Source-linked AI summary
Accelerating high-throughput searches for new alloys with active learning of interatomic potentials
Konstantin Gubaev, Evgeny V. Podryabinkin, Gus L. W. Hart, Alexander V. Shapeev
TL;DR
Stable-phase searches for multicomponent alloys are constrained by the cost of DFT calculations and by methods limited to particular lattice types. The paper combines a general machine-learning interatomic potential with active learning to select training data automatically and optimize structures using the potential. Across Cu-Pd, Co-Nb-V, and Al-Ni-Ti, it reports substantially faster searches and previously unreported stable structures relative to AFLOW.
Problem
DFT is the bottleneck in exhaustive materials searches, while cluster expansion and standard machine-learning surrogates lack broad applicability across structure types.
Method
The method uses moment tensor potentials to approximate quantum-mechanical energies and active learning to generate and refine training data automatically during structural equilibration.
Results
Three to four orders of magnitude faster than high-throughput DFT, the method found new stable structures in Cu-Pd, Co-Nb-V, and Al-Ni-Ti.
Takeaways & Limitations
The approach explores candidate structures using fast potential-based relaxations and broadens alloy-phase discovery beyond structures represented in the training data.
Abstract
from arXiv · showhide
We propose an approach to materials prediction that uses a machine-learning interatomic potential to approximate quantum-mechanical energies and an active learning algorithm for the automatic selection of an optimal training dataset. Our approach significantly reduces the amount of DFT calculations needed, resorting to DFT only to produce the training data, while structural optimization is performed using the interatomic potentials. Our approach is not limited to one (or a small number of) lattice types (as is the case for cluster expansion, for example) and can predict structures with lattice types not present in the training dataset. We demonstrate the effectiveness of our algorithm by predicting the convex hull for the following three systems: Cu-Pd, Co-Nb-V, and Al-Ni-Ti. Our method is three to four orders of magnitude faster than conventional high-throughput DFT calculations and explores a wider range of materials space. In all three systems, we found unreported stable structures compared to the AFLOW database. Because our method is much cheaper and explores much more of materials space than high-throughput methods or cluster expansion, and because our interatomic potentials have a systematically improvable accuracy compared to empirical potentials such as EAM, etc., it will have a significant impact in the discovery of new alloy phases, particularly those with three or more components.
I. INTRODUCTION
Stable-phase prediction in multicomponent alloys is limited by the cost of DFT energy evaluations and by surrogate methods tied to restricted structure types. The paper addresses this with general interatomic potentials and active learning that builds training data during structural equilibration.
- DFT energy evaluations remain the bottleneck in materials-prediction workflows, making exhaustive structural searches impractical.
- Cluster expansion performs well for derivatives of particular lattices but is unsuitable when stable structures fall outside those lattice types.
- The approach combines a completely general interatomic-potential form with active learning that generates and refines the training set.
- The model reproduces DFT for off-equilibrium structures without restricting them to a particular lattice and learns interactions on-the-fly during equilibration.
- The method extends moment tensor potentials and active learning to atomistic configurations containing multiple element types.
- Active learning is presented as the mechanism that makes machine-learning interatomic potentials practical for accelerating computational materials discovery.
A. Machine-learning potentials
The moment tensor potential represents energy through local atomic neighborhoods, using symmetry-preserving descriptors and a systematically expandable basis of many-body terms. Its multicomponent radial functions encode species-dependent local environments while model complexity grows less than quadratically with the number of species.
- The potential parameters are fitted by minimizing a loss that brings predicted energies close to reference quantum-mechanical energies.
- The model partitions total energy E into local contributions V(ni) from individual atomic neighborhoods.
- Each neighborhood is described by neighboring-atom positions and chemical types, with interactions truncated beyond a cutoff distance Rcut usually around 5 Å.
- Moment tensor descriptors and their scalar contractions encode rotational, translational, and permutation symmetries while representing higher-order many-body terms.
- Increasing levmax adds basis functions with higher-body contributions, giving the potential a systematically improvable functional form.
- Species-dependent radial functions distinguish central and neighboring atom types, while their parameter count grows less than quadratically with the number of species.
B. Active Learning
Active learning constructs representative training sets by detecting extrapolation and selecting configurations that maximize information for fitting the interatomic potential. This keeps relaxation trajectories within the model’s interpolative domain.
- Motivation: A good training set includes representative structures so the potential avoids extrapolation while searching for stable phases.For flexible MTPs, severe extrapolation can produce highly unphysical structures during relaxation.
- Selection criterion: The generalized D-optimality criterion selects an m × m training-set submatrix with maximal determinant volume.This criterion is generalized to models with nonlinear parameter dependence.
- Selection criterion: For a candidate configuration, the extrapolation grade γ(x∗) measures the maximal determinant growth possible when that configuration is added.The maxvol algorithm is used to compute this grade in practice.
- Selection criterion: A configuration is added when γ(x∗) ≥ γtsh, where the threshold controls how much extrapolation is allowed.The threshold satisfies γtsh ≥ 1.
- Effect: Active learning detects extrapolative structures and trains on them, keeping structures encountered during relaxation interpolative with respect to the training set.The algorithm selects configurations arising during relaxation, while it can also optimize a predefined configuration set.
C. Algorithm
The algorithm repeatedly relaxes candidate structures with an MTP, adds configurations where extrapolation is detected, selects representative examples, and refits the potential until relaxations converge. Refitting remains a small fraction of the time spent on ab initio calculations.
- Inputs: The algorithm accepts a broad, diverse candidate-structure set and initializes a randomly parameterized MTP with an empty training set.The broader candidate set is possible because the approach is not restricted to DFT-only evaluation.
- Inputs: DFT, implemented in VASP 5.4.1, supplies the quantum-mechanical reference model used by the algorithm.The quantum-mechanical model is denoted Eqm(x).
- Relaxation: Two thresholds govern extrapolation: γtsh triggers training-set addition, while the larger Γtsh terminates relaxation when predictions are unreliable.They satisfy Γtsh > γtsh > 1.
- Relaxation: Each candidate is relaxed with the current MTP until it either converges or encounters a configuration on which the potential extrapolates.Extrapolative configurations terminate the relaxation and enter the preselected set.
- Selection and refitting: The algorithm uses D-optimality to reduce potentially hundreds of thousands of preselected configurations to up to a few hundred representative training examples.This extends the MTP’s training domain before refitting.
- Selection and refitting: Step 3 refits the MTP on the updated training set, and steps 1–3 repeat until all relaxations converge.Although refitting takes longer as the training set grows, it remains a small fraction of ab initio calculation time.
- Algorithm name: The repeated refitting during relaxation is termed “relaxation while learning on-the-fly”.The training set is dynamically updated during the relaxation process.
III. RESULTS AND DISCUSSION
The algorithm was tested on binary and ternary alloy systems using active learning to construct convex hulls while limiting expensive DFT calculations. It reproduced known stable phases and identified structures below the AFLOW convex hull.
- Cu-Pd system: Cu-Pd tested whether the MTP could handle multiple lattice types, including fcc elemental structures and a bcc-derived equimolar phase.The candidate pool contained 40,000 unrelaxed bcc, fcc, and hcp configurations.
- Cu-Pd system: A structure at 16.6% Pd was 0.5 meV/atom below AFLOW’s convex hull and was absent from the AFLOW library.Both hulls were post-relaxed with DFT using identical settings for direct comparison.
- Cu-Pd system: The MTP reproduced the stable phases in AFLOW while evaluating the 40,000-candidate Cu-Pd search with 523 single-point DFT calculations.Relaxing all candidates with DFT was estimated to require about 10,000 times more computing time.
- Co-Nb-V system: Co-Nb-V yielded a new Co3Nb2V structure 50 meV/atom below the AFLOW convex hull, with geometry unlike any initial-pool structure.The search covered about 27,000 bcc-like and close-packed candidates.
- Al-Ni-Ti system: The final Al-Ni-Ti DFT hull retained all AFLOW structures and added three new MTP-discovered structures, all Ni-rich.The new structures’ levels below the AFLOW convex hull were computed using DFT.
IV. CONCLUSIONS
The MTP-based algorithm constructs alloy convex hulls by approximating ab initio energies, forces, and stresses while active learning automatically builds the training set. Across Cu-Pd, Co-Nb-V, and Al-Ni-Ti, it explored large candidate spaces, used far fewer DFT calculations, and found stable structures absent from AFLOW.
- MTPs approximate ab initio energies, forces, and stresses for fast atomistic calculations, while active learning automatically constructs the training set.The method was applied to Cu-Pd, Co-Nb-V, and Al-Ni-Ti convex-hull construction.
- Three to four orders of magnitude speedup over high-throughput DFT enabled exploration of 40,000 Cu-Pd, 27,000 Co-Nb-V, and 377,000 Al-Ni-Ti candidates.Only about 1% of relaxed configurations required single-point DFT calculations for training-data generation.
- Co-Nb-V: The Co-Nb-V search discovered Co3Nb2V, a structure 50 meV/atom below the AFLOW convex-hull level and geometrically unlike the initial candidate structures.Its discovery required no similar crystal prototype in the initial pool.
- Al-Ni-Ti: The Al-Ni-Ti MTP convex hull retained all AFLOW structures and added three newly discovered stable structures.The newly discovered structures were all Ni-rich, and their positions below the AFLOW hull were computed using DFT.