# Nature-Inspired Optimization Algorithms for the 3D Reconstruction of Porous Media
## 1 Introduction  
Nowadays, porous media have attracted multidisciplinary attention due to their notable properties, which have broadened their applications in the petroleum [1] and chemical industries [2], hydrology [3], etc. This increased interest makes the accurate analysis of the microstructural behavior of the examined porous media a great field of research. To accurately measure the transport properties of a porous material, e.g., diffusivity, permeability, and conductivity, the 3D material structure needs to be known. However, the acquisition of the 3D structure of a material requires microscopes of high technology and high cost, as well as a high processing time. Alternatively, the 3D material structure can be derived by applying a computational reconstruction technique that uses a single 2D image of the material that is acquired using conventional imaging equipment [4]. The first reconstruction method was proposed quite early by [PERSON] [5] in the yearswhen imaging systems were limited and displayed marginal performance. Lately, [PERSON] et al. [6] generalized [PERSON]'s method to measure the flow in porous media, while [PERSON] and [PERSON] [7] proposed a simplified version of [PERSON]'s method, which is free of filter parameter calculations but adds a significant computational overhead. Since then, several algorithms have been proposed [8; 9; 10; 11] aiming to improve the reconstruction accuracy. Almost all algorithms make use of specific correlation functions for measuring the morphology of the material's microstructure. The spatial correlation functions [12], such as auto-correlation functions, have proved to be good descriptors of the porous space morphology, while their simplicity accelerates the overall reconstruction procedure. More recent attempts to develop a reliable 3D reconstruction of porous media from a single 2D image were targeted toward investigating the connectivity of the flow paths by utilizing reconstruction approaches using multiple-point statistics [13; 14; 15], cross-correlation functions [16; 17; 18], spatial correlation functions [19], and multiple statistical functions [20]. The majority of these approaches consist of several simple processing steps in an iterative manner, where the 3D material is reconstructed layer by layer through repetitive comparisons with the 2D slice reference image. Of course, the reconstruction accuracy is higher if more information is retrieved from the initial 2D image. Very recent works [21; 22; 23] have tried to utilize the advantages of the deep learning models to represent some initial information (2D thin image) with massive abstract features and to generate possible 3D reconstructions as adversarial images of the input information. However, these approaches are time-consuming and need many annotated samples from the same material for model training, which in most cases are difficult to collect. Among the reconstruction methods presented in the literature, the work of [PERSON] and [PERSON] [9; 10] exhibits some remarkable properties relative to its simplicity and efficiency. In their work [PERSON] and [PERSON] tackled the reconstruction procedure as an optimization problem, which they solved by applying the simulated annealing (SA) algorithm. Of course, the main weakness of this method is the high computation time stemming from the low convergence time of the SA algorithm. Motivated by the method of [PERSON] and [PERSON] [9; 10], in this study, we examine the reconstruction performance of porous media when several traditional, as well as recently proposed, nature-inspired optimization algorithms are used instead of SA.