Optimizing the Lennard-Jones parameters using the NLP loss function (equation ( )) shifts the intersection points of the graphs to a balancing where approximately 25% to 30% of the overall weight is assigned to the density weighting factor (see figure ). All resulting parameter sets and their corresponding errors are listed in tables 6, 7, 8 and 9 in section 5. On average, the combined errors (i.e. the sum of the density and RCE errors) using the NLP loss function are higher than the combined errors using the original loss function. However, the optimizations resulting in the lowest combined error are predominately achieved when applying the NLP to the loss function (see figure ). Similar to the resulting parameters using the original loss function, there is an even larger diversity of the optimization results (see figure ). This is more evidence that the loss landscape is highly multi-modal and gradientbased optimization can get stuck in wildly different local optima even depending on the weighting strategy in the loss function.