Dual-Level Parametrically Managed Neural Network Method for Learning a Potential Energy Surface for Efficient Dynamics

A general difficulty with machine-learned potential energy
surfaces
is their unreliability in regions with little or no training data.
The goal of the present work is to remedy this by a low-cost method
for incorporating well understood features of potential energy surfaces
into an efficient data-driven machine learning algorithm. Our focus
is on regions where conventional surface fitting does not need large
amounts of accurate data, in particular, geometries with large separations
of subsystems–where it is well recognized that the potential
should reach its asymptotic form–and geometries with very close
atoms–where the potential should be repulsive enough to prevent
trajectories from reaching classically inaccessible regions but need
not be highly quantitative. The new method involves a neural network
(NN) with a parametrically managed activation function (PMAF) and
two levels of electronic structure, a higher level (HL) and a lower
level (LL). The resulting NN is called a dual-level parametrically
managed neural network (DL-PMNN). For the present example, the HL
is an accurate density functional method (CF22D/may-cc-pVTZ), and
the LL is an inexpensive density functional method (MPW1K/MIDIY).
We use the LL to ensure correct behavior of the potential at large
and small distances; the goal is to reach HL accuracy for dynamics
without making HL calculations in regions where the LL can guide the
fit. To illustrate the new method, we fit the potential energy surface
for dissociation of the S–H bond of ortho-fluorothiophenol
in the ground electronic state, and we show that the method yields
a good fit and efficient trajectory calculations without crashes.