations, translations, and inversion and thereby capture full crystal symmetry, and achieve high-quality prediction using a small training set of ∼ 10 3 examples with over 64 atom types. Our predictive model reproduces key features of experimental data and even generalizes to materials with unseen elements,and is naturally suited to efficiently predict alloy systems without additional computational cost. We demonstrate the potential of our network by predicting a broad number of high phononic specific heat capacity materials. Our work indicates an efficient approach to explore materials' phonon structure, and can further enable rapid screening for high-performance thermal storage materials and phonon-mediated superconductors.

This is the second part of a project on the foundations of first-principle calculations of the electron transport in crystals at finite temperatures, aiming at a predictive first-principles platform that combines ab-initio molecular dynamics (AIMD) and a finite-temperature Kubo-formula with dissipation for thermally disordered crystalline phases. The latter are encoded in an ergodic dynamical system (Ω,G,dP) , where Ω is the configuration space of the atomic degrees of freedom, G is the space group acting on Ω and dP is the ergodic Gibbs measure relative to the G -action. We first demonstrate how to pass from the continuum Kohn-Sham theory to a discrete atomic-orbitals based formalism without breaking the covariance of the physical observables w.r.t. (Ω,G,dP) . Then we show how to implement the Kubo-formula, investigate its self-averaging property and derive an optimal finite-volume approximation for it. We also describe a numerical innovation that made possible AIMD simulations with longer orbits and elaborate on the details of our simulations. Lastly, we present numerical results on the transport coefficients of crystal silicon at different temperatures.

Several applications in the scientific simulation of physical systems can be formulated as control/optimization problems. The computational models for such systems generally contain hyperparameters, which control solution fidelity and computational expense. The tuning of these parameters is non-trivial and the general approach is to manually `spot-check' for good combinations. This is because optimal hyperparameter configuration search becomes impractical when the parameter space is large and when they may vary dynamically. To address this issue, we present a framework based on deep reinforcement learning (RL) to train a deep neural network agent that controls a model solve by varying parameters dynamically. First, we validate our RL framework for the problem of controlling chaos in chaotic systems by dynamically changing the parameters of the system. Subsequently, we illustrate the capabilities of our framework for accelerating the convergence of a steady-state CFD solver by automatically adjusting the relaxation factors of discretized Navier-Stokes equations during run-time. The results indicate that the run-time control of the relaxation factors by the learned policy leads to a significant reduction in the number of iterations for convergence compared to the random selection of the relaxation factors. Our results point to potential benefits for learning adaptive hyperparameter learning strategies across different geometries and boundary conditions with implications for reduced computational campaign expenses. \footnote{Data and codes available at \url{this https URL}}

There is growing interest in warm dense matter (WDM) -- an exotic state on the border between condensed matter and plasmas. Due to the simultaneous importance of quantum and correlation effects WDM is complicated to treat theoretically. A key role has been played by \textit{ab initio} path integral Monte Carlo (PIMC) simulations, and recently extensive results for thermodynamic quantities have been obtained. The first extension of PIMC simulations to the dynamic structure factor of the uniform electron gas were reported by Dornheim \textit{et al.} [Phys. Rev. Lett. \textbf{121}, 255001 (2018)]. This was based on an accurate reconstruction of the dynamic local field correction. Here we extend this concept to other dynamical quantities of the warm dense electron gas including the dynamic susceptibility, the dielectric function and the conductivity.

The selective entrapment of mutually annihilating species within a phase-changing carrier fluid is explored by both analytical and numerical means. The model takes full account of the dynamic heterogeneity which arises as a result of the coupling between hydrodynamic transport, dynamic phase-transitions and chemical reactions between the participating species, in the presence of a selective droplet interface. Special attention is paid to the dynamic symmetry breaking between the mass of the two species entrapped within the expanding droplet as a function of time. It is found that selective sources are much more effective symmetry breakers than selective diffusion. The present study may be of interest for a broad variety of advection-diffusion-reaction phenomena with selective fluid interfaces, including the problem of electroweak baryogenesis.

Parameterization of interatomic forcefields is a necessary first step in performing molecular dynamics simulations. This is a non-trivial global optimization problem involving quantification of multiple empirical variables against one or more properties. We present EZFF, a lightweight Python library for parameterization of several types of interatomic forcefields implemented in several molecular dynamics engines against multiple objectives using genetic-algorithm-based global optimization methods. The EZFF scheme provides unique functionality such as the parameterization of hybrid forcefields composed of multiple forcefield interactions as well as built-in quantification of uncertainty in forcefield parameters and can be easily extended to other forcefield functional forms as well as MD engines.

Finding low-energy molecular conformers is challenging due to the high dimensionality of the search space and the computational cost of accurate quantum chemical methods for determining conformer structures and energies. Here, we combine active-learning Bayesian optimization (BO) algorithms with quantum chemistry methods to address this challenge. Using cysteine as an example, we show that our procedure is both efficient and accurate. After only one thousand single-point calculations and approximately thirty structure relaxations, which is less than 10% computational cost of the current fastest method, we have found the low-energy conformers in good agreement with experimental measurements and reference calculations.

Molecular dynamics simulations of biomolecules have been widely adopted in biomedical studies. As classical point-charge models continue to be used in routine biomolecular applications, there have been growing demands on developing polarizable force fields for handling more complicated biomolecular processes. Here we focus on a recently proposed polarizable Gaussian Multipole (pGM) model for biomolecular simulations. A key benefit of pGM is its screening of all short-range electrostatic interactions in a physically consistent manner, which is critical for stable charge-fitting and is needed to reproduce molecular anisotropy. Another advantage of pGM is that each atom's multipoles are represented by a single Gaussian function or its derivatives, allowing for more efficient electrostatics than other Gaussian-based models. In this study we present an efficient formulation for the pGM model defined with respect to a local frame formed with a set of covalent basis vectors. The covalent basis vectors are chosen to be along each atom's covalent bonding directions. The new local frame allows molecular flexibility during molecular simulations and facilitates an efficient formulation of analytical electrostatic forces without explicit torque computation. Subsequent numerical tests show that analytical atomic forces agree excellently with numerical finite-difference forces for the tested system. Finally, the new pGM electrostatics algorithm is interfaced with the PME implementation in Amber for molecular simulations under the periodic boundary conditions. To validate the overall pGM/PME electrostatics, we conducted an NVE simulation for a small water box of 512 water molecules. Our results show that, to achieve energy conservation in the polarizable model, it is important to ensure enough accuracy on both PME and induction iteration.

We present an efficient, linear-scaling implementation for building the (screened) Hartree-Fock exchange (HFX) matrix for periodic systems within the framework of numerical atomic orbital (NAO) basis functions. Our implementation is based on the localized resolution of the identity approximation by which two-electron Coulomb repulsion integrals can be obtained by only computing two-center quantities -- a feature that is highly beneficial to NAOs. By exploiting the locality of basis functions and efficient prescreening of the intermediate three- and two-index tensors, one can achieve a linear scaling of the computational cost for building the HFX matrix with respect to the system size. Our implementation is massively parallel, thanks to a MPI/OpenMP hybrid parallelization strategy for distributing the computational load and memory storage. All these factors add together to enable highly efficient hybrid functional calculations for large-scale periodic systems. In this work we describe the key algorithms and implementation details for the HFX build as implemented in the ABACUS code package. The performance and scalability of our implementation with respect to the system size and the number of CPU cores are demonstrated for selected benchmark systems up to 4096 atoms.