To find optimal solutions for the weights given a value of θ, we use the forces method 10 as implemented in the open-source BioEn software available at . An open-source Julia 37 implementation using the package Optim.jl 38 can be downloaded from free of charge. To generate synthetic data, we use bio-phys/RefinementModels.jl for the double-well model and for the von Mises polymer model. We use uniform reference weights for all systems.