Specialized Neural Network Interpolant for Accelerated Pair Interaction in Systems of Rigid Bodies

Motivated by the limitations of conventional coarse-grained molecular dynamics for simulation of large systems of nanoparticles, an approach to enable the use of complex iteraction models for nanoparticles derived from molecular dynamics simulation data in large scale simulation through the use of a class of specialized deep neural networks for interpolation in the relative coordinate space of rigid bodies has been developed.<br/><br/>The first layer of the network transforms the relative position and orientation with a flexibly parametrized geometric representation to a form more suitable to conventional fully connected layers, which, folowed by a weighted sum can be used to approximate a potential. Through backpropagation of the gradient of the potential, the force and torque on the particles can then be calculated through the geometric representation. Compared to training a more general network on the components of the force and torque vectors, this method has the advantage of being guranteed to produce an energy conserving interaction, and due to only being trained on a scalar value, requires fewer internal parameters to be trained. Furthermore since the training data is a scalar potential, the network can be trained to replicate models with no obvious gradient. As the parameters of the geometric transformation are trained along with the other weights in the network, the representation becomes optimized for the geometry of the potential.<br/><br/>The network is fitted to a variety of interaction potentials, investigating training and convergence characteristiscs and noise sensitivity, to demonstrate both the utility and limitations of the method. Additionally, further generalization to use on soft bodies and polydisperse systems is discussed.