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Less is more: sampling chemical space with active learning

Justin S. Smith, Ben Nebgen, Nicholas Lubbers, Olexandr Isayev, Adrian E. Roitberg

arXiv:1801.09319v2physics.comp-phcs.LGphysics.chem-phstat.ML

TL;DR

Accurate, transferable ML potentials require effective training-data generation, but dataset design is poorly understood and often shaped by human selection. The paper automates dataset reduction and active learning with Query by Committee to sample unreliable regions of chemical space. The resulting ANI-1x potential achieves strong energy and force predictions across COMP6 with substantially less data than ANI-1.

  • Problem

    Training accurate and transferable ML potentials is challenging because the process of generating their training data is not well understood.

  • Method

    The method combines dataset reduction with Query by Committee, selecting new reference data where an ensemble of ANI models disagrees and validating on COMP6.

  • Results

    ANI-1x outperforms ANI-1 across all reported COMP6 properties using 5.5 million data points, 25% of ANI-1's 22 million.

  • Takeaways & Limitations

    Active learning produces a universal CHNO ANI potential with accurate energy and force predictions across the COMP6 benchmark using substantially reduced data.

Abstract

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The development of accurate and transferable machine learning (ML) potentials for predicting molecular energetics is a challenging task. The process of data generation to train such ML potentials is a task neither well understood nor researched in detail. In this work, we present a fully automated approach for the generation of datasets with the intent of training universal ML potentials. It is based on the concept of active learning (AL) via Query by Committee (QBC), which uses the disagreement between an ensemble of ML potentials to infer the reliability of the ensemble's prediction. QBC allows the presented AL algorithm to automatically sample regions of chemical space where the ML potential fails to accurately predict the potential energy. AL improves the overall fitness of ANAKIN-ME (ANI) deep learning potentials in rigorous test cases by mitigating human biases in deciding what new training data to use. AL also reduces the training set size to a fraction of the data required when using naive random sampling techniques. To provide validation of our AL approach we develop the COMP6 benchmark (publicly available on GitHub), which contains a diverse set of organic molecules. Through the AL process, it is shown that the AL-based potentials perform as well as the ANI-1 potential on COMP6 with only 10% of the data, and vastly outperforms ANI-1 with 25% the amount of data. Finally, we show that our proposed AL technique develops a universal ANI potential (ANI-1x) that provides accurate energy and force predictions on the entire COMP6 benchmark. This universal ML potential achieves a level of accuracy on par with the best ML potentials for single molecule or materials, while remaining applicable to the general class of organic molecules comprised of the elements CHNO.

I. INTRODUCTION

Universal molecular force fields remain difficult to develop because classical force fields use restrictive forms and tedious atom typing, while ML dataset design is often guided by human intuition. The paper proposes automated active-learning data generation using Query by Committee to target poorly predicted chemical-space regions.

  • Universal classical force fields remain elusive because restrictive functional forms and atom typing limit applicability across chemical systems.
  • ML potentials can bridge force-field speed and quantum-mechanical accuracy, but training datasets are often designed one chemical system at a time.
  • Human-driven dataset design tends to produce clustered, sparse, and incomplete data by favoring successful experiments over failed ones.
  • The proposed approach combines dataset reduction with Query by Committee selection of new training data and introduces the COMP6 benchmark for diverse CHNO molecules and non-covalent interactions.
  • QBC selects new reference data where ensemble models disagree beyond a preset criterion, targeting regions where the potential is likely inaccurate.
  • ρ̂ = 0.23 selected 58% of test data, whose energy RMSE was 7.4 kcal/mol for ρ > ρ̂ versus 1.5 kcal/mol for ρ ≤ ρ̂.

B. Automatic chemical space sampling via active learning

The automated workflow reduces an existing dataset, searches new molecular configurations, and samples non-equilibrium conformations. Query by Committee identifies molecules requiring reference quantum calculations for iterative training.

  • The workflow has three stages: existing-dataset reduction, configurational search, and conformational search.
  • Existing dataset reduction: Dataset reduction begins from a 2% random subsample and iteratively adds 2% subsets of fail cases until fewer than 5% of remaining data fail.
  • Configurational search: Configurational search samples external molecular databases, generated dimers, and dipeptides before 3D embedding and force-field optimization.
  • Configurational search: An ensemble of five ANI models computes ρ_i = σ_i/√N, and molecules with ρ_i > ρ̂ enter conformer sampling and receive reference QM optimization.
  • Conformational search: Conformational search generates non-equilibrium structures using diverse normal-mode sampling, random-trajectory sampling, and dimer sampling.
  • The final ANI-1x dataset contains 5.5 million structures, 25% of the 22-million-structure ANI-1 training set.

C. Development of the COMP6 benchmark suite

COMP6 is a diverse benchmark suite for evaluating ANI potentials across broad organic and biochemical chemical space, with six datasets spanning varied molecular sizes and conformational regimes.

  • Dataset characterization: Table 1 reports dataset composition using mean relative energy ranges and the benchmark’s actual energy prediction ranges in kcal/mol.
  • Benchmark composition: COMP6 comprises five new benchmarks plus the existing S66x850 noncovalent interaction benchmark for molecules containing C, N, O, and H.The new sets are GDB7to9, GDB10to13, Tripeptides, DrugBank, and ANI-MD.
  • Benchmark composition: The benchmark suite covers mean molecule sizes from 17 to 75 atoms, with the largest molecule containing 312 atoms.
  • Benchmark composition: S66x8 contains 66 dimeric systems representing hydrogen bonding, π-π stacking, London interactions, and mixed interactions.
  • Dataset construction: The ANI-MD subset uses 14 drug molecules and two small proteins, sampling 128 frames from each 1 ns vacuum molecular-dynamics trajectory.Reference DFT energies and forces are computed for the selected frames.
  • Dataset construction: GDB7to9, GDB10to13, Tripeptide, and DrugBank subsets use selected molecular structures followed by optimization, normal-mode calculations, and diverse normal-mode sampling.

D. Error metrics for validation on the COMP6 benchmark suite

Validation compares ANI potentials using potential energy, conformer energy differences, and atomic force components, with both MAE and RMSE reported to expose average errors and outliers.

  • Validation metrics: Three validation metrics are used: potential energy E, conformer energy difference ΔE, and atomic force component errors F.
  • Validation metrics: Conformer energy differences are computed between conformers i and j within each supplied conformer set k for a given model M.
  • Validation metrics: Atomic force error compares the x, y, and z components of every atom’s force vector across benchmark conformations.
  • Error reporting: MAE and RMSE are both reported because equal MAE values can conceal substantially different sensitivity to prediction outliers.

E. Property prediction with an ensemble of ANI models

ANI predictions use the mean of an ensemble of five models trained on five cross-validation splits, reducing energy, conformer-energy, and force errors across COMP6.

  • Ensemble prediction: All reported ANI potentials use the mean prediction from L=5 models trained on a 5-fold cross-validation split of the training dataset.
  • Ensemble prediction: The ensemble reduces COMP6 RMSE by 0.67 kcal/mol for E, 0.68 kcal/mol for ΔE, and 2.1 kcal/mol × Å−1 for F.These correspond to error reductions of 17%, 19%, and 28%, respectively.

III. RESULTS AND DISCUSSIONS

Active learning progressively improves ANI potentials across the diverse COMP6 benchmark while using substantially less training data than ANI-1. The final ANI-1x model predicts energies, conformer energy differences, and forces across broad molecular benchmarks, including ANI-MD.

  • Force prediction: ANI-1x predicts analytic, energy-conservative forces without direct force training, supporting its use in molecular dynamics simulations.Force comparisons use DFT reference calculations across the combined COMP6 trajectories.
  • Training efficiency: 2 million data points already let active-learned ANI potentials outperform ANI-1 across the entire COMP6 benchmark.At 5.5 million points, the active-learned potential is reported to outperform ANI-1 fivefold in energy RMSE.
  • Active-learning progression: 1.8 million conformations allow AL3 to statistically match or outperform ANI-1 on most metrics, despite ANI-1 containing 22 million conformations.AL3 sampled molecules with up to seven heavy atoms, whereas ANI-1 included larger molecules with up to eight heavy atoms.
  • COMP6 benchmark: 1.9/3.4 kcal/mol (E), 1.8/3.0 kcal/mol (∆E), and 3.1/5.3 kcal/mol × Å−1 (F) are ANI-1x’s MAE/RMSE errors across the complete COMP6 benchmark.These values cover the full benchmark energy range.
  • Training efficiency: 5.5 million training data points yield ANI-1x, which outperforms ANI-1 on all properties across all benchmarks using 25% of ANI-1’s 22 million points.The active-learned dataset is substantially smaller than the original ANI-1 dataset.

IV. CONCLUSIONS

The work introduces an automated active-learning workflow for generating training data and develops ANI-1x, a universal potential evaluated on the COMP6 benchmark. The workflow reduces dataset size while retaining broad energy and force-prediction accuracy.

  • IV. CONCLUSIONS: ANI-1x was developed through successive generations of active learning and achieves energy and force errors on the complete COMP6 benchmark.For points within 100 kcal/mol of energy minima, its MAE/RMSE values are 1.6/3.0 kcal/mol for E, 1.4/2.3 kcal/mol for ΔE, and 2.7/4.5 kcal/mol × Å−1 for F.
  • IV. CONCLUSIONS: The COMP6 suite contains six diverse benchmark test sets and is publicly available for comparing universal ML potentials.The suite uses ωB97x/6-31G(d) reference properties and reports exact error metrics for evaluation in the extrapolative regime.
  • IV. CONCLUSIONS: ANI-1x used fewer than 100 conformations per molecular configuration, compared with 400 for ANI-1, while matching the accuracy level of leading single-molecule or materials potentials.The passage contrasts this with single-system ML potentials that often require hundreds to thousands of conformations for one system.
  • IV. CONCLUSIONS: The authors attribute universal accuracy to neural networks learning low-level interactions from localized atomic-environment descriptors.They hypothesize that spatially localized descriptors within a cutoff contribute substantially to this capability.
  • IV. CONCLUSIONS: The workflow is presented as a building block for automated, data-driven discovery and for generating universal potentials across current and future ML models.Its stated scope includes accurate, transferable, and extensible ML potentials for a wide variety of models.

SUPPLEMENTARY INFORMATION

The supplementary information provides technical details, benchmark tables, model-cycle information, and author affiliation metadata. It also documents additional ANI-1x benchmark results across selected energy ranges.

  • SUPPLEMENTARY INFORMATION: The supplementary material contains complete technical details on neural-network ensemble training and sampling methods.These details are identified as sections S1.1 and S1.2.
  • SUPPLEMENTARY INFORMATION: Tables S1–S10 list individual and complete COMP6 benchmarks, while Table S11 details ANI potentials across active-learning cycles.Tables S12–S17 report ANI-1x COMP6 benchmarks within selected energy ranges.
  • SUPPLEMENTARY INFORMATION: The paper lists authors from the University of Florida, UNC Eshelman School of Pharmacy, and Los Alamos National Laboratory.The listed affiliations are in Gainesville, Chapel Hill, and Los Alamos, respectively.

S1 Methods

The methods train ANI ensembles using five-fold cross-validation and select model architectures as dataset sizes change during active learning. COMP6 benchmarks are used to assess ensemble fitness instead of a conventional held-out split.

  • S1 Methods: ANI network architectures vary with active-learning dataset size, with depth and parameter counts selected through hyperparameter searches at each sampling step.Atomic-environment-vector parameters remain constant during active learning.
  • S1 Methods: ANI ensembles are prepared using a five-fold cross-validation split so that the ensemble is trained across the entire dataset.The stated goal is maximum ensemble performance.
  • S1 Methods: COMP6 benchmarks determine ensemble fitness instead of testing models on a 10% held-out training subset.The method therefore evaluates ensemble predictions against the external COMP6 benchmark suite.

S1.2.1 Diverse Normal Mode Sampling (DNMS).

Diverse normal mode sampling generates non-equilibrium molecular conformations after quantum-mechanical optimization and frequency analysis. Query by committee then selects conformers whose ensemble disagreement exceeds a threshold for new quantum calculations.

  • S1.2.1 Diverse Normal Mode Sampling (DNMS).: DNMS begins by optimizing each molecule at the ωB97x/6-31G(d) quantum-mechanical level and calculating frequencies, normal-mode coordinates, and harmonic force constants.These quantities provide the basis for generating non-equilibrium conformations.
  • S1.2.1 Diverse Normal Mode Sampling (DNMS).: The modified normal mode sampling technique generates random non-equilibrium conformations to avoid clustering the dataset around equilibrium structures.The procedure follows normal mode sampling while changing the sampling behavior to reduce equilibrium-centered clustering.
  • S1.2.1 Diverse Normal Mode Sampling (DNMS).: Query by committee tests conformers from selected diverse structures and adds quantum-mechanical energies and forces when their disagreement exceeds the threshold ρ̂.The newly calculated data are added to the training set in the next active-learning iteration.

S1.2.2 K Random Trajectory Sampling (KRTS).

Random trajectory sampling generates molecular dynamics data while monitoring model uncertainty and terminating trajectories when uncertainty exceeds a threshold.

  • 300K Boltzmann-distributed velocities initialize Langevin molecular dynamics with a 0.25fs timestep.The system is then heated linearly to 1000K over 4ps.
  • The uncertainty measure ρ_i is evaluated every five dynamics steps during trajectory generation.Sampling uses seed molecules from the conformational sampling dataset.
  • Trajectories terminate when ρ_i exceeds the threshold ρ̂.

S1.2.3 MD Generated Dimer Sampling

The active-learning scheme samples dimers from molecular-dynamics trajectories of randomly arranged small molecules, then selects close-contact pairs for further processing. The benchmark tables report ANI potential errors across multiple COMP6 subsets and prediction targets.

  • Dimer generation: Hundreds of randomly selected small molecules are placed with random positions and orientations in a large box for active-learning sampling.The molecules are drawn from the conformational sampling set.
  • Dimer generation: Molecular dynamics at 300 K with periodic boundary conditions is run using the current ANI active-learned potential.The trajectory length is denoted X ps in the passage.
  • Dimer generation: After dynamics, the box is decomposed into all dimers with intermolecular distances below 5.0 Å.This distance criterion defines which molecular pairs are extracted from the simulated box.
  • Benchmark evaluation: COMP6 results compare active-learned ANI potentials with ANI-1 across conformer energy differences, potential energies, and force components.The comparisons cover combined and individual benchmark subsets, including DrugBank, tripeptides, GDB, S66x8, and ANI-MD.
  • Benchmark evaluation: ANI-MD evaluations also report ANI-1x errors against DFT references for 128 conformations per molecule, with some tables including prediction timings.The reported quantities include energy and force errors, and timing information for ANI-1x predictions.
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