Operator Autoencoders: Learning Physical Operations on Encoded Molecular Graphs

Molecular dynamics simulations produce data with complex nonlinear dynamics. If the timestep behavior of such a dynamic system can be represented by a linear operator, future states can be inferred directly without expensive simulations. The use of an autoencoder in combination with a physical timestep operator allows both the relevant structural characteristics of the molecular graphs and the underlying physics of the system to be isolated during the training process. In this work, we develop a pipeline for establishing graph-structured representations of time-series volumetric data from molecular dynamics simulations. We then train an autoencoder to find nonlinear mappings to a latent space where future timesteps can be predicted through application of a linear operator trained in tandem with the autoencoder. Increasing the dimensionality of the autoencoder output is shown to improve the accuracy of the physical timestep operator.