Publications

The long-standing problem of predicting the electronic structure of matter on ultra-large scales (beyond 100,000 atoms) is solved with machine learning.

The focus of this project is to accelerate and transform the workflow of multiscale materials modeling by developing an integrated toolchain seamlessly combining DFT, SNAP, LAMMPS, (shown in Figure 1-1) and a machine-learning (ML) model that will more efficiently extract information from a smaller set of first-principles calculations. Our ML model enables us to accelerate first-principles data generation by interpolating existing high fidelity data, and extend the simulation scale by extrapolating high fidelity data (10² atoms) to the mesoscale (10⁴ atoms). It encodes the underlying physics of atomic interactions on the microscopic scale by adapting a variety of ML techniques such as deep neural networks (DNNs), and graph neural networks (GNNs). We developed a new surrogate model for density functional theory using deep neural networks. The developed ML surrogate is demonstrated in a workflow to generate accurate band energies, total energies, and density of the 298K and 933K Aluminum systems. Furthermore, the models can be used to predict the quantities of interest for systems with more number of atoms than the training data set. We have demonstrated that the ML model can be used to compute the quantities of interest for systems with 100,000 Al atoms. When compared with 2000 Al system the new surrogate model is as accurate as DFT, but three orders of magnitude faster. We also explored optimal experimental design techniques to choose the training data and novel Graph Neural Networks to train on smaller data sets. These are promising methods that need to be explored in the future.

In many recent applications, particularly in the field of atom-centered descriptors for interatomic potentials, tensor products of spherical harmonics have been used to characterize complex atomic environments. When coupled with a radial basis, the atomic cluster expansion (ACE) basis is obtained. However, symmetrization with respect to both rotation and permutation results in an overcomplete set of ACE descriptors with linear dependencies occurring within blocks of functions corresponding to particular generalized Wigner symbols. All practical applications of ACE employ semi-numerical constructions to generate a complete, fully independent basis. While computationally tractable, the resultant basis cannot be expressed analytically, is susceptible to numerical instability, and thus has limited reproducibility. Here we present a procedure for generating explicit analytic expressions for a complete and independent set of ACE descriptors. The procedure uses a coupling scheme that is maximally symmetric w.r.t. permutation of the atoms, exposing the permutational symmetries of the generalized Wigner symbols, and yields a permutation-adapted rotationally and permutationally invariant basis (PA-RPI ACE). Theoretical support for the approach is presented, as well as numerical evidence of completeness and independence. A summary of explicit enumeration of PA-RPI functions up to rank 6 and polynomial degree 32 is provided. The PA-RPI blocks corresponding to particular generalized Wigner symbols may be either larger or smaller than the corresponding blocks in the simpler rotationally invariant basis. Finally, we demonstrate that basis functions of high polynomial degree persist under strong regularization, indicating the importance of not restricting the maximum degree of basis functions in ACE models a priori.

Since the classical molecular dynamics simulator LAMMPS was released as an open source code in 2004, it has become a widely-used tool for particle-based modeling of materials at length scales ranging from atomic to mesoscale to continuum. Reasons for its popularity are that it provides a wide variety of particle interaction models for different materials, that it runs on any platform from a single CPU core to the largest supercomputers with accelerators, and that it gives users control over simulation details, either via the input script or by adding code for new interatomic potentials, constraints, diagnostics, or other features needed for their models. As a result, hundreds of people have contributed new capabilities to LAMMPS and it has grown from fifty thousand lines of code in 2004 to a million lines today. In this paper several of the fundamental algorithms used in LAMMPS are described along with the design strategies which have made it flexible for both users and developers. We also highlight some capabilities recently added to the code which were enabled by this flexibility, including dynamic load balancing, on-the-fly visualization, magnetic spin dynamics models, and quantum-accuracy machine learning interatomic potentials. Program Summary: Program Title: Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) CPC Library link to program files: https://doi.org/10.17632/cxbxs9btsv.1 Developer's repository link: https://github.com/lammps/lammps Licensing provisions: GPLv2 Programming language: C++, Python, C, Fortran Supplementary material: https://www.lammps.org Nature of problem: Many science applications in physics, chemistry, materials science, and related fields require parallel, scalable, and efficient generation of long, stable classical particle dynamics trajectories. Within this common problem definition, there lies a great diversity of use cases, distinguished by different particle interaction models, external constraints, as well as timescales and lengthscales ranging from atomic to mesoscale to macroscopic. Solution method: The LAMMPS code uses parallel spatial decomposition, distributed neighbor lists, and parallel FFTs for long-range Coulombic interactions [1]. The time integration algorithm is based on the Størmer-Verlet symplectic integrator [2], which provides better stability than higher-order non-symplectic methods. In addition, LAMMPS supports a wide range of interatomic potentials, constraints, diagnostics, software interfaces, and pre- and post-processing features. Additional comments including restrictions and unusual features: This paper serves as the definitive reference for the LAMMPS code. References: [1] S. Plimpton, Fast parallel algorithms for short-range molecular dynamics. J. Comp. Phys. 117 (1995) 1–19. [2] L. Verlet, Computer experiments on classical fluids: I. Thermodynamical properties of Lennard–Jones molecules, Phys. Rev. 159 (1967) 98–103.

The atomic cluster expansion is a general polynomial expansion of the atomic energy in multi-atom basis functions. Here we implement the atomic cluster expansion in the performant C++ code PACE that is suitable for use in large-scale atomistic simulations. We briefly review the atomic cluster expansion and give detailed expressions for energies and forces as well as efficient algorithms for their evaluation. We demonstrate that the atomic cluster expansion as implemented in PACE shifts a previously established Pareto front for machine learning interatomic potentials toward faster and more accurate calculations. Moreover, general purpose parameterizations are presented for copper and silicon and evaluated in detail. We show that the Cu and Si potentials significantly improve on the best available potentials for highly accurate large-scale atomistic simulations.

A data-driven framework is presented for building magneto-elastic machine-learning interatomic potentials (ML-IAPs) for large-scale spin-lattice dynamics simulations. The magneto-elastic ML-IAPs are constructed by coupling a collective atomic spin model with an ML-IAP. Together they represent a potential energy surface from which the mechanical forces on the atoms and the precession dynamics of the atomic spins are computed. Both the atomic spin model and the ML-IAP are parametrized on data from first-principles calculations. We demonstrate the efficacy of our data-driven framework across magneto-structural phase transitions by generating a magneto-elastic ML-IAP for α-iron. The combined potential energy surface yields excellent agreement with first-principles magneto-elastic calculations and quantitative predictions of diverse materials properties including bulk modulus, magnetization, and specific heat across the ferromagnetic–paramagnetic phase transition.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

We present a numerical modeling workflow based on machine learning which reproduces the total energies produced by Kohn-Sham density functional theory (DFT) at finite electronic temperature to within chemical accuracy at negligible computational cost. Based on deep neural networks, our workflow yields the local density of states (LDOS) for a given atomic configuration. From the LDOS, spatially resolved, energy-resolved, and integrated quantities can be calculated, including the DFT total free energy, which serves as the Born-Oppenheimer potential energy surface for the atoms. We demonstrate the efficacy of this approach for both solid and liquid metals and compare results between independent and unified machine-learning models for solid and liquid aluminum. Our machine-learning density functional theory framework opens up the path towards multiscale materials modeling for matter under ambient and extreme conditions at a computational scale and cost that is unattainable with current algorithms.

Abstract not provided.

Erosion of the beryllium first wall material in tokamak reactors has been shown to result in transport and deposition on the tungsten divertor. Experimental studies of beryllium implantation in tungsten indicate that mixed W-Be intermetallic deposits can form, which have lower melting temperatures than tungsten and can trap tritium at higher rates. To better understand the formation and growth rate of these intermetallics, cumulative molecular dynamics (MD) simulations of both high and low energy beryllium deposition in tungsten were performed. In both cases, a W-Be mixed material layer (MML) emerged at the surface within several nanoseconds, either through energetic implantation or a thermally-activated exchange mechanism, respectively. While some ordering of the material into intermetallics occurred, fully ordered structures did not emerge from the deposition simulations. Targeted MD simulations of the MML to further study the rate of Be diffusion and intermetallic growth rates indicate that for both cases, the gradual re-structuring of the material into an ordered intermetallic layer is beyond accessible MD time scales(≼1 μs). However, the rapid formation of the MML within nanoseconds indicates that beryllium deposition can influence other plasma species interactions at the surface and begin to alter the tungsten material properties. Therefore, beryllium deposition on the divertor surface, even in small amounts, is likely to cause significant changes in plasma-surface interactions and will need to be considered in future studies.

Abstract not provided.

Abstract not provided.

Atomistic simulations can capture physics of free expansion into two-phase region.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

Abstract not provided.

The atomic cluster expansion is a general polynomial expansion of the atomic energy in multi-atom basis functions. Here we implement the atomic cluster expansion in the performant C++ code PACE that is suitable for use in large scale atomistic simulations. We briefly review the atomic cluster expansion and give detailed expressions for energies and forces as well as efficient algorithms for their evaluation. We demonstrate that the atomic cluster expansion as implemented in PACE shifts a previously established Pareto front for machine learning interatomic potentials towards faster and more accurate calculations. Moreover, general purpose parameterizations are presented for copper and silicon and evaluated in detail. We show that the new Cu and Si potentials significantly improve on the best available potentials for highly accurate large-scale atomistic simulations.

Abstract not provided.