We showcase our first approach to developing reduced Lagrangian models of turbulence. We begin with applying Neural Ordinary Differential Equations as a learning algorithm to capture the physics of molecular dynamics from simulated trajectories. We test two methods: learning the high dimensional forcing function (less informed), and learning the potential function (physics informed). In learning the potential function we leverage the known physical symmetries and propose hard coding the gradient of the potential within the forward pass of the NN. We test these methods on molecular dynamics simulation data obtained using the Verlet method with a spherically symmetric potential function (a natural benchmark on our way to incorporating smooth particle hydrodynamics). The goal is to develop new data driven methods for reduced order models from high fidelity sources of ground truth data.
