In practice, the calculation of a single gradient element is roughly equal to 20% of the original MD simulation. On the other hand, pure numerical gradients of the surface tension involve running separate simulations where the parameter is perturbed by a small step, and repeating this procedure for each parameter being optimized. We used a central difference approximation, which implies the computational cost of the gradient is 2N param times the cost of simulating the property itself. Compared to the semi-analytic gradients, the numerical gradients involve running separate simulations with nearly fully independent samples (save for the same initial condition). The noise in the gradients also increases with decreasing parameter step size because the statistical error in the property is roughly independent of parameter size, resulting in large numerical errors for steps that are too small. It is also important to avoid step sizes that are too large and no longer within the linear regime.