<p>Homogenization has enabled the analysis and tailoring of lattice structures to achieve desired properties. The observation of size effects in these structures, along with the inability of conventional or first-order homogenization techniques to capture them, has driven higher-order homogenization methods. In tailoring, higher-order techniques enable the optimization of lattices even with few cells, overcoming the limitation of first-order approaches which may result in unmanufacturable small features. However, their high computational cost remains a bottleneck for industrial adoption. To address this, we propose a machine learning-assisted surrogate model that accelerates second-order asymptotic homogenization, enabling both rapid forward prediction of higher-order properties and size-effect-aware inverse design. The model applies to cubic unit-cell lattices of linear elastic, homogeneous, isotropic materials under very small deformations and rotations, and computes the equivalent strain-gradient tensors instantaneously. Inputs are unit-cell overall dimension, strut radius, and the constituent Young’s modulus and Poisson’s ratio. In the model, relationships between the overall cell dimension and Young’s modulus with the equivalent tensors are derived analytically. Effects of strut radius and Poisson’s ratio are captured using machine learning: polynomial surrogates with data-driven degrees trained on an FEM-generated second-order homogenization database. Model verification showed ~ 1% error for most parameters. To validate performance, we solved several tailoring problems. In the most size-effect-dominated case, our model achieved 4.13% error versus the prescribed target, whereas first-order homogenization yielded 92.21% error. Coupled with a reduction in optimization time—from many hours to minutes—this demonstrates the proposed approach’s potential for efficient and accurate porous structural tailoring.</p>