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Kriging atomic properties with a variable number of inputs.

Stuart J Davie1, Nicodemo Di Pasquale1, Paul L A Popelier1

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A new machine learning method extends kriging for molecular simulations with variable atomic inputs. This approach accurately predicts properties of water clusters, outperforming traditional methods for complex chemical systems.

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Area of Science:

  • Computational Chemistry
  • Machine Learning in Materials Science
  • Molecular Dynamics Simulations

Background:

  • Traditional kriging methods require fixed-dimension inputs, limiting their application in molecular simulations where the number of interacting atoms varies.
  • The FFLUX force field utilizes kriging to link atomic properties with their surrounding coordinates, but requires a generalized approach for variable inputs.
  • Molecular simulations often employ cutoff radii, leading to systems with a non-constant number of neighboring atoms.

Purpose of the Study:

  • To develop a general machine learning method for applying kriging to chemical systems with a variable number of geometrical inputs.
  • To adapt kriging for molecular simulations where the number of atoms within an interaction cutoff radius is not fixed.
  • To demonstrate the method's utility in predicting energetic and electrostatic properties of water clusters with varying molecular counts.

Main Methods:

  • A novel, general kriging approach designed to handle variable input dimensionality was developed.
  • The method was applied to predict 54 energetic and electrostatic properties of central water molecules in 5000 water clusters (4 Å radius) with variable numbers of molecules.
  • Results were validated against models using fixed-size (decamer) water clusters and a naive approach for handling variable inputs.

Main Results:

  • The new kriging method successfully predicted multiple properties of water clusters with variable numbers of surrounding water molecules.
  • Models derived from 4 Å water clusters using the presented method showed comparable or superior performance to decamer-based models for all properties.
  • The generalized kriging approach significantly outperformed truncated models in handling the variable input problem.

Conclusions:

  • The developed general kriging method effectively addresses the challenge of variable inputs in molecular simulations.
  • This approach offers a robust and accurate way to model chemical systems with dynamic atomic environments.
  • The method shows promise for broader applications in machine learning for computational chemistry and other fields requiring interpolation of variable-dimension data.