Agent-based models (ABMs) are powerful computational tools for studying viral infections such as EBV and HIV, capturing spatial heterogeneity in infected cell distributions, immune cell positioning, and cell-cell interactions that critically influence disease progression and therapeutic outcomes. However, the computational expense of ABMs limits parameter exploration, making systematic optimization of antiviral treatment strategies infeasible. Traditional mean-field ordinary differential equation (ODE) approximations offer computational efficiency but sacrifice critical spatial details, such as infected cell clustering and localized immune responses, which are essential drivers of viral dynamics. We develop scientific machine learning (SciML) approaches based on the Sparse Identification of Nonlinear Dynamics (SINDy) method to learn computationally tractable ODE surrogate models from ABM simulations while explicitly preserving biologically relevant spatial correlation structure [1][2]. To incorporate spatial correlations into the learned equations, we modify SINDy by augmenting the candidate library with spatial correlation functions that quantify clustering between cell types (e.g., infected vs. uninfected cells, activated vs. naive immune cells). To promote reliable selection of these correlation terms, we investigate modified penalty terms that reduce selection costs for spatial correlation functions. We apply this framework to ABM simulations of HIV and EBV infections to demonstrate potential applications to real-world data. By demonstrating that spatial correlations can be systematically preserved in data-driven surrogates, this work bridges mechanistic modeling and machine learning to advance computational systems biology.