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Register a new userComparing optimization strategies for force field parameterization
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Classical molecular dynamics (MD) simulations enable modeling of materials and examination of microscopic details that are not accessible experimentally. The predictive capability of MD relies on the force field (FF) used to describe interatomic interactions. FF parameters are typically determined to reproduce selected material properties computed from density functional theory (DFT) and/or measured experimentally. A common practice in parameterizing FFs is to use least-squares local minimization algorithms. Genetic algorithms (GAs) have also been demonstrated as a viable global optimization approach, even for complex FFs. However, an understanding of the relative effectiveness and efficiency of different optimization techniques for the determination of FF parameters is still lacking. In this work, we evaluate various FF parameter optimization schemes, using as example a training data set calculated from DFT for different polymorphs of Ir$O_2$. The Morse functional form is chosen for the pairwise interactions and the optimization of the parameters against the training data is carried out using (1) multi-start local optimization algorithms: Simplex, Levenberg-Marquardt, and POUNDERS, (2) single-objective GA, and (3) multi-objective GA. Using random search as a baseline, we compare the algorithms in terms of reaching the lowest error, and number of function evaluations. We also compare the effectiveness of different approaches for FF parameterization using a test data set with known ground truth (i.e generated from a specific Morse FF). We find that the performance of optimization approaches differs when using the Test data vs. the DFT data. Overall, this study provides insight for selecting a suitable optimization method for FF parameterization, which in turn can enable more accurate prediction of material properties and chemical phenomena.
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In this work, we present a highly accurate spectral neighbor analysis potential (SNAP) model for molybdenum (Mo) developed through the rigorous application of machine learning techniques on large materials data sets. Despite Mos importance as a structural metal, existing force fields for Mo based on the embedded atom and modified embedded atom methods still do not provide satisfactory accuracy on many properties. We will show that by fitting to the energies, forces and stress tensors of a large density functional theory (DFT)-computed dataset on a diverse set of Mo structures, a Mo SNAP model can be developed that achieves close to DFT accuracy in the prediction of a broad range of properties, including energies, forces, stresses, elastic constants, melting point, phonon spectra, surface energies, grain boundary energies, etc. We will outline a systematic model development process, which includes a rigorous approach to structural selection based on principal component analysis, as well as a differential evolution algorithm for optimizing the hyperparameters in the model fitting so that both the model error and the property prediction error can be simultaneously lowered. We expect that this newly developed Mo SNAP model will find broad applications in large-scale, long-time scale simulations.
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.
Abstract Machine learning models, trained on data from ab initio quantum simulations, are yielding molecular dynamics potentials with unprecedented accuracy. One limiting factor is the quantity of available training data, which can be expensive to obtain. A quantum simulation often provides all atomic forces, in addition to the total energy of the system. These forces provide much more information than the energy alone. It may appear that training a model to this large quantity of force data would introduce significant computational costs. Actually, training to all available force data should only be a few times more expensive than training to energies alone. Here, we present a new algorithm for efficient force training, and benchmark its accuracy by training to forces from real-world datasets for organic chemistry and bulk aluminum.
Thermal and other transport coefficients were recently shown to be largely independent of the microscopic representation of the energy (current) densities or, more generally, of the relevant conserved densities/currents. In this paper we show how this gauge invariance, which is intimately related to the intrinsic indeterminacy of the energy of isolated atoms, can be exploited to optimize the statistical properties of the current time series from which the transport coefficients can be evaluated. To this end, we make use of a variational principle that relies on the metric properties of the conserved currents, treated as elements of an abstract linear space. Different metrics would result in different variational principles. We finally show how a recently proposed data-analysis methodology based on the theory of transport in multi-component systems can be recovered by a suitable choice of this metric.
This work develops a new open source API and software package called textit{SymPhas} for simulations of phase-field, phase-field crystal and reaction-diffusion models, supporting up to three dimensions and an arbitrary number of fields. textit{SymPhas} delivers two novel program capabilities: 1) User specification of models from the associated dynamical equations in an unconstrained form and 2) extensive support for integrating user-developed discrete-grid-based numerical solvers into the API. The capability to specify general phase-field models is primarily achieved by developing a novel symbolic algebra functionality that can formulate mathematical expressions at compile time, is able to apply rules of symbolic algebra such as distribution, factoring and automatic simplification, and support user-driven expression tree manipulation. A modular design based on the CC++ template meta-programming paradigm is applied to the symbolic algebra library and general API implementation to minimize application runtime and increase the accessibility of the API for third party development. textit{SymPhas} is written in C/CC++ and emphasizes high-performance capabilities via parallelization with OpenMP and the CC++ standard library. textit{SymPhas} is equipped with a forward Euler solver and a semi-implicit Fourier spectral solver. Sample implementations and simulations of several phase-field models are presented, generated using the semi-implicit Fourier spectral solver.
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