Parsimonious Potential Energy Surface Expansions Using Dictionary Learning with Multipass Greedy Selection.

Area of Science:

• Computational chemistry
• Quantum chemistry
• Machine learning in science

Background:

• Basis set expansions accurately represent electronic energies for chemical dynamics, kinetics, and spectroscopy.
• The computational cost of these expansions scales poorly with system size, limiting their application to small molecules (<10 atoms).

Purpose of the Study:

• To develop a computationally efficient method for generating accurate potential energy surfaces.
• To overcome the system size limitations of traditional basis set expansions.

Main Methods:

• Dictionary learning was employed to optimize subsets of conventional basis functions.
• A novel multipass greedy regression algorithm, inspired by statistical and machine learning selection methods, was developed.

Main Results:

• The optimized representations achieved accuracy comparable to full basis set expansions.
• The number of terms in the optimized expansions was reduced by one to two orders of magnitude.
• The optimized expansions exhibited near-linear scaling with the number of atoms, a significant improvement over traditional methods.

Conclusions:

• Dictionary learning provides a scalable and efficient approach to constructing accurate potential energy surfaces.
• This method enables high-accuracy computational chemistry applications for larger and more complex molecular systems.