Physics

We formulate and implement Helical DFT -- a self-consistent first principles simulation method for nanostructures with helical symmetries. Such materials are well represented in all of nanotechnology, chemistry and biology, and are expected to be associated with unprecedented material properties. We rigorously demonstrate the existence and completeness of special solutions to the single electron problem for helical nanostructures, called helical Bloch waves. We describe how the Kohn-Sham Density Functional Theory equations for a helical nanostructure can be reduced to a fundamental domain with the aid of these solutions. A key component in our mathematical treatment is the definition and use of a helical Bloch-Floquet transform to perform a block-diagonalization of the Hamiltonian in the sense of direct integrals. We develop a symmetry-adapted finite-difference strategy in helical coordinates to discretize the governing equations, and obtain a working realization of the proposed approach. We verify the accuracy and convergence properties of our numerical implementation through examples. Finally, we employ Helical DFT to study the properties of zigzag and chiral single wall black phosphorus (i.e., phosphorene) nanotubes. We use our simulations to evaluate the torsional stiffness of a zigzag nanotube ab initio. Additionally, we observe an insulator-to-metal-like transition in the electronic properties of this nanotube as it is subjected to twisting. We also find that a similar transition can be effected in chiral phosphorene nanotubes by means of axial strains. Notably, self-consistent ab initio simulations of this nature are unprecedented and well outside the scope of any other systematic first principles method in existence. We end with a discussion on various future avenues and applications.

Analog computers perceive a revival as a feasible technology platform for low precision, energy efficient and fast computing. We quantify this statement by measuring the performance of a modern analog computer and comparing it with traditional digital processors. General statements are made about ordinary and partial differential equations. As an example for large scale scientific computing applications, computational fluid dynamics are discussed. Several models are proposed which demonstrate the benefits of analog and digital-analog hybrid computing.

Simulations are vital for understanding and predicting the evolution of complex molecular systems. However, despite advances in algorithms and special purpose hardware, accessing the timescales necessary to capture the structural evolution of bio-molecules remains a daunting task. In this work we present a novel framework to advance simulation timescales by up to three orders of magnitude, by learning the effective dynamics (LED) of molecular systems. LED augments the equation-free methodology by employing a probabilistic mapping between coarse and fine scales using mixture density network (MDN) autoencoders and evolves the non-Markovian latent dynamics using long short-term memory MDNs. We demonstrate the effectiveness of LED in the Müeller-Brown potential, the Trp Cage protein, and the alanine dipeptide. LED identifies explainable reduced-order representations and can generate, at any instant, the respective all-atom molecular trajectories. We believe that the proposed framework provides a dramatic increase to simulation capabilities and opens new horizons for the effective modeling of complex molecular systems.

Machine learning methods have nowadays become easy-to-use tools for constructing high-dimensional interatomic potentials with ab initio accuracy. Although machine learned interatomic potentials are generally orders of magnitude faster than first-principles calculations, they remain much slower than classical force fields, at the price of using more complex structural descriptors. To bridge this efficiency gap, we propose an embedded atom neural network approach with simple piecewise switching function based descriptors, resulting in a favorable linear scaling with the number of neighbor atoms. Numerical examples validate that this piecewise machine learning model can be over an order of magnitude faster than various popular machine learned potentials with comparable accuracy for both metallic and covalent materials, approaching the speed of the fastest embedded atom method (i.e. several {\mu}s/atom per CPU core). The extreme efficiency of this approach promises its potential in first-principles atomistic simulations of very large systems and/or in long timescale.

The limits of molecular dynamics (MD) simulations of macromolecules are steadily pushed forward by the relentless developments of computer architectures and algorithms. This explosion in the number and extent (in size and time) of MD trajectories induces the need of automated and transferable methods to rationalise the raw data and make quantitative sense out of them. Recently, an algorithmic approach was developed by some of us to identify the subset of a protein's atoms, or mapping, that enables the most informative description of it. This method relies on the computation, for a given reduced representation, of the associated mapping entropy, that is, a measure of the information loss due to the simplification. Albeit relatively straightforward, this calculation can be time consuming. Here, we describe the implementation of a deep learning approach aimed at accelerating the calculation of the mapping entropy. The method relies on deep graph networks, which provide extreme flexibility in the input format. We show that deep graph networks are accurate and remarkably efficient, with a speedup factor as large as 10 5 with respect to the algorithmic computation of the mapping entropy. Applications of this method, which entails a great potential in the study of biomolecules when used to reconstruct its mapping entropy landscape, reach much farther than this, being the scheme easily transferable to the computation of arbitrary functions of a molecule's structure.

We report the development of a discontinuous spectral element flow solver that includes the implementation of both spectral difference and flux reconstruction formulations. With this high order framework, we have constructed a foundation upon which to provide a fair and accurate assessment of these two schemes in terms of accuracy, stability, and performance with special attention to the true spectral difference scheme and the modified spectral difference scheme recovered via the flux reconstruction formulation. Building on previous analysis of the spectral difference and flux reconstruction schemes, we provide a novel nonlinear stability analysis of the spectral difference scheme. Through various numerical experiments, we demonstrate the additional stability afforded by the true, baseline spectral difference scheme without explicit filtering or de-aliasing due to its inherent feature of staggered flux points. This arrangement leads to favorable suppression of aliasing errors and improves stability needed for under-resolved simulations of turbulent flows.

This paper focuses on the three-dimensional simulation of the photoionization in streamer discharges, and provides a general framework to efficiently and accurately calculate the photoionization model using the integral form. The simulation is based on the kernel-independent fast multipole method. The accuracy of this method is studied quantitatively for different domains and various pressures in comparison with other existing models based on partial differential equations (PDEs). The comparison indicates the numerical error of the fast multipole method is much smaller than those of other PDE-based methods, with the reference solution given by direct numerical integration. Such accuracy can be achieved with affordable computational cost, and its performance in both efficiency and accuracy is quite stable for different domains and pressures. Meanwhile, the simulation accelerated by the fast multipole method exhibits good scalability using up to 1280 cores, which shows its capability of three-dimensional simulations using parallel (distributed) computing. The difference of the proposed method and other efficient approximations are also studied in a three-dimensional dynamic problem where two streamers interact.

Recently, machine learning (ML) has been used to address the computational cost that has been limiting ab initio molecular dynamics (AIMD). Here, we present GNNFF, a graph neural network framework to directly predict atomic forces from automatically extracted features of the local atomic environment that are translationally-invariant, but rotationally-covariant to the coordinate of the atoms. We demonstrate that GNNFF not only achieves high performance in terms of force prediction accuracy and computational speed on various materials systems, but also accurately predicts the forces of a large MD system after being trained on forces obtained from a smaller system. Finally, we use our framework to perform an MD simulation of Li7P3S11, a superionic conductor, and show that resulting Li diffusion coefficient is within 14% of that obtained directly from AIMD. The high performance exhibited by GNNFF can be easily generalized to study atomistic level dynamics of other material systems.

Iterative solvers are widely used to accurately simulate physical systems. These solvers require initial guesses to generate a sequence of improving approximate solutions. In this contribution, we introduce a novel method to accelerate iterative solvers for physical systems with graph networks (GNs) by predicting the initial guesses to reduce the number of iterations. Unlike existing methods that aim to learn physical systems in an end-to-end manner, our approach guarantees long-term stability and therefore leads to more accurate solutions. Furthermore, our method improves the run time performance of traditional iterative solvers. To explore our method we make use of position-based dynamics (PBD) as a common solver for physical systems and evaluate it by simulating the dynamics of elastic rods. Our approach is able to generalize across different initial conditions, discretizations, and realistic material properties. Finally, we demonstrate that our method also performs well when taking discontinuous effects into account such as collisions between individual rods. Finally, to illustrate the scalability of our approach, we simulate complex 3D tree models composed of over a thousand individual branch segments swaying in wind fields. A video showing dynamic results of our graph learning assisted simulations of elastic rods can be found on the project website available at this http URL .

Next-generation high-power lasers that can be focused to intensities exceeding 10^23 W/cm^2 are enabling new physics and applications. The physics of how these lasers interact with matter is highly nonlinear, relativistic, and can involve lowest-order quantum effects. The current tool of choice for modeling these interactions is the particle-in-cell (PIC) method. In strong fields, the motion of charged particles and their spin is affected by radiation reaction. Standard PIC codes usually use Boris or its variants to advance the particles, which requires very small time steps in the strong-field regime to obtain accurate results. In addition, some problems require tracking the spin of particles, which creates a 9D particle phase space (x, u, s). Therefore, numerical algorithms that enable high-fidelity modeling of the 9D phase space in the strong-field regime are desired. We present a new 9D phase space particle pusher based on analytical solutions to the position, momentum and spin advance from the Lorentz force, together with the semi-classical form of RR in the Landau-Lifshitz equation and spin evolution given by the Bargmann-Michel-Telegdi equation. These analytical solutions are obtained by assuming a locally uniform and constant electromagnetic field during a time step. The solutions provide the 9D phase space advance in terms of a particle's proper time, and a mapping is used to determine the proper time step for each particle from the simulation time step. Due to the analytical integration, the constraint on the time step needed to resolve trajectories in ultra-high fields can be greatly reduced. We present single-particle simulations and full PIC simulations to show that the proposed particle pusher can greatly improve the accuracy of particle trajectories in 9D phase space for given laser fields. A discussion on the numerical efficiency of the proposed pusher is also provided.