Machine-learning-assisted multiscale topology optimization of functionally graded superimposed lattice structures
2026-08-28 • Computational Engineering, Finance, and Science
Computational Engineering, Finance, and Science
AI summaryⓘ
The authors developed a method to design lightweight 3D structures made from tiny repeating lattice units with different stiffness and density. They combined three types of lattice shapes and used computer simulations to understand their stiffness, training neural networks to quickly predict these properties. This approach helps speed up a two-step optimization process: first, they design a solid shape, then they fine-tune the lattice properties inside it. Their method was tested on a common engineering beam, showing it can create materials that save weight while maintaining strength.
Functionally graded lattice structuresMultiscale topology optimizationComputational homogenizationNeural network surrogateCholesky decompositionRelative densitySIMP methodMethod of moving asymptotes (MMA)Messerschmitt-Bölkow-Blohm (MBB) beamCompliance minimization
Authors
Prashant Kumar Gupta, Jonathan Stollberg, Dominik Schillinger, Mohammad Ashraf Iqbal
Abstract
Functionally graded lattice structures enable lightweight designs with spatially tunable stiffness and density, but their use in multiscale topology optimization is limited by the cost of repeated computational homogenization. This work presents a machine learning-assisted multiscale optimization framework for regular superimposed lattice structures. The unit cell is formed by combining body-centered cubic, face-centered cubic, and simple cubic lattice components, each controlled by an independent geometric parameter. Offline computational homogenization is used to generate effective stiffness data, which are then used to train a Cholesky-constrained neural network surrogate. This representation reconstructs the homogenized stiffness tensor in a physically admissible form. A separate neural network is trained to predict relative density from Monte Carlo-based density estimates. We incorporate our surrogates into a two-stage topology optimization strategy. First, a macroscale topology is obtained using the solid isotropic material with penalization (SIMP) method. The resulting solid region is then used for microscale lattice optimization, where the local lattice parameters are updated using the method of moving asymptotes (MMA). The trained stiffness and density surrogates replace repeated online homogenization during this stage. The method is demonstrated on a three-dimensional Messerschmitt-Bölkow-Blohm (MBB) beam benchmark, producing spatially varying lattice parameters and relative density fields consistent with compliance minimization under a material constraint.