Generating Minimal Training Sets for Machine Learned Potentials

This Letter presents a novel approach for identifying uncorrelated atomic configurations from extensive datasets with a nonstandard neural network workflow known as random network distillation (RND) for training machine-learned interatomic potentials (MLPs). This method is coupled with a DFT workflow wherein initial data are generated with cheaper classical methods before only the minimal subset is passed to a more computationally expensive ab initio calculation. This benefits training not only by reducing the number of expensive DFT calculations required but also by providing a pathway to the use of more accurate quantum mechanical calculations. The method’s efficacy is demonstrated by constructing machine-learned interatomic potentials for the molten salts KCl and NaCl. Our RND method allows accurate models to be fit on minimal datasets, as small as 32 configurations, reducing the required structures by at least 1 order of magnitude compared to alternative methods. This reduction in dataset sizes not only substantially reduces computational overhead for training data generation but also provides a more comprehensive starting point for active-learning procedures.

Figure 1

Use of random network distillation to fill a training set $\mathcal{T}$. In the initial stage, classical MD simulations are used to sample configuration space and build the data pool $\mathcal{P}$ before the RND architecture is used to select unique configurations and add these to the training data. This method involves passing a representation of the configuration into the two neural networks, $f$, and $g$. These representations are then compared using a selected distance metric, $d$, and based on their distance, are either added to the training data, or thrown away as they have already been seen. These training data are then passed through a DFT calculation to label the configurations with a corrected energy, $\mathrm{\Delta }{\epsilon }_{\mathrm{DFT}}$, and forces before training a machine-learned potential.

Figure 2

The RMSE and L4 loss compared to the number of training configurations for different data selection algorithms show the convergence of the model loss. Circles correspond to those models that could be used to run a stable MD simulation, whereas a square indicates that the potential leads to a breakdown of the MD simulation after some time. This labeling measures how well the training data represent the configuration space.

Figure 3

Density of each salt at different temperatures computed with the machine learned potentials trained on 32 configurations (orange crosses), using pure DFT-MD (blue stars) and experimental data (black dots) taken from Ref. [41]. The experimental data are provided with 4 significant digits, making the error smaller than the symbol size in this figure.

Figure 4

Comparison of radial distribution functions generated from MD simulations performed in an NVT ensemble using the machine learned potentials trained on 32 (short dashed blue) and 128 (long dashed orange) configurations, respectively, and the underlying density functional theory data (solid black).