FE2 modelling provides a rigorous mechanistic link between a material’s microstructure and its macroscopic response, but its practical use is hindered by the high computational cost of solving a microscale boundary value problem at every macroscale integration point. Existing research [1, 2, 3] has extensively explored accelerating FE2 through surrogate models of the microscale problem. While effective for a fixed microscale problem, these approaches are not suitable for applications in which the microstructure or the mechanical behaviour of microscale constituents (henceforth termed “microbehavior”) varies spatially, must be optimized, or needs to be inferred from observed macro-scale responses. There is a need for hyper-homogenization, i.e., ability to predict the homogenized response for multi-phase microstructures with arbitrary morphology and microbehavior. To address this need, a hypernetwork-based surrogate modelling framework is proposed following [4], i.e. one neural network (the ”hypernetwork”) controls the weights of another neural network (the ”target network”). In particular, the hypernetwork takes as input descriptors of microstructural geometry and constituent behavior, and predicts the parameters of a target constitutive network. Microstructural geometry is characterized using the two-point correlation function, while microbehavior is encoded via POD coefficients obtained from a synthetic database of material model responses. The target network is constructed to guarantee objectivity, material symmetry, and polyconvexity by design, ensuring physical admissibility of the surrogate. The resulting model demonstrates strong predictive accuracy and generalization across a wide range of microstructures, material behaviors, and loading conditions, achieving stress prediction R2 values exceeding 0.95 on unseen cases. The framework is further shown to extend naturally to diffusion-type phenomena, including heat transfer, electrophysiology, and magnetostatics, in both linear and nonlinear regimes. REFERENCES [1] Temizer, İ. and Wriggers, P., CMAME, 196 (2007). [2] Zahr M.J., Avery P., and Charbel F. A, IJNME, 112 (2017). [3] Alheit B., Bargmann S., and Reddy B.D., Acta Biomat., 145 (2022). [4] Zheng L., Kochmann D.M., and Kumar S., Extreme Mech. Lett., 72 (2024).