Physics-Guided Generative Inverse Design of Thermally Anisotropic Microstructures via FEM-Validated Conditional GANs

Inverse design problems governed by physical laws are challenging due to the nonlinear, high-dimensional, and non-unique relationships between the internal structure and the macroscopic response. While data-driven generative models have been applied to inverse microstructure design, maintaining physical consistency and scalability remains an important consideration for practical use. In this work, we present a physics-guided generative inverse design framework that combines finite element method (FEM) simulations with a conditional Wasserstein generative adversarial network (GAN) to generate microstructural images conditioned on target physical properties. Rather than incorporating governing equations directly into the learning objective, physical laws are enforced through FEM-based data generation and assessed through closed-loop FEM re-simulation of the generated microstructures. All forward simulations are carried out using FEniCS, an open-source Python-based FEM platform that supports automated, scalable parallel execution. The framework is demonstrated through the inverse design of thermally anisotropic microstructures containing parallel elliptical pores, a geometry motivated by its relevance to established ceramic processing routes. FEM validation indicates that the generated microstructures reproduce prescribed directional thermal conductivities with relative errors typically below 5-10% across a broad range of anisotropy conditions, while preserving key geometric characteristics without explicit geometric constraints. These results suggest that physics-guided generative modeling provides a practical and flexible approach for inverse microstructure design in physically governed systems.