Co-PiLOT: Constrained Physics-Informed Latent Optimization for Target-Driven Inverse Design

Inverse design of physical systems (molecules, devices, microstructures) often reduces to optimizing a high-dimensional structure against an expensive black-box simulator. Direct search is difficult because the space is non-Euclidean, feasibility is hard to encode, and each evaluation is expensive. We present Co-PiLOT, a latent optimization approach that maps candidates through a generative encoder--decoder, uses the decoder as a learned validity prior, and searches the latent space with physics-informed black-box optimization. The framework is applied on the inverse design of magnesium alloy microstructure/texture. We develop a vision transformer based--encoder; paired with latent diffusion, diffusion transformer and rectified-flow transformer--based decoders on $\sim80{,}000$ EBSD-derived microstructure dataset to learn a minimal bottleneck, $z$. The ViT-FMDiT model ($z$=$768$) reconstructs high-fidelity microstructure images (FID $23.19$, MS-SSIM $0.178$), which our self-segmenting orientation codec converts into input grids for crystal plasticity solver. Finally, we introduce Meridian, an active latent optimizer driven by deep-kernel Gaussian-process uncertainty, feasibility prediction, active trust regions, and target-aware acquisition. Within the evaluation budget, the ViT-FMDiT and Meridian combination yields the best target-driven objective score, outperforming DANTE, TuRBO, and BAxUS by $\sim6$\% in relative error on the same decoder.