The purpose of this paper is to investigate the utilization of artificial neural networks (ANNs) in learning models that address the nonlinear anisotropic flow and hysteresis retention behavior of deformable porous materials. Herein, the micro-geometries of various networks of porous Bentheimer Sandstones subjected to several degrees of strain from the literature are considered. For the generation of the database required for the training, validation, and testing of the machine learning (ML) models, single-phase and biphasic lattice Boltzmann (LB) simulations are performed. The anisotropic nature of the intrinsic permeability is investigated for the single-phase LB simulations. Thereafter, the database contains the computed average fluid velocities versus the pressure gradients. In this database, the range of applied fluid pressure gradients includes Darcy as well as non-Darcy flows. The generated output from the single-phase flow simulations is implemented in a feed-forward neural network, representing a path-independent informed graph-based model. Concerning the two-phase LB simulations, the Shan-Chen multiphase LB model is used to generate the retention curves of the cyclic drying/wetting processes in the deformed porous networks. Consequently, two different ML path-dependent approaches, that is, 1D convolutional neural network and the recurrent neural network, are used to model the biphasic flow through the deformable porous materials. A comparison in terms of accuracy and speed of training between the two approaches is presented. Conclusively, the outcomes of the papers show the capability of the ML models in representing constitutive relations for permeability and hysteretic retention curves accurately and efficiently.