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This research applies conditional rectified flow and latent-space refinement to solve a concurrent two-scale topology optimization problem for printable bone scaffolds. By integrating machine learning with exact finite-element homogenization sensitivities, the method achieves sub-1% error in reproducing mechanical compliance while ensuring geometric feasibility for additive manufacturing. The work demonstrates a viable pathway for using generative AI to design complex microstructures that satisfy strict multiscale engineering constraints.
Concurrent two-scale topology optimization of printable bone scaffolds via rectified-flow generation and exact latent-space refinement
arXiv:2610.25565v1 Announce Type: cross Abstract: Bone scaffolds must reconcile a macroscale mechanical response with microscale geometric feasibility, yet conventional approaches to their design restrict attainable constitutive properties. This work presents a concurrent two-scale topology optimization framework; a conditional rectified flow generates periodic lattice microstructures, which are then refined in latent space by exact finite-element homogenization sensitivities. The resulting unit-cell geometries and their spatial assignments are jointly optimized under mechanical and feature-size constraints. In a distal rabbit femur benchmark, all eight flow-started refinements produce printable cells with maximum relative errors under 1\% across six prescribed engineering moduli. Constructing the implant from a single tiled cell reproduces intact whole-femur compliance within 0.1\% and regional strain energy within 0.35\% under four loading conditions. In human femoral reconstruction, multiscale concurrent optimization produces a cortical mid-shaft scaffold with porosity 63\% while satisfying the compliance constraint within 2\% under walking and stair-climbing loads. It achieves an 84\% porosity on a proximal cancellous scaffold with strain-energy deviations below 0.25\% under the same loads. Analysis of the learned representations reveals distinct architectural families in latent space. Further, the attention heads of the rectified-flow transformer specialize for spatial shifts -- learning the analogue of a finite-difference stencil -- and coordinate symmetries, with ablations showing their influence on generated topologies. These results establish a route to printable, mechanically constrained scaffold designs. The framework is general enough for extending to many other multiscale structural design applications including topology-microstructure co-design in metal additive manufacturing.
Abstract:Bone scaffolds must reconcile a macroscale mechanical response with microscale geometric feasibility, yet conventional approaches to their design restrict attainable constitutive properties. This work presents a concurrent two-scale topology optimization framework; a conditional rectified flow generates periodic lattice microstructures, which are then refined in latent space by exact finite-element homogenization sensitivities. The resulting unit-cell geometries and their spatial assignments are jointly optimized under mechanical and feature-size constraints. In a distal rabbit femur benchmark, all eight flow-started refinements produce printable cells with maximum relative errors under 1\% across six prescribed engineering moduli. Constructing the implant from a single tiled cell reproduces intact whole-femur compliance within 0.1\% and regional strain energy within 0.35\% under four loading conditions. In human femoral reconstruction, multiscale concurrent optimization produces a cortical mid-shaft scaffold with porosity 63\% while satisfying the compliance constraint within 2\% under walking and stair-climbing loads. It achieves an 84\% porosity on a proximal cancellous scaffold with strain-energy deviations below 0.25\% under the same loads. Analysis of the learned representations reveals distinct architectural families in latent space. Further, the attention heads of the rectified-flow transformer specialize for spatial shifts -- learning the analogue of a finite-difference stencil -- and coordinate symmetries, with ablations showing their influence on generated topologies. These results establish a route to printable, mechanically constrained scaffold designs. The framework is general enough for extending to many other multiscale structural design applications including topology-microstructure co-design in metal additive manufacturing.
Computational Physics (physics.comp-ph); Machine Learning (cs.LG)
arXiv:2610.25565 [physics.comp-ph]
(or arXiv:2610.25565v1 [physics.comp-ph] for this version)
https://doi.org/10.48550/arXiv.2610.25565 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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