Subsurface porous media, like aquifers, petroleum reservoirs, and geothermal systems, are vital for natural resources and environmental management. Extensive research has been conducted to understand flow and transport in these media, addressing challenges in hydrocarbon extraction, carbon storage and waste management. Classifying the type of porous media (e.g., sandstone, carbonate) is often the first step in the rock characterization process, and it provides critical information regarding the physical properties of the porous media. Therefore, we utilize multivariate statistical methods with discriminant analysis to categorize porous media samples which proved to be efficient by achieving excellent classification accuracy on testing datasets and served as a surrogate tool to study key porous media characteristics. While recent advances in three-dimensional (3D) imaging of core samples have enabled digital subsurface characterization, the exorbitant computational cost associated with direct numerical simulation in 3D remains a persistent challenge. In contrast, machine learning (ML) models are much more efficient, though their use in subsurface characterization is still in its infancy. Therefore, we introduce a novel 3D convolution neural network (CNN) for end-to-end prediction of permeability. By increasing dataset size, diversity, and optimizing the network architecture, our model surpasses the accuracy of existing 3D CNN models for permeability prediction. It demonstrates excellent generalizability, accurately predicting permeability in previously unseen samples. However, despite the efficiency of the developed 3D CNN model for accurate and fast permeability prediction, its utility remains limited to small subdomains of the digital rock samples. Therefore, we introduce an upscaling technique using a new analytical solution to calculate effective permeability in a 3D digital rock composed of 2 × 2 × 2 anisotropic cells. By incorporating this solution into physics-informed neural network (PINN) models, we achieve highly accurate results. Even when upscaling previously unseen samples at multiple levels, the PINN with the physics-informed module maintains excellent accuracy. This advancement enhances the capability of ML models, like 3D CNN, for efficient and accurate digital rock analysis at the core scale. After successfully applying ML models in permeability prediction, we now extend their application to another important parameter in subsurface engineering projects: effective thermal conductivity, which is a key parameter in engineering projects like radioactive waste repositories, geothermal energy production, and underground energy storage. To address the need for large training data and processing power in ML models, we propose a novel framework based on transfer learning. This approach allows prior knowledge from previous applications to be transferred, resulting in faster and more efficient implementation of new relevant applications. We introduce CNN models trained on various porous media samples that leverage transfer learning to predict porous media sample thermal conductivity accurately. Our approach reduces training time, processing power, and data requirements, enabling effective prediction and analysis of porous media properties such as permeability and thermal conductivity. It also facilitates the application of ML to other properties, improving efficiency and accuracy. / Thesis / Doctor of Philosophy (PhD)