As the size of the test problem grows, convergence of the algorithm becomes progressively more challenging. No optimisation converged to a locally minimum point for TP5 and TP7, and instead the vast majority of the optimisations terminate based on the alternate termination criteria. A few algorithmic failures are also recorded for these problems, which arise when a significant number of structures fail the lattice energy minimisation, indicating that the optimiser has entered a region of unphysical parameter values. Under this circumstance, the optimiser is unable to recover and the algorithm terminates prematurely. For TP6, slightly over half of the optimisations converged to the same locally minimum point while the rest of the optimisations converged to a sub-optimal point. Again, the reasons for poor convergence of the algorithm appear to be small discontinuities in the T M F at or close to its minimum point(s). Despite this, the parameter estimates obtained from sub-optimal convergence can still be adopted. The final T M F values obtained from each Sobol' point are plotted in Figure for TP5 and TP7. For both, although no locally minimum points are identified, most of the optimisations achieve similarly low values for the final T M F value. In general, with increasing dissimilarity to the best Sobol' solution (as indicated by the Euclidean distance), the T M F value exhibits a corresponding increase. In Figure , the trend between the number of residuals and the best T M F value observed for each test problem is shown. Although TP5 and TP7 do not converge to an optima, their T M F values adhere well to the projected trend for the remaining test problems (in fact the best solution in TP7 lies below the trendline). Altogether, these indicate that while the very best possible values parameter estimates may not have been obtained in TP5 and TP7, the algorithm is progressing towards the correct region in solution space and the final T M F is likely in the proximity of the true optimum. some of the other optimisation strategies discussed earlier. Analytical gradient calculations significantly reduce the computational cost of each iteration relative to finite difference approaches, while the improved accuracy in the gradients may also reduce the number of iterations required for the algorithm to reach termination. The number of Sobol' samples used for each of the test problems is also significantly reduced (by approximately an order of magnitude) compared to the work of Bowskill et al. , but the sample size used here seems more than sufficient to achieve reliable parameter estimates. This is likely to be a reflection of the more robust local optimisation procedure, which allows the parameter space to be sampled much more sparsely without any loss in the performance of the best parameter estimates obtained. The combination of faster optimisations and reduced sampling leads to a reduction in overall computational cost of 3-4 orders of magnitude.