# Nature-Inspired Optimization Algorithms for the 3D Reconstruction of Porous Media
## 5 Conclusion and Future Work  
The problem of the 3D reconstruction of porous media from a single 2D material image using six nature-inspired optimization algorithms was studied. Although the reconstruction results were very accurate in terms of \(MSE\) for the case of the \(\{R_{z},~{}\varepsilon\}\) statistical functions, the visual representation deviated significantly from the desired materials' microstructures. This contradiction between the numerical and visual performance of the reconstruction methodology was due to the existence of more than one different 3D microstructure having the same statistical properties \(\{R_{z},~{}\varepsilon\}\). Moreover, the suboptimal configuration of the algorithms also affected the numerical accuracy of the methodology, and a sensitivity analysis of the optimization algorithms regarding their free parameters is needed. However, this study sheds light on two important issues: (1) a nature-inspired algorithm could reconstruct the 3D porous media by applying an appropriate data representation scheme despite the complex search space and (2) there are needs for more descriptive and higher-order [46; 47] functions for measuring the material's phase distribution to increase the fidelity of the reconstructed microstructure. These outcomes pave the way for future research toward the development of an efficient reconstruction algorithm in terms of accuracy and processing time.  
As far as the computation time is concerned, the high computational burden stemming from the sources described in Section 3.3 can be reduced by applying modern parallel computing frameworks (e.g., MPI - Message Passing Interface, GPU programming, thread programming, MapReduce, Spark, cluster computing, and grid computing). For example, the high parallelism of all the nature-inspired algorithms enables the implementation of the algorithms (fitness computation) by utilizing the parallel computing capabilities of a GPU (graphics processing unit) Nvidia card within the CUDA architecture [48]. The development of an accelerated nature-inspired algorithm in conjunction with the proposed data representation scheme will allow for the execution of an algorithm with a larger population size and more iterations that can increase the reconstruction accuracy.  
Finally, additional research should be arranged toward the direction of applying higher-order statistics to describe the microstructure of the material uniquely. The proposed generic form of the objective function can help in this direction since it enables the incorporation of any number and type of functions with minimal modifications.  
Methodology, G.A.P., J.W.N., and A.C.M.; software, G.A.P. and J.W.N.; validation, J.W.N. and A.C.M.; investigation, G.A.P.; writing--original draft preparation, G.A.P.; writing--review and editing, J.W.N. and A.C.M.; supervision, G.A.P. and J.W.N.; project administration, A.C.M.; funding acquisition, A.C.M. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Thalis \"NANOCAPILARY MIS 375233\" research project of the Greek Ministry of National Education and Religious Affairs.  
The authors declare no conflict of interest.