A physics-based
machine learning model called MLRNet has been developed
to construct the high-accuracy two-body intermolecular potential energy
surface (IPES). The outputs of the neural network are integrated into
the physically realistic Morse/long-range (MLR) function, which ensures
that the MLRNet has meaningful extrapolation at both short and long
ranges and solves the asymptotic problem in common neural network
potential (NNP) models. The neural network representation of the MLR
parameters is more flexible and more efficient than the polynomial
expansion in the conventional mdMLR model, especially for systems
containing nonrigid monomer(s). The present work illustrates the basic
framework of the current MLRNet model, including (i) how to combine
the physically meaningful MLR function with different possible NN
structures, (ii) the preservation of permutation symmetry, and (iii)
the predetermination of the long-range function u
LR. We choose two realistic systems to demonstrate the
performance of MLRNet: the three-dimensional IPES of CO2–He including the CO2 antisymmetric vibration Q
3 and the six-dimensional IPES of the H2O–Ar system. In both cases, the fitting errors of the
MLRNet are several times smaller than those of the conventional mdMLR
model. Both short-range and long-range extrapolation tests were performed
to illustrate the extrapolation ability of the MLRNet and its damping
function version. Moreover, for the 6-D H2O–Ar system,
the MLRNet only needs 1596 trainable parameters, which is almost equal
to the number needed for the 5-D mdMLR model (1509) and half that
needed for the PIP-NN model (3501) within similar accuracy, which
illustrates the model efficiency in high-dimensional IPES fitting.