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Machine learning potentials for complex aqueous systems made simple

Christoph Schran, Fabian L. Thiemann, Patrick Rowe, Erich A. Müller, Ondrej Marsalek, Angelos Michaelides

arXiv:2106.00048v2physics.chem-ph

TL;DR

Complex aqueous systems require accurate simulations beyond AIMD’s accessible scales, while broadly transferable potentials can be difficult and costly to develop. This work builds state-specific C-NNPs through active learning and automated validation, then applies them to extended simulations. Across six systems, the models reproduce reference structural, dynamical, and force properties and reveal detailed interfacial water behavior on rutile TiO2(110).

  • Problem

    Complex aqueous systems need accurate atomistic insight, but AIMD has limited time and length scales and highly general machine-learning potentials can require extensive development.

  • Method

    The framework constructs committee neural network potentials from a reference simulation using data-driven active learning, intrinsic error estimates, and automated validation at a selected thermodynamic condition.

  • Results

    Across six aqueous systems, the models reproduce RDF scores of 100 to 98%, VDOS scores of 98 to 96%, and force scores of 95 to 86%, while extended TiO2 simulations resolve structured and immobile interfacial water.

  • Takeaways & Limitations

    State-specific C-NNPs provide a straightforward way to extend simulation time and length scales for complex aqueous and solid-liquid systems.

  • Takeaways & Limitations

    The study is limited to aqueous systems with four species and does not explore reactive processes.

Abstract

from arXiv · show

Simulation techniques based on accurate and efficient representations of potential energy surfaces are urgently needed for the understanding of complex aqueous systems such as solid-liquid interfaces. Here, we present a machine learning framework that enables the efficient development and validation of models for complex aqueous systems. Instead of trying to deliver a globally-optimal machine learning potential, we propose to develop models applicable to specific thermodynamic state points in a simple and user-friendly process. After an initial ab initio simulation, a machine learning potential is constructed with minimum human effort through a data-driven active learning protocol. Such models can afterwards be applied in exhaustive simulations to provide reliable answers for the scientific question at hand. We showcase this methodology on a diverse set of aqueous systems with increasing degrees of complexity. The systems chosen here comprise bulk water with different ions in solution, water on a titanium dioxide surface, as well as water confined in nanotubes and between molybdenum disulfide sheets. Highlighting the accuracy of our approach with respect to the underlying ab initio reference, the resulting models are evaluated in detail with an automated validation protocol that includes structural and dynamical properties and the precision of the force prediction of the models. Finally, we demonstrate the capabilities of our approach for the description of water on the rutile titanium dioxide (110) surface to analyze the structure and mobility of water on this surface. Such machine learning models provide a straightforward and uncomplicated but accurate extension of simulation time and length scales for complex systems.

RAPID DEVELOPMENT OF COMMITTEE NEURAL NETWORK POTENTIALS

The framework rapidly develops committee neural network potentials from a reference AIMD trajectory through automated active learning and validation. Models are tailored to specific thermodynamic conditions, trading generality for efficient, user-friendly construction and extended simulations.

  • RAPID DEVELOPMENT OF COMMITTEE NEURAL NETWORK POTENTIALS: Committee neural network potentials combine independently trained NNPs whose averaged prediction improves performance while disagreement estimates model error.The disagreement can be scaled against validation error to provide an objective accuracy estimate.
  • RAPID DEVELOPMENT OF COMMITTEE NEURAL NETWORK POTENTIALS: A small-scale AIMD trajectory is used to sample the target system and thermodynamic condition before model construction.AIMD trajectories of 30 ps were sufficient in practice for this initial sampling.
  • RAPID DEVELOPMENT OF COMMITTEE NEURAL NETWORK POTENTIALS: Active learning iteratively adds configurations with the highest committee disagreement to the training set, beginning from 20 randomly selected structures and adding 20 queried configurations.This procedure aims to provide a varied training set for an accurate and robust model.
  • RAPID DEVELOPMENT OF COMMITTEE NEURAL NETWORK POTENTIALS: The protocol uses systematic atomic descriptors and fixed hyperparameters so users mainly provide a reference trajectory for the chosen conditions.The resulting C-NNP can be obtained without further adjustments and in a short time.
  • RAPID DEVELOPMENT OF COMMITTEE NEURAL NETWORK POTENTIALS: C-NNPs extend simulations near the sampled state point at orders-of-magnitude lower computational cost than the ab initio reference.Committee disagreement remains available during simulation as an intrinsic validity monitor, while the state-dependent design sacrifices generality for speed and simplicity.
  • RAPID DEVELOPMENT OF COMMITTEE NEURAL NETWORK POTENTIALS: The workflow produced six aqueous-system models from AIMD structures alone, spanning bulk, interface, and confinement environments with up to four elements.The electronic-structure reference method remains an important user choice because model quality depends on it.

AUTOMATED QUALITY ASSESSMENT OF COMMITTEE NEURAL NETWORK POTENTIALS

An automated validation protocol compares six C-NNP models with their ab initio references using structural, dynamical, and force-prediction properties. The models reproduce the tested properties accurately enough to support substantially extended simulations and detailed analysis.

  • AUTOMATED QUALITY ASSESSMENT OF COMMITTEE NEURAL NETWORK POTENTIALS: The automated protocol evaluates structural properties, dynamical properties, and force-prediction precision for each model.It condenses these tests into an efficient summary of model accuracy.
  • AUTOMATED QUALITY ASSESSMENT OF COMMITTEE NEURAL NETWORK POTENTIALS: RDF scores range from 100 to 98%, VDOS scores from 98 to 96%, and force scores from 95 to 86% across all six systems.The fluoride/water model’s individual RDF, VDOS, and force-correlation functions illustrate how the aggregate scores are formed.
  • AUTOMATED QUALITY ASSESSMENT OF COMMITTEE NEURAL NETWORK POTENTIALS: Additional tests for confined water and water on TiO2 show good agreement in density profiles, hydrogen bonding, and interfacial water orientation.These tests examine global structures and interfacial organization beyond the three summary metrics.
  • AUTOMATED QUALITY ASSESSMENT OF COMMITTEE NEURAL NETWORK POTENTIALS: The six models provide robust, accurate descriptions at their selected thermodynamic conditions, making exhaustive simulations accessible after validation.The quality assessment supports using the models for detailed studies of the chosen systems and suggests the protocol may apply to other solid-liquid systems.

REACHING LONGER LENGTH AND TIME SCALES

The validated C-NNP framework enables long simulations of water on rutile TiO2(110), revealing structured interfacial layers and strongly altered water mobility. Extended sampling also resolves force reliability and free-energy features that short AIMD cannot converge.

  • REACHING LONGER LENGTH AND TIME SCALES: A 30 ps AIMD trajectory at 300 K seeded a 1728-atom TiO2/H2O model whose C-NNP was run for 5 ns.The setup used a four-trilayer slab, 80 water molecules, and a 1.5 nm water film before constructing a 2×2 interface model.
  • REACHING LONGER LENGTH AND TIME SCALES: The C-NNP simulation reproduces the AIMD density profile while resolving highly structured water in the first two adsorption layers and up to about 1 nm into the liquid.The first two peaks correspond to water near fivefold and sixfold coordinated titanium sites.
  • REACHING LONGER LENGTH AND TIME SCALES: Force error estimates remain between 40 and 80 meV/Å across the water region and average about 60 meV/Å without deterioration over 5 ns.Errors are only slightly higher near the TiO2 surface, where interactions are more complex.
  • REACHING LONGER LENGTH AND TIME SCALES: Only the extensively sampled C-NNP simulation converges the free-energy profile, showing strongest adsorption above fivefold titanium sites and barriers between contact sites.The barriers support the immobile character of the two contact layers.
  • REACHING LONGER LENGTH AND TIME SCALES: The extended simulations provide detailed structural and dynamical insight into water on rutile, including pronounced layering and interfacial mobility changes.These results demonstrate the framework’s use for understanding technologically relevant solid-liquid systems.
  • REACHING LONGER LENGTH AND TIME SCALES: Water diffusion is strongly influenced by the TiO2 interface over more than 1 nm into the liquid, with minimal diffusion close to the interface.The diffusion analysis separates parallel and perpendicular components using spatially decomposed mean-square displacement.

CONCLUSION

The framework makes accurate machine-learning potentials for complex aqueous systems straightforward by focusing development on specific thermodynamic conditions and automating training and validation. The authors demonstrate broad applicability while identifying clear scope boundaries and future extensions.

  • Framework and contribution: The framework generates robust machine-learning potentials from a single reference simulation through a straightforward, data-driven process with limited user input.It uses committee neural-network potentials, avoids hyperparameter adjustment, and integrates automated validation.
  • Framework and contribution: Six complex liquid and solid-liquid systems were modeled and evaluated across structural, dynamical, and force-prediction properties.The validation protocol is fully integrated and based on open-source solutions.
  • Scope and novelty: The approach deliberately sacrifices broad transferability by concentrating on the thermodynamic condition relevant to the scientific question.This narrower scope is presented as a change in perspective rather than a defect, because it enables relatively low-effort models that remain robust and accurate within the targeted phase-space region.
  • Limitations and outlook: The demonstrated study is limited to aqueous systems with four species and does not explore reactive processes.Successful future applications to reactions depend on the initial ab initio simulation sampling the relevant reactive process.
  • Limitations and outlook: Different DFT functionals were used across the six showcase systems, reflecting the absence of a perfect functional for water and complex aqueous interfaces.The framework may nevertheless facilitate systematic comparisons of DFT methods in realistic disordered systems.
  • Scientific applications: The methodology is expected to support simulations of interfacial water structuring, wetting, ice formation, free-energy surfaces, and dynamical properties.The paper also suggests applicability beyond aqueous systems to other liquids and materials in contact with solids.

MATERIALS AND METHODS

The implementation combines open-source simulation and optimization tools into a user-friendly workflow that generates and validates committee neural-network potentials from reference AIMD trajectories. Extended simulations are then used to assess model behavior, including a 5 ns TiO2–water application.

  • Software and model generation: The AML Python package interleaves simulation and data-manipulation steps to generate C-NNP models from reference trajectories.It is freely available, and all six showcase models were developed with it.
  • Software and model generation: The open-source n2p2 code performs NNP optimization using template-provided parameters and symmetry functions.Training inputs, datasets, and final-model parameters are publicly available.
  • Reference simulations: Reference AIMD simulations used different DFT settings and typically contained 64–110 water molecules over 30–130 ps.All reference simulations were performed with CP2K.
  • Production simulations: Validation C-NNP simulations ran for at least 0.5 ns, while the TiO2–water system was propagated for 5 ns.The TiO2 setup contained 1728 atoms and 320 water molecules in a 2×2×1 supercell, using a 1 fs timestep at 300 K.

Supporting information for: Machine learning potentials for complex aqueous systems made simple

The supporting-information material identifies the manuscript authors, their institutional affiliations, the manuscript date, and the paper’s keywords.

  • Authorship and affiliations: The manuscript lists Christoph Schran, Fabian L. Thiemann, Patrick Rowe, Erich A. Müller, Ondrej Marsalek, and Angelos Michaelides as authors.Affiliation markers connect the authors to institutions in the United Kingdom and Czech Republic.
  • Document information: The manuscript was compiled on 15 September 2021.
  • Document information: The paper’s keywords are Machine Learning Potentials, Solid-liquid systems, and Aqueous Phase.

QUALITY ASSESSMENT

The validation protocol compares machine-learning potentials with AIMD references using structural, dynamical, and force-prediction measures. These measures are condensed into scores that assess similarity of RDFs and VDOS and the scale of force errors relative to force fluctuations.

  • Validation design: The protocol evaluates three categories: structural properties, dynamical properties, and force-prediction precision.It is designed to compare models for different systems in a direct and condensed manner.
  • Structural properties: Structural accuracy is assessed by comparing all system RDFs from AIMD and independent C-NNP simulations.The RDF similarity norm ranges from 0 for most different to 1 for identical, and averaged norms yield a structural score.
  • Dynamical properties: Dynamical accuracy is assessed with species-resolved VDOS obtained by Fourier transforming velocity autocorrelation functions.Averaged similarity measures across species provide the dynamical-property score.
  • Force prediction: Force prediction is evaluated with RMSE values computed for each species using a 1000-structure test set sampled from the original AIMD simulation.The force score accounts for differing force magnitudes by relating RMSE to average force fluctuations.
  • Force prediction: Force RMSE values are averaged and converted into percentages to produce the C-NNP force score.

Properties evaluated for Quality Assessment

The automated validation compares C-NNP and AIMD structural, dynamical, force, and interfacial properties across the six aqueous systems. The models show essentially perfect agreement for RDFs, VDOS, and force predictions, with substantial agreement for additional confinement and interface properties.

  • Essentially perfect agreement is observed between AIMD and C-NNP RDF, VDOS, and force properties across all six systems.The full validation results are provided for the six C-NNP models in Fig. S1–Fig. S6.
  • Substantial agreement is observed for density profiles, hydrogen-bond numbers, and water orientations in four confined or interfacial systems.These systems are carbon nanotube water, boron nitride nanotube water, molybdenum disulfide-confined water, and titanium dioxide-surface water.

C-NNP models

The C-NNP models use atom-centered symmetry functions and neural networks trained within an active-learning workflow. Eight diverse committee members are iteratively improved using structures selected by force disagreement until the committee converges.

  • All six C-NNP models were trained with the active-learning workflow implemented in the AML Python package.The package is available at the stated GitHub repository.
  • Twenty random trajectory structures initialize each model, after which structures with the largest mean force committee disagreement are added iteratively until convergence.Fifteen active-learning steps were performed for all systems studied.
  • Atom-centered symmetry functions transform each atomic chemical environment into neural-network inputs using automatically generated radial and angular descriptors.The descriptors use a 12-bohr radial cutoff and a general set applicable across systems.
  • Each neural network contains two hidden layers with 20 neurons and uses hyperbolic-tangent activations except for a linear output neuron.
  • Each C-NNP contains eight independently initialized neural-network members trained on randomly subsampled reference data with 10% of points omitted per member.The omitted points impose diversity among committee members.

AIMD simulations

AIMD reference simulations provide trajectories for aqueous ions, nanotube confinement, molybdenum disulfide confinement, and a titanium dioxide interface. Supplementary validation figures compare the resulting C-NNP models with these AIMD references using structural, dynamical, and force measures.

  • AIMD simulations were performed with the CP2K software package.
  • The fluoride-water reference contains one fluoride ion and 64 water molecules in a periodic 12.445 Å box using revPBE0 with D3 dispersion.
  • The sulfate-water reference contains one sulfate ion and 64 water molecules in a periodic 12.41 Å box using BLYP with D3 dispersion.
  • The carbon and boron nitride nanotube systems use (12,12) armchair nanotubes with three unit cells and water density of 1.0 g/cm3.The carbon nanotube contains 65 water molecules, while the boron nitride nanotube contains 68.
  • The molybdenum disulfide reference contains 109 water molecules confined by single-layer MoS2 sheets in a periodic 22.545, 22.314, 11.500 Å box.
  • The titanium dioxide system contains 80 water molecules forming a 1.5 nm film on four O-Ti-O trilayers, with 15 Å vacuum separating periodic images.The system uses a 30 ps, 300 K NVT propagation after equilibration.
  • Supplementary figures S1–S5 compare AIMD and C-NNP RDFs, VDOS, and force correlations for fluoride, sulfate, carbon nanotube, boron nitride nanotube, and molybdenum disulfide water systems.
  • Figure S7 compiles density profiles for water in carbon and boron nitride nanotubes, water confined by MoS2, and water at rutile TiO2.
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