Gaussian processes for finite size extrapolation of many-body simulations

Area of Science:

• Computational materials science
• Quantum chemistry
• Machine learning applications

Background:

• Accurate modeling of materials requires predicting properties in the thermodynamic limit.
• Many-body electronic structure methods are computationally expensive for large systems.
• Extrapolation from smaller systems is commonly used but relies on simplified scaling expressions.

Purpose of the Study:

• To develop a more accurate and efficient method for extrapolating many-body simulations to the thermodynamic limit.
• To leverage machine learning for correcting finite-size effects in simulations.

Main Methods:

• Utilized Gaussian processes (GPR) for extrapolation.
• Trained GPR models on Smooth Overlap of Atomic Positions (SOAP) descriptors.
• Extrapolated energies of 1D hydrogen chains simulated with coupled cluster theory and Auxiliary Field Quantum Monte Carlo (AFQMC).

Main Results:

• Gaussian processes accurately predicted thermodynamic limit energies of hydrogen chains with sub-milliHartree accuracy.
• The method was effective for both homogeneous and inhomogeneous hydrogen chains.
• Achieved high accuracy using training data from relatively small 10-30 atom chains.

Conclusions:

• Gaussian processes offer a generalizable and accurate approach to extrapolate many-body simulations to the thermodynamic limit.
• This machine learning-based method is independent of system geometry and dimensionality.
• Highlights the potential of machine learning to enhance the interpretation of finite-size simulations.