Refinement and Performance Benchmark for Range-Separated Water Force Field

TL;DR

This study tackles the data scarcity and training instability inherent to CCSD(T)/CBS-level water force fields by introducing a robust training workflow that combines DeePKS-based ML-DFT force labels, transfer learning, active learning, and ensemble knowledge distillation within a range-separated PhyNEO framework. The authors demonstrate that this TL+AL+EKD approach yields sub-chemical accuracy on cluster energies/forces while delivering state-of-the-art bulk properties (density, RDFs, dielectric constant, diffusivity, IR spectra) using far less CCSD(T) data (~3×10^4 points). The resulting PhyNEO water force field balances accuracy and stability across both finite clusters and bulk liquid simulations, outperforming prior CCSD(T)-level potentials in several metrics. This workflow provides a generalizable blueprint for building high-accuracy ML potentials when high-level ab initio data are scarce or expensive to obtain for bulk systems.

Abstract

In our previous work, we developed a CCSD(T)-level range-separated water force field that combines the power of physics-driven and machine learning models. However, it was found that expensive CCSD(T)/CBS calculations lead to limited number of QM data as well as the missing of force labels, both of which lead to training instability issues. Bulk properties show large variations that cannot be resolved by simply reducing the fitting error in small cluster QM dataset. Such instability in bulk phase simulation is a universal problem in the training of machine learning potentials (MLPs), and is particularly severe at CCSD(T) level of theory.In this work, using our range-separated water model as an example, we aim to overcome these limitations by developing a new training workflow. It is composed by several techniques including: 1. an active learning protocol that ensures more thorough sampling in different temperatures and densities; 2. an intermediate force label technique employing machine learning density functional; and 3. an ensemble knowledge distillation (EKD) method. These techniques significantly stabilize the resulting water model, consistently achieving sub-chemical accuracies in both cluster energies and experimental properties. Benchmarks are carried out for various properties including densities, radial distribution functions (RDFs), dielectric constants, diffusivity, and infrared spectra, all showing state-of-the-art (SOTA) performances and proving the effectiveness of the training protocol.

Figures (6)

• Figure 1: The workflow of the training protocol. First, a ML-DFT (DeePKS) model is trained using the initial CCSD(T) energy data and then is used to generate cheap energy/force (E/F) labels. The models are pretrained using DeePKS E/F labels and then transferred to CCSD(T) level using the original CCSD(T) E labels. Active learning using force prediction uncertainties are then conducted iteratively to generate an augmented dataset and the TL+AL model ensemble. In the final stage, the TL+AL model ensemble is distilled using bulk data to generate the final TL+AL+EKD model ensemble.
• Figure 2: The intermolecular interaction energies predicted by the Initial, EKD, TL+AL, and TL+AL+EKD PhyNEO models on (a) hexamers test set and (b) dodecamers test set, compared with CCSD(T)/CBS reference. (c) The molecular structures of 8 isomers of water hexamer. (d) The molecular structures of 7 isomers of water dodecamer.
• Figure 3: Comparison of the density distributions given by the Initial, EKD, TL+AL, and TL+AL+EKD model ensembles. The three groups of points and filled area from left to right correspond to simulated densities and the variations at 277 K, 298 K, and 318 K, respectively, compared with the experimental referencegs1975density (black dashed lines).
• Figure 4: Densities of liquid water at 248 K, 268 K, 277 K, 298 K, 318 K, 338 K, and at 1 atmosphere predicted by the final PhyNEO model in this work, compared with experimentsgs1975density and the reported results of MB-pol(2023)zhu2023mb.
• Figure 5: OO radial distribution function (panel a) and OH radial distribution function (panel b) from MD simulations at 298 K using the PhyNEO model in this work, compared with experimental datasoperRadial2000.