arXiv subjects

Alexander Shapeev

Publications and source records attributed to Alexander Shapeev.

28 records · Page 2Linked to original sources

arXiv2021

Magnetic Moment Tensor Potentials for collinear spin-polarized materials reproduce different magnetic states of bcc Fe

We present the magnetic Moment Tensor Potentials (mMTPs), a class of machine-learning interatomic potentials, accurately reproducing both vibrational and magnetic degrees of freedom as provided, e.g., from first-principles calculations. The accuracy is achieved by a two-step minimization scheme that coarse-grains the atomic and the spin space. The performance of the mMTPs is demonstrated for the prototype magnetic system bcc iron, with applications to phonon calculations for different magnetic states, and molecular dynamics simulations with fluctuating magnetic moments.

physics.atom-ph↗

arXiv2021

Machine-learning potentials enable predictive $\textit{and}$ tractable high-throughput screening of random alloys

We present an automated procedure for computing stacking fault energies in random alloys from large-scale simulations using moment tensor potentials (MTPs) with the accuracy of density functional theory (DFT). To that end, we develop an algorithm for training MTPs on random alloys. In the first step, our algorithm constructs a set of ~10000 or more training candidate configurations with 50-100 atoms that are representative for the atomic neighborhoods occurring in the large-scale simulation. In the second step, we use active learning to reduce this set to ~100 most distinct configurations - for which DFT energies and forces are computed and on which the potential is ultimately trained. We validate our algorithm for the MoNbTa medium-entropy alloy by showing that the MTP reproduces the DFT $\frac{1}{4}[111]$ unstable stacking fault energy over the entire compositional space up to a few percent. Contrary to state-of-the-art methods, e.g., the coherent potential approximation (CPA) or special quasi-random structures (SQSs), our algorithm naturally accounts for relaxation, is not limited by DFT cell sizes, and opens opportunities to efficiently investigate follow-up problems, such as chemical ordering. In a broader sense, our algorithm can be easily modified to compute related properties of random alloys, for instance, misfit volumes, or grain boundary energies. Moreover, it forms the basis for an efficient construction of MTPs to be used in large-scale simulations of multicomponent systems.

cond-mat.mtrl-sci↗

arXiv2021

Free energy of (CoxMn1-x)3O4 mixed phases from machine-learning-enhanced ab initio calculations

(CoxMn1-x)3O4 is a promising candidate material for solar thermochemical energy storage. A high-temperature model for this system would provide a valuable tool for evaluating its potential. However, predicting phase diagrams of complex systems with ab initio calculations is challenging due to the varied sources affecting the free energy, and with the prohibitive amount of configurations needed in the configurational entropy calculation. In this work, we compare three different machine learning (ML) approaches for sampling the configuration space of (CoxMn1-x)3O4, including a simpler ML approach, which would be suitable for application in high-throughput studies. We use experimental data for a feature of the phase diagram to assess the accuracy of model predictions. We find that with some methods, data pre-treatment is needed to obtain accurate predictions due to inherently composition-imbalanced training data for a mixed phase. We highlight that the important entropy contributions depend on the physical regimes of the system under investigation and that energy predictions with ML models are more challenging at compositions where there are energetically competing ground state crystal structures. Similar methods to those outlined here can be used to screen other candidate materials for thermochemical energy storage

cond-mat.mtrl-sci↗

arXiv2020

In operando active learning of interatomic interaction during large-scale simulations

A well-known drawback of state-of-the-art machine-learning interatomic potentials is their poor ability to extrapolate beyond the training domain. For small-scale problems with tens to hundreds of atoms this can be solved by using active learning which is able to select atomic configurations on which a potential attempts extrapolation and add them to the ab initio-computed training set. In this sense an active learning algorithm can be viewed as an on-the-fly interpolation of an ab initio model. For large-scale problems, possibly involving tens of thousands of atoms, this is not feasible because one cannot afford even a single density functional theory computation with such a large number of atoms. This work marks a new milestone toward fully automatic ab initio-accurate large-scale atomistic simulations. We develop an active learning algorithm that identifies local subregions of the simulation region where the potential extrapolates. Then the algorithm constructs periodic configurations out of these local, non-periodic subregions, sufficiently small to be computable with plane-wave density functional theory codes, in order to obtain accurate ab initio energies. We benchmark our algorithm on the problem of the screw dislocation motion in bcc tungsten and show that our algorithm reaches ab initio accuracy, down to typical magnitudes of numerical noise in DFT codes. We show that our algorithm reproduces material properties such as core structure, Peierls barrier, and Peierls stress. This unleashes new capabilities for computational materials science toward applications which have currently been out of scope if approached solely by ab initio methods.

physics.comp-ph↗

arXiv2019

Impact of lattice relaxations on phase transitions in a high-entropy alloy studied by machine-learning potentials

Recently, high-entropy alloys (HEAs) have attracted wide attention due to their extraordinary materials properties. A main challenge in identifying new HEAs is the lack of efficient approaches for exploring their huge compositional space. Ab initio calculations have emerged as a powerful approach that complements experiment. However, for multicomponent alloys existing approaches suffer from the chemical complexity involved. In this work we propose a method for studying HEAs computationally. Our approach is based on the application of machine-learning potentials based on ab initio data in combination with Monte Carlo simulations. The high efficiency and performance of the approach are demonstrated on the prototype bcc NbMoTaW HEA. The approach is employed to study phase stability, phase transitions, and chemical short-range order. The importance of including local relaxation effects is revealed: they significantly stabilize single-phase formation of bcc NbMoTaW down to room temperature. Finally, a so-far unknown mechanism that drives chemical order due to atomic relaxation at ambient temperatures is discovered.

cond-mat.mtrl-sci↗

arXiv2019

Ab initio vibrational free energies including anharmonicity for multicomponent alloys

A density-functional-theory based approach to efficiently compute numerically exact vibrational free energies - including anharmonicity - for chemically complex multicomponent alloys is developed. It is based on a combination of thermodynamic integration and a machine-learning potential. We demonstrate the performance of the approach by computing the anharmonic free energy of the prototypical five-component VNbMoTaW refractory high entropy alloy.

cond-mat.mtrl-sci↗

arXiv2019

Deeper Connections between Neural Networks and Gaussian Processes Speed-up Active Learning

Active learning methods for neural networks are usually based on greedy criteria which ultimately give a single new design point for the evaluation. Such an approach requires either some heuristics to sample a batch of design points at one active learning iteration, or retraining the neural network after adding each data point, which is computationally inefficient. Moreover, uncertainty estimates for neural networks sometimes are overconfident for the points lying far from the training sample. In this work we propose to approximate Bayesian neural networks (BNN) by Gaussian processes, which allows us to update the uncertainty estimates of predictions efficiently without retraining the neural network, while avoiding overconfident uncertainty prediction for out-of-sample points. In a series of experiments on real-world data including large-scale problems of chemical and physical modeling, we show superiority of the proposed approach over the state-of-the-art methods.

cs.LG↗

arXiv2018

Dropout-based Active Learning for Regression

Active learning is relevant and challenging for high-dimensional regression models when the annotation of the samples is expensive. Yet most of the existing sampling methods cannot be applied to large-scale problems, consuming too much time for data processing. In this paper, we propose a fast active learning algorithm for regression, tailored for neural network models. It is based on uncertainty estimation from stochastic dropout output of the network. Experiments on both synthetic and real-world datasets show comparable or better performance (depending on the accuracy metric) as compared to the baselines. This approach can be generalized to other deep learning architectures. It can be used to systematically improve a machine-learning model as it offers a computationally efficient way of sampling additional data.

cs.LG↗

arXiv2017

Accurate representation of formation energies of crystalline alloys with many components

In this paper I propose a new model for representing the formation energies of multicomponent crystalline alloys as a function of atom types. In the cases when displacements of atoms from their equilibrium positions are not large, the proposed method has a similar accuracy as the state-of-the-art cluster expansion method, and a better accuracy when the fitting dataset size is small. The proposed model has only two tunable parameters - one for the interaction range and one for the interaction complexity.

physics.comp-ph↗

arXiv2013

(In-)Stability and Stabilisation of QNL-Type Atomistic-to-Continuum Coupling Methods

We study the stability of ghost force-free energy-based atomistic-to-continuum coupling methods. In 1D we essentially complete the theory by introducing a universally stable a/c coupling as well as a stabilisation mechanism for unstable coupling schemes. We then present a comprehensive study of a two-dimensional scalar planar interface setting, as a step towards a general 2D/3D vectorial analysis. Our results point out various new challenges. For example, we find that none of the ghost force-free methods known to us are universally stable (i.e., stable under general interaction and general loads). We then explore to what extent our 1D stabilisation mechanism can be extended.

math.NA↗