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The MLIP package: Moment Tensor Potentials with MPI and Active Learning
Ivan S. Novikov, Konstantin Gubaev, Evgeny V. Podryabinkin, Alexander V. Shapeev
TL;DR
Constructing reliable machine-learning interatomic potentials requires effective training-set construction and control of configurations that lie beyond the training data. This paper presents MTPs with MLIP’s active-learning workflow and practical simulation examples, reporting reduced prediction error during active training, accurate phase-boundary and convex-hull results, and lower computational cost in an Ag-Pd example.
Problem
Training-set construction is time-consuming, and predictions can be poor for configurations far from the training set, potentially causing atomistic-simulation instability.
Method
The paper formulates MTPs and uses MLIP’s active-learning algorithms to select training configurations, including D-optimality and extrapolation-grade criteria.
Results
Active training reduced validation error from 13.5% to 12%; MTP predicted an Al phase-boundary temperature of 885 K, 3 K below accurate DFT, and achieved a 2 meV/atom error with less than 10% computational cost in the Ag-Pd example.
Takeaways & Limitations
MLIP provides a reproducible workflow for constructing MTPs and applying active learning to practical atomistic simulations.
Takeaways & Limitations
The cited approximation result does not cover every partitioning of total energy into local contributions, and the effect on the best partitioning remains unresolved.
Abstract
from arXiv · showhide
The subject of this paper is the technology (the "how") of constructing machine-learning interatomic potentials, rather than science (the "what" and "why") of atomistic simulations using machine-learning potentials. Namely, we illustrate how to construct moment tensor potentials using active learning as implemented in the MLIP package, focusing on the efficient ways to sample configurations for the training set, how expanding the training set changes the error of predictions, how to set up ab initio calculations in a cost-effective manner, etc. The MLIP package (short for Machine-Learning Interatomic Potentials) is available at https://mlip.skoltech.ru/download/.
1 Introduction
The paper situates moment tensor potentials within machine-learning interatomic potentials and focuses on constructing them with MLIP and active learning. It emphasizes automated training-set refinement, extrapolation-aware sampling, and practical atomistic simulation workflows.
- Machine-learning interatomic potentials: Machine-learning potentials use flexible functional forms to approximate quantum-mechanical interactions from atomic positions and types, subject to assumptions such as locality.They predict potential energy and its derivatives for variable-size atomic systems.
- Machine-learning interatomic potentials: Moment tensor potentials are polynomial-based, basis-function models and the main focus of this work’s machine-learning potential methodology.MTPs are presented alongside SNAP and other polynomial-based approaches; multicomponent extensions may go beyond linear regression.
- Scope and caveat: The paper notes that the claimed approximation result for two- and three-body descriptors does not cover every partitioning of total energy into local contributions.The effect on approximating the best partitioning remains to be investigated.
- Machine-learning interatomic potentials: MTPs, SOAP-GAP, ACE, and PIP can provably approximate arbitrary local interactions, while MTPs also show a balance between accuracy and computational efficiency.The cited benchmark comparisons report excellent accuracy for MTP and GAP, with MTP additionally showing a favorable accuracy-efficiency balance.
- Active learning: Training-set construction is a crucial, time-consuming step that active learning can automate instead of relying on manual trial-and-error refinement.The paper connects this approach to earlier learning-and-forgetting, learning-and-remembering, and query-by-committee strategies.
- Active learning: MLIP uses a D-optimality-based query strategy in which extrapolation grade identifies configurations that are extrapolative relative to the training set.The approach was proposed for linear single-component MTPs and generalized to nonlinear multicomponent MTPs.
- Paper scope: The manuscript formulates MTPs and active learning, describes the MLIP package, and demonstrates the methodology through three reproducible atomistic simulation examples.The examples target familiar but sufficiently advanced workflows, with files and data supplied in the supplemental information.
2 Theory
MTP represents atomic energies through invariant moment-tensor basis functions and fits its parameters to quantum-mechanical energies, forces, and stresses. Active learning uses extrapolation grades and D-optimality to automate training-set refinement and improve simulation stability.
- Moment Tensor Potential: MTP decomposes configuration energy into contributions from local atomic environments defined by atomic types and neighbor positions.Each neighborhood contains the central atom type, neighboring atom types, and relative positions.
- Moment Tensor Potential: Moment tensors combine radial basis functions with angular information from neighbor positions to construct descriptors of atomic neighborhoods.The radial basis is defined between Rmin and Rcut, while the angular part is formed from outer products of relative-position vectors.
- Moment Tensor Potential: MTP basis functions are contractions of moments and are invariant to atomic permutations, rotations, and reflections.The functional form includes all basis functions whose level does not exceed levmax.
- Moment Tensor Potential: The hyperparameters levmax and NQ control model complexity, accuracy, computational efficiency, and the number of required quantum-mechanical calculations.The number of basis functions grows exponentially with levmax, whereas radial-function and parameter counts scale as O(NQ levmax).
- Training on a quantum-mechanical database: Passive training fits MTP parameters to quantum-mechanical energies, forces, and stresses, with configurable weights and validation errors used to assess prediction quality.A held-out validation or test set provides an error estimate less affected by overfitting.
- Active learning: Active learning replaces manual trial-and-error training-set construction with extrapolation-grade selection based on D-optimality and maximal-volume active configurations.The two-threshold scheme selects configurations beyond γselect and terminates simulations beyond γbreak; iterations extend the training region and improve MTP stability.
3 MLIP Package
MLIP is a software package for constructing and using moment tensor potentials, offering parallel training and relaxation alongside serial tools for data conversion, evaluation, active-learning selection, and configuration relaxation.
- Package overview: MLIP implements moment tensor potentials and is distributed free for non-commercial purposes.The package is available from the MLIP website.
- Package overview: The package provides a library interface, notably for LAMMPS, and an mlp binary for basic operations.The binary supports conversion, training, distance checks, energy-force-stress evaluation, extrapolation grading, configuration selection, and relaxation.
- Active learning and datasets: The select-add command chooses a limited number of extrapolative configurations from a large set for addition to the training set.This supports active-learning dataset expansion.
- Package overview: The relax command minimizes the potential energy of configurations using MLIP’s internal structure-relaxation algorithm.It operates on configurations supplied in a file.
- Execution and configuration: Training and relaxation use MPI parallelism, while the remaining commands are serial; untrained MTPs are provided at levels 2 through 28.The package behavior is controlled through an MLIP settings file, commonly mlip.ini, which specifies potentials and active-learning thresholds.
4 Example 1: Elastic Constants of Molybdenum
A five-potential MTP ensemble was trained for bcc-Mo and used to estimate prediction uncertainty. Its lattice constant and elastic constants agree closely with DFT, with DFT values within the MTP 95% confidence intervals; LAMMPS cross-checks differ by 0–2 GPa.
- Training and validation: Five MTPs with level 16, eight radial basis functions, Rcut = 5.2 Å, and Rmin = 1.9 Å were trained to estimate prediction uncertainty.Training and test configurations were filtered using a 1.9 Å minimum interatomic distance.
- Training and validation: Training and validation RMS errors were close, while their 95% confidence uncertainty was small, indicating reliable training.The ensemble was generated by repeating training with different random parameter initialization.
- Energy-volume curve: 3.15928 ± 0.00097 Å was the MTP lattice constant, while the DFT value was 3.15918 Å and fell within the MTP confidence interval.The energy-volume curve was computed from energies evaluated on compressed and stretched bcc-Mo configurations.
- Elastic constants: The MTP and DFT elastic constants C11, C12, and C44 were close, with the DFT constants well within the MTP 95% confidence interval.MTP stresses used calc-efs, while DFT stresses used VASP, after applying ±2% strains to individual unit-cell components.
- Elastic constants: 0–2 GPa was the difference between LAMMPS and finite-difference elastic-constant results for the trained MTP.The LAMMPS in.elastic script was adapted by declaring the MLIP pair_style and assigning the MTP settings file.
5 Example 2: Melting point of Aluminum
The aluminum example demonstrates an on-the-fly active-learning workflow that iteratively selects extrapolative MD configurations, evaluates them with DFT, and refits the MTP. Expanding the training set chiefly improves simulation reliability, while higher-fidelity data substantially reduces prediction error.
- Active-learning workflow: The workflow prepares an active-learning state, runs MD with extrapolation detection, selects representative configurations, computes DFT labels, and refits the potential.Selection maximizes a determinant and keeps the selected set below the number of potential parameters; failed DFT configurations can be selected again.
- Initialization: The initial training set is sampled from a 90-fs VASP MD trajectory, with every tenth configuration retained to reduce correlation.The trajectory uses a 108-atom fcc aluminum cell at 900 K, Γ-point integration, and a 410 eV energy cutoff.
- Stage 1a: 225 configurations were actively selected by the 58th iteration, after which a 10-ps MD simulation produced no extrapolative configurations.The same initial velocities were reused across iterations solely to illustrate the gradual increase in reliable MD time.
- Stage 1a: 13.5% to 12%: validation error changed only slightly, while reliability increased from 0 to 100% after 235 training configurations.The initial 10 configurations already supplied 1080 forces and a good validation error, but additional configurations were needed for perfect simulation reliability.
- Higher-fidelity data: 17% to 4.5%: improving the k-point accuracy reduced the error, showing that Stage 1 error was largely caused by k-point noise.The resulting high-accuracy calculation gave an aluminum melting point of 885 K, 3 K below the cited extremely accurate DFT value.
6 Example 3: Stable convex hull of Ag-Pd structures
The Ag-Pd example applies active learning to relaxation trajectories from a large, general candidate pool and constructs a convex hull from the resulting MTP energies. MTP reproduces the DFT ground-state structures while requiring substantially fewer expensive calculations.
- Candidate structures: The study generates 39k Ag-Pd crystal structures with up to 12 atoms across fcc, bcc, and hcp lattices and varying compositions.These structures form a general candidate pool for active-learning relaxation.
- Active-learning relaxation: Active learning uses MLIP relaxations of candidate structures, stopping trajectories when extrapolative configurations occur and retaining successfully relaxed structures.The final relaxed configurations provide MTP energies for formation-energy and convex-hull construction.
- Accuracy: 442 configurations yielded MTP energy MAE and RMSE values of 1.9 meV/atom and 2.4 meV/atom, respectively.The reported error could cause some ground-state structures to lie slightly above the MTP-based convex hull.
- Convex-hull comparison: MTP included all DFT ground-state structures despite the 2 meV/atom RMS energy error, while also producing extra structures from broader compositional coverage.The comparison used 302 Aflow candidate structures relaxed with DFT; post-relaxation can remove MTP errors when complete elimination is needed.
- Computational savings: 442 static calculations were cheaper than 302 relaxations, while training and relaxing 39k samples cost less than 10% and produced a 2 meV/atom error.The paper compares these costs with repeated DFT relaxations and notes that the error is comparable to differences from pseudopotentials or convergence settings.
7 Concluding Remarks
The paper presents MTP formulation, active learning, and MLIP implementation through three reproducible atomistic examples. Its emphasis is practical: showing how to construct training sets and apply the workflow to realistic simulations.
- Scope and contribution: The manuscript formulates MTPs and active learning, describes the MLIP code, and gives three detailed examples of atomistic simulations.The examples are designed to be reproducible and include components relevant to computational materials science.
- Practical emphasis: The examples focus on practical methodology, including configuration sampling, training-set refinement, and application of MTPs with active learning.Supplemental materials provide files needed to reproduce the examples.