Input vector optimization of feed-forward neural networks for fitting ab initio potential-energy databases

Area of Science:

• Computational Chemistry
• Materials Science
• Machine Learning

Background:

• Neural networks (NNs) are increasingly used to fit potential energy surfaces from ab initio electronic structure calculations.
• The accuracy of NN fitting depends heavily on the choice of input vector elements.
• Existing methods often use Z-matrix coordinates, which can lead to fitting inaccuracies due to discontinuities.

Purpose of the Study:

• To investigate how the number and nature of elements in the input vector affect NN fitting accuracy.
• To identify optimal input vector representations for fitting ab initio potential energy databases.
• To compare the efficiency of input vector optimization versus increasing database size or NN complexity.

Main Methods:

• Ab initio electronic structure calculations were performed for H(2)O(2), HONO, Si(5), and H(2)C[Double Bond]CHBr using DFT/B3LYP, MP2, and MP4 methods.
• A total of 31 input vectors were tested, including interatomic distances, inverse powers, angles, and dihedral angles (both redundant and nonredundant).
• The Levenberg-Marquardt algorithm was adapted to optimize parameters within the R(ij)^(-n) input vector form.

Main Results:

• Z-matrix variables resulted in the lowest NN fitting accuracy, attributed to discontinuities in dihedral angles.
• Using trigonometric functions of angles improved accuracy by eliminating discontinuities.
• Input vectors of the form R(ij)^(-n) yielded the most accurate fitting, with optimal powers n in the range of 1.625-2.38.
• Optimizing n for each bond type did not significantly improve accuracy for vinyl bromide.
• R(ij)^(-n) input vectors reduced root-mean-square errors by factors of 1.31 to 2.83 compared to simple interatomic distances.

Conclusions:

• Input vectors based on interatomic distances, particularly R(ij)^(-n), significantly enhance NN fitting accuracy for ab initio potential energy surfaces.
• This method offers a computationally inexpensive way to improve accuracy compared to increasing dataset size or NN complexity.
• The R(ij)^(-n) form effectively handles various chemical systems and bonding types, proving robust for diverse molecular structures.