RuNNer 2.0: A Software Suite for High-Dimensional Neural Network Potentials

We present RuNNer 2.0, the "Ruhr University Neural Network energy representation", a highly optimized software suite for training and evaluating high-dimensional neural network potentials (HDNNPs) of the second, third, and fourth generation. Long-range electrostatics and charge equilibration (QEq) for the description of non-local charge transfer in fourth-generation (4G) HDNNPs are accelerated by quasi-linear-scaling plane-wave methods, reducing QEq computational complexity from $\mathcal{O}(N^3)$ to $\mathcal{O}(N\log^2 N)$ such that linear or quasi-linear scaling is achieved across all HDNNP generations. An optimized memory management strategy eliminates the training overhead traditionally associated with long-range interactions, allowing 4G-HDNNPs to be trained with the same efficiency as their local counterparts. Developed in modern Fortran (2003/2008 standards), combined with a hybrid MPI/OpenMP parallelization scheme, RuNNer 2.0 has been designed to run efficiently in any CPU environment, from cost-effective local workstations to massive HPC clusters. Its modular library architecture facilitates straightforward binding to external simulation software; native interfaces to LAMMPS and the Atomic Simulation Environment (ASE) provide full access to all its features, including built-in committee-based uncertainty quantification. The high efficiency and scalability of the RuNNer 2.0 ecosystem are demonstrated through detailed benchmarks.