Constrained Multiphysics Inverse Design of Two-Phase Composites with Differentiable Surrogates

We study the inverse design of two-phase composite microstructures that realize prescribed effective macroscopic mechanical and thermal properties. We accelerate effective-property calculations, which would otherwise require expensive simulations of the governing partial differential equations (PDE), using differentiable machine-learning surrogates. The surrogates are incorporated into an inverse design framework in which the target effective properties are imposed as constraints, while a regularity objective promotes smooth, nearly binary microstructures. Each optimized microstructure is validated using finite element (FE) simulations. Validation results for these designs show that the surrogate predictions of the stiffness and thermal conductivity agree with the FE results to within a few percent relative error, while the thermal expansion predictions are slightly less accurate.