A comprehensive understanding of genetic diversity and the categorization of germplasm is important to effectively identify appropriate parental candidates for the goal of breeding. It is necessary to have a technique of tissue culture that is both effective and reproducible to perform genetic engineering on fodder pea genotypes (Pisum sativum var. arvense L.). In this investigation, the genetic diversity of forty-two fodder pea genotypes was assessed based on their ability of callus induction (CI), the percentage of embryogenic callus by explant number (ECNEP), the percentage of responding embryogenic calluses by explant number (RECNEP), the number of somatic embryogenesis (NSE), the number of responding somatic embryogenesis (RSE), the regeneration efficiency (RE), and the number of regenerated plantlets (NRP). The findings of the ANOVA showed that there were significant differences (p < 0.001) between the genotypes for all in vitro parameters. The method of principal component analysis (PCA) was used to study the correlations that exist between the factors associated with tissue culture. While RE and NRP variables were most strongly associated with Doğruyol, Ovaçevirme-4, Doşeli-1, Yolgeçmez, and Incili-3 genotypes, RECNEP, NSE, RDE, and RECNEP variables were strongly associated with Avcılar, Ovaçevirme-3, and Ardahan Merkez-2 genotypes. The in vitro process is a complex multivariate process and more robust analyses are needed for linear and nonlinear parameters. Within the scope of this study, artificial neural network (ANN), random forest (RF), and multivariate adaptive regression spline (MARS) algorithms were used for RE estimation, and these algorithms were also compared. The results that we acquired from our research led us to the conclusion that the employed ANN-multilayer perceptron (ANN-MLP) model (R2 = 0.941) performs better than the RF model (R2 = 0.754) and the MARS model (R2 = 0.214). Despite this, it has been shown that the RF model is capable of accurately predicting RE in the early stages of the in vitro process. The current work is an inquiry regarding the use of RF, MARS, and ANN models in plant tissue culture, and it indicates the possibilities of application in a variety of economically important fodder peas.