For stochastic gradient descent optimizations, we need to estimate gradients of the observables of interest as a function of force field parameters. In this paper, gradients are calculated using a reweighted finite difference scheme, where the derivative of an observable with respect to a parameter is calculated using the central difference method with a relative step (Δ ∕ ) size of ℎ = 10 -4 . Values of atℎ and + ℎ are estimated by reweighting from the sampled ensemble using pymbar , which is accurate for the properties of interest over the small step size ℎ. All optimizations were performed using the ForceBalance software package using the built-in OpenFF Evaluator target . Optimizations were run using the Levenberg-Marquardt non-linear least squares algorithm with adaptive trust radius to iteratively minimize the objective function until it was observed to fluctuate around a minimum value in each optimization. This algorithm has been used successfully with ForceBalance for force field optimization previously . In all cases 12 iterations was sufficient to meet this criteria. Each iteration consists of 1) estimation of each physical property measurement in the training set using the current force field parameters, 2) comparison of those estimated values to the experimental values in ThermoML, 3) adjustment of the target parameters with the ForceBalance optimizer. A weighted least squares objective function, , was used to measure deviations of the reference and estimated physical property values. An L2 penalty function based on the norm of the parameter displacement vector (from the initial parameters) is used to regularize the optimization, with a prior over the ForceBalance mathematical parameters of 0.1 for and 1.0 for .