Accelerating fourth-generation machine learning potentials by quasi-linear scaling particle mesh charge equilibration

Accelerating fourth-generation machine learning potentials by quasi-linear scaling particle mesh charge equilibration

15 Mar 2024 | Moritz Gubler, Jonas A. Finkler, Moritz R. Schäfer, Jörg Behler, Stefan Goedecker
This paper presents a quasi-linear scaling method for charge equilibration in fourth-generation machine learning potentials (MLPs). The method avoids the need to explicitly compute the Coulomb matrix, enabling efficient calculation of electrostatic energy, forces, and stress in periodic systems. The approach is based on particle mesh charge equilibration (PMCE), which uses Fourier space to solve Poisson's equation efficiently. The method allows for the calculation of energy derivatives that consider the global structure-dependence of atomic charges, making it suitable for a wide range of force fields and MLPs. The key innovation is the use of a conjugate gradient method combined with matrix-vector multiplications, which results in a quasi-linear scaling with respect to the number of atoms. This significantly reduces the computational cost compared to traditional methods that require solving dense linear systems. The method is validated through benchmark simulations, showing improved performance for large systems. The results demonstrate that the new approach can efficiently handle systems with thousands of atoms, enabling more accurate and computationally feasible simulations of complex systems with long-range charge transfer effects. The method is general and can be applied to various force fields and MLPs, making it a valuable tool for atomistic simulations in computational chemistry and materials science.This paper presents a quasi-linear scaling method for charge equilibration in fourth-generation machine learning potentials (MLPs). The method avoids the need to explicitly compute the Coulomb matrix, enabling efficient calculation of electrostatic energy, forces, and stress in periodic systems. The approach is based on particle mesh charge equilibration (PMCE), which uses Fourier space to solve Poisson's equation efficiently. The method allows for the calculation of energy derivatives that consider the global structure-dependence of atomic charges, making it suitable for a wide range of force fields and MLPs. The key innovation is the use of a conjugate gradient method combined with matrix-vector multiplications, which results in a quasi-linear scaling with respect to the number of atoms. This significantly reduces the computational cost compared to traditional methods that require solving dense linear systems. The method is validated through benchmark simulations, showing improved performance for large systems. The results demonstrate that the new approach can efficiently handle systems with thousands of atoms, enabling more accurate and computationally feasible simulations of complex systems with long-range charge transfer effects. The method is general and can be applied to various force fields and MLPs, making it a valuable tool for atomistic simulations in computational chemistry and materials science.
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Understanding Accelerating Fourth-Generation Machine Learning Potentials Using Quasi-Linear Scaling Particle Mesh Charge Equilibration