Parallelized Natural Extension Reference Frame: Parallelized Conversion from Internal to Cartesian Coordinates.

The conversion of polymer parameterization from internal coordinates (bond lengths, angles, and torsions) to Cartesian coordinates is a fundamental task in molecular modeling, often performed using the natural extension reference frame (NeRF) algorithm. NeRF can be parallelized to process multiple polymers simultaneously, but is not parallelizable along the length of a single polymer. A mathematically equivalent algorithm, pNeRF, has been derived that is parallelizable along a polymer's length. Empirical analysis demonstrates an order-of-magnitude speed up using modern GPUs and CPUs. In machine learning-based workflows, in which partial derivatives are backpropagated through NeRF equations and neural network primitives, switching to pNeRF can reduce the fractional computational cost of coordinate conversion from over two-thirds to around 10%. An optimized TensorFlow-based implementation of pNeRF is available on GitHub at https://github.com/aqlaboratory/pnerf © 2018 Wiley Periodicals, Inc.