
Deep learning inferential methodsOur research interests lie in the intersection of mathematics, computer science, physics, and chemistry. Our current work is focused on using recurrent neural networks to create a novel and more capable method of calculating free energies based upon high dimensional statistical sampling. This will involve the use of Riemannian metrics with a possibility of further extensions through the use of enhanced sampling techniques. First, the data provided by molecular dynamics simulations will be transformed into a Riemannian Manifold which will then serve as an input to a neural network. The neural network will be used to create a transition probability matrix. From this matrix one can determine the free energies. This process has been developed by first starting with one and two dimensional toy models. After fully developing the methodologies involved we will move on to working with molecular dynamics simulation data. Free energy calculations are a keystone of computational chemistry work. By creating a potential energy surface (PES), various properties such as transition free energies, minimal energy pathways, and equilibrium states can be determined. Our research lies at the intersection of topology, chemical dynamics, artificial intelligence, and statistical physics. By combining these fields we are creating a novel methodology for estimating the PES. Our method involves taking molecular dynamics simulation data along minimal energy pathways, transforming it from cartesian coordinates into a Riemannian manifold, and then using this data as an input to a recursive neural network. The output of our neural networks will generate probabilities which are then analyzed to calculate a PES. 

