  Learning pair interactions from experimental or simulation data is of great
interest for molecular simulations. We propose a general stochastic method for
learning pair interactions from data using differentiable simulations
(DiffSim). DiffSim defines a loss function based on structural observables,
such as the radial distribution function, through molecular dynamics (MD)
simulations. The interaction potentials are then learned directly by stochastic
gradient descent, using backpropagation to calculate the gradient of the
structural loss metric with respect to the interaction potential through the MD
simulation. This gradient-based method is flexible and can be configured to
simulate and optimize multiple systems simultaneously. For example, it is
possible to simultaneously learn potentials for different temperatures or for
different compositions. We demonstrate the approach by recovering simple pair
potentials, such as Lennard-Jones systems, from radial distribution functions.
We find that DiffSim can be used to probe a wider functional space of pair
potentials compared to traditional methods like Iterative Boltzmann Inversion.
We show that our methods can be used to simultaneously fit potentials for
simulations at different compositions and temperatures to improve the
transferability of the learned potentials.
