Given these successes, in the following, we present ∂-HylleraasMD (∂-HyMD), a reimplementation of the HylleraasMD (HyMD) 9,17 code for hamiltonian hybrid particle-field (HhPF) molecular dynamics in the JAX differentiable framework, that allows us to perform general force field parameterization on any target observable that depends on the simulation trajectory. Our main goal is to optimize the intermolecular interactions described by HhPF. As a test case, we apply our optimization protocol on a diverse set of lipids, providing a library of parameters that can be used for future studies. We also test the performance of these parameters for the self-assembly of lipid bilayers and the transferability to similar systems such as triglycerides.