With dynamic starting points, E04USA is not directly solving problem (PE), but rather driving the parameters in the required direction. From this perspective, the convergence of the re-evaluated T M F value is more crucial. The final convergence criteria which CrystalEstimator considers is whether the user-specified reinitialisation limit has been reached. If none of these secondary termination criteria are met, the T M F is optimised again. Because the first two of these criteria (B4 and B5 in Figure ) require comparison to the T M F in a preceding iteration, they are naturally skipped in the m = 0 iteration where only the third criteria is assessed. In this manner, T M F optimisations are reattempted until one of the four convergence criteria are satisfied. In each iteration, the dynamic starting points are reinitialised such that the first T M F evaluation by E04USA uses Ω †,[0] s = Ω ref s . As described earlier, whilst progressing towards the optimum parameter estimates, intermediate parameter values may prove ill-suited for the lattice energy minimisation of some structures in the training set. This results in failed lattice energy minimisation and no proper way to evaluate the residuals associated with those structures. The algorithm could continue despite this with the introduction of a penalty to the objective function, but, through testing, we find this tends to lead to unsatisfactory progress in the optimisation. Our strategy for handling lattice minimisation failures is therefore to remove the problematic structure(s) from the training set and reinitialise the parameter estimation algorithm (D3 in Figure ). When a failure is encountered, the T M F optimisation is aborted and the failed structure is temporarily removed from the training set. The algorithm is then reinitialised with the reduced training set and the optimisation is restarted from the parameter estimates at the last iteration. This allows the optimisation to 'escape' from regions of the parameter space where the lattice minimisation cannot be reliably solved for certain structures. On the basis of the remaining structures, CrystalEstimator will proceed until one of the previously described termination criteria (B3 to B6) are met. Following this, any removed structures are reintroduced into the training set and a final T M F optimisation and T M F re-evaluation are conducted (A3 to A5 in Figure ). This optimal result is reported without any possibility of further iterations of T M F optimisation. It should be noted, that the dynamic starting point and structure removal strategies are fully modular, and in principle one could choose to enable any combination of these strategies with the basic CrystalEstimator algorithm.