**4. Conclusions**

The development and refinement of metamodelling (or surrogate modelling) approaches is a beneficial step in expanding the capabilities in simulation-based SMC compression moulding process optimisation and reducing computational demand.

In this paper, an ensemble metamodelling approach is proposed, in which the spatial discretisation necessary for process and structural simulation is exploited. Hereby, the initial filling states of each element are used as input variables for the metamodel. To mitigate the effects of overfitting, an ensemble modelling approach is used in which the mean outputs of 100 FF-NN is used as output of the metamodel. Training of the FF-NN is conducted on datasets obtained by process and structural simulation with random starting weights. Contrary to metamodelling approaches successfully implemented in the

past, this approach enables defining the preform without inherent geometry restrictions, as viable geometries are only dependent on the discretisation itself.

The approach is used to predict the preform geometry and position-dependent maximum deflection of a plate geometry under cantilever bending load. Maximum absolute deflection can be accurately predicted by the metamodel, with deviations between metamodel prediction and FEM validation ranging from 0.26% to 2.67%.

The usability of the metamodel in a subsequently conducted preform optimisation routine can be shown, but it is believed to be limited by the closeness of local optima to each other and chosen boundary conditions for mould coverage. For purpose of procedure development, a fairly simple plate geometry was chosen, limiting the potential in finding non-obvious solutions.

Further work will focus on the evaluation of alternative optimisation routines, which make use of the prediction accuracy of this metamodelling approach more e fficiently. These could be derived from methodologies found in topology optimisation. One method that could be applicable to the metamodel is Solid Isotropic Material with Penalisation (SIMP), which was initially proposed by Bendsoe and Kikuchi [73]. An additional focus will be the application to parts with higher geometric complexity and alternative load cases, for which the potential of deriving non-apparent preform geometries and positions and thus potential for industrial applicability is higher. Subsequently, comparison with experimentally obtained part behaviour will be conducted.

**Author Contributions:** J.N. and R.L.P.G. conceived and implemented the methodologies and procedures. J.N. prepared the original draft and visualisations. C.H., K.F. and D.S. reviewed and edited the original draft and provided project supervision. All authors have read and agreed to the published version of the manuscript.

**Funding:** The investigations set out in this report received financial support from the European Regional Development Fund (No.: EFRE-0801121), to whom we extend our thanks.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
