A statistically guided grid generation method and its application to intermolecular potential energy surfaces.

Area of Science:

• Computational Chemistry
• Data Science
• Mathematical Modeling

Background:

• Fitting nonlinear parametric models requires extensive training data.
• Obtaining data points can be computationally expensive and time-consuming.
• Current systematic sampling methods may not be optimal for complex models.

Purpose of the Study:

• To introduce a novel, efficient method for selecting optimal grid points for training data generation.
• To reduce the number of required data points for fitting nonlinear parametric models.
• To demonstrate the method's effectiveness in fitting complex potential energy surfaces.

Main Methods:

• The iterative variance minimizing grid approach utilizes statistical information from an initial sparse grid fit.
• Optimal grid points are selected iteratively to minimize variance.
• The method is demonstrated for six-dimensional intermolecular potential energy surfaces (PESs) fitted to ab initio data.

Main Results:

• The proposed method reduces the number of required grid points by approximately 50% compared to systematic sampling.
• Achieved significant reduction in data points needed for fitting complex PESs.
• Demonstrated the method's applicability beyond PES fitting.

Conclusions:

• The iterative variance minimizing grid approach offers a computationally efficient strategy for generating training data.
• This method is broadly applicable to various parametric model fitting scenarios where data acquisition is costly.
• Significant potential for accelerating scientific discovery by reducing computational overhead.