VortexOp: Autonomous Physics-Guided Discovery of Functionally Graded Metamaterials

Abstract Designing functionally graded lattices requires control of the architecture under complex loading, yet conventional workflows often rely on static datasets and sequential simulations. We developed VortexOp, a physics-informed active-learning framework for the automated design of functionally graded triply periodic minimal surface (TPMS) lattices. The workflow combines implicit TPMS generation, a GPU-accelerated finite element solver, and constrained Bayesian optimization. Gaussian Process surrogates search a five-dimensional mixed continuous–integer design space for architectures that balance structural reliability and material use. The integrated solver agreed well with commercial simulation software, and linear fits constrained through the origin gave coefficients of determination of 0.93–0.99 for the surrogate predictions along the optimization trajectory. The search identified non-dominated designs, with fitness histories stabilizing within about 30 iterations. Proof-of-concept compression tests on additively manufactured specimens, with one specimen tested per architecture and volume-fraction configuration, produced deformation patterns consistent with the simulated stress redistribution. Relative to uniform lattices, the optimized designs reduced the mean nodal failure index by 21.4–47.0% and FI90 by 21.2–52.4%; stated in the opposite direction, the uniform baselines had mean failure indices 27.3–88.7% higher. These failure-index values, the percentage reductions derived from them, and the corresponding design comparisons are specific to the meshes employed in this study; their stability under systematic volumetric mesh refinement has not been established. The optimized designs traded initial stiffness and peak stress for a wider range of stable deformation. These results show how an integrated solver–optimizer can support lightweight lattice design under specified loading and manufacturing assumptions.