Permutation invariant potential energy surfaces for polyatomic reactions using atomistic neural networks

Abstract

The applicability and accuracy of the Behler-Parrinello atomistic neural network method for fitting reactive potential energy surfaces is critically examined in three systems, H + H2 → H2 + H, H + H2O → H2 + OH, and H + CH4 → H2 + CH3. A pragmatic Monte Carlo method is proposed to make efficient choice of the atom-centered mapping functions. The accuracy of the potential energy surfaces is not only tested by fitting errors but also validated by direct comparison in dynamically important regions and by quantum scattering calculations. Our results suggest this method is both accurate and efficient in representing multidimensional potential energy surfaces even when dissociation continua are involved.

Multiscale Quantum Mechanics/Molecular Mechanics Simulations with Neural Networks

“…On one hand, there is a difference of −1.3 kcal/mol between the reweighted results from direct QM/MM and QM/MM-NN potential energies, reflecting the error of NN predictions. It can be remedied with further improvements on the quality of NN in different ways, for example, the use of advanced training algorithms, 76 the Morte Carlo sampling of symmetry functions, 77 or the interpolation of gradients. 78 On the other hand, even if we applied direct HF/6–31G(d)/MM potential energies, the low-level free-energy profile cannot be reweighted to the accurate PMF obtained from ab initio QM/MM MD simulations.…”

A critical comparison of neural network potentials for molecular reaction dynamics with exact permutation symmetry

“…It should be noted that in their work, the points of the three systems have been sampled from pre-existing well-behaved analytical PESs, not from ab initio data sets. 36 In addition, Lu et al employed the HD-NNP approach to fit the PES of the H 2 + SH reaction based on ab initio calculated points, and the quantum dynamical results of the HD-NNP and PIP-NN PESs have been found to be essentially the same. 37 Building on the extensive work of Bowman and coworkers on molecular PESs based on permutation invariant polynomials (PIPs), 10,29 in 2013, Guo and co-workers proposed to use PIPs in the input layer of a NN to obtain another type of NN potential with exact permutation invariance.…”

Fitting potential energy surfaces to sum-of-products form with neural networks using exponential neurons

“…If exact symmetry plays a key role in the properties computed from the PES, new developments will be needed within the NN-expnn approach. NN approaches based on PIP, [26][27][28][29][30] i.e. outside NN-expnn, were highlighted in the introduction, and a recent review by Manzhos et al…”

“…Guo and co-workers developed a NN-based method which exhibits permutational invariance 26 symmetry (PIP-NN). [27][28][29][30] The PIP-NN method takes advantage of the e±ciency of NNs for the PES¯tting.…”