  Molecular dynamics simulations use statistical mechanics at the atomistic
scale to enable both the elucidation of fundamental mechanisms and the
engineering of matter for desired tasks. The behavior of molecular systems at
the microscale is typically simulated with differential equations parameterized
by a Hamiltonian, or energy function. The Hamiltonian describes the state of
the system and its interactions with the environment. In order to derive
predictive microscopic models, one wishes to infer a molecular Hamiltonian that
agrees with observed macroscopic quantities. From the perspective of
engineering, one wishes to control the Hamiltonian to achieve desired
simulation outcomes and structures, as in self-assembly and optical control, to
then realize systems with the desired Hamiltonian in the lab. In both cases,
the goal is to modify the Hamiltonian such that emergent properties of the
simulated system match a given target. We demonstrate how this can be achieved
using differentiable simulations where bulk target observables and simulation
outcomes can be analytically differentiated with respect to Hamiltonians,
opening up new routes for parameterizing Hamiltonians to infer macroscopic
models and develop control protocols.
