Parallel Multistream Training of High-Dimensional Neural Network Potentials.

Over the past years high-dimensional neural network potentials (HDNNPs), fitted to accurately reproduce ab initio potential energy surfaces, have become a powerful tool in chemistry, physics and materials science. Here, we focus on the training of the neural networks that lies at the heart of the HDNNP method. We present an efficient approach for optimizing the weight parameters of the neural network via multistream Kalman filtering, using potential energies and forces as reference data. In this procedure, the choice of the free parameters of the Kalman filter can have a significant impact on the fit quality. Carrying out a large parameter study, we determine optimal settings and demonstrate how to optimize training results of HDNNPs. Moreover, we illustrate our HDNNP training approach by revisiting previously presented fits for water and developing a new potential for copper sulfide. This material, accessible in computer simulations so far only via first-principles methods, forms a particularly complex solid structure at low temperatures and undergoes a phase transition to a superionic state upon heating. Analyzing MD simulations carried out with the CuS HDNNP, we confirm that the underlying ab initio reference method indeed reproduces this behavior.