Abstract <p>This paper presents a neural operator-based approach for numerical homogenization of elliptic equations in heterogeneous media. Traditional methods require solving expensive local cell problems to determine effective coefficients, creating computational bottlenecks. We develop a learning framework using Fourier neural operators (FNOs) to directly map heterogeneous permeability fields to effective tensors, bypassing iterative cell problem solutions. The methodology exploits function-to-function learning to capture relationships between microscale heterogeneities and macroscale properties. Training data consists of stochastic permeability fields generated via Karhunen–Loève expansion with reference solutions from classical homogenization. Numerical experiments demonstrate significant computational speedup with preserved accuracy in predicting effective permeability tensors. The approach shows excellent generalization across different permeability configurations and mesh resolutions, with particular promise for applications requiring repeated homogenization computations.</p>