  In molecular dynamics (MD), neural network (NN) potentials trained bottom-up
on quantum mechanical data have seen tremendous success recently. Top-down
approaches that learn NN potentials directly from experimental data have
received less attention, typically facing numerical and computational
challenges when backpropagating through MD simulations. We present the
Differentiable Trajectory Reweighting (DiffTRe) method, which bypasses
differentiation through the MD simulation for time-independent observables.
Leveraging thermodynamic perturbation theory, we avoid exploding gradients and
achieve around 2 orders of magnitude speed-up in gradient computation for
top-down learning. We show effectiveness of DiffTRe in learning NN potentials
for an atomistic model of diamond and a coarse-grained model of water based on
diverse experimental observables including thermodynamic, structural and
mechanical properties. Importantly, DiffTRe also generalizes bottom-up
structural coarse-graining methods such as iterative Boltzmann inversion to
arbitrary potentials. The presented method constitutes an important milestone
towards enriching NN potentials with experimental data, particularly when
accurate bottom-up data is unavailable.
