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

Abstract

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 $27.86$, 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, failure-aware feasibility prediction, manifold-aware trust regions, and target-aware acquisition. Within a budget of $160$ simulations, the ViT-FMDiT and MERIDIAN combination yields the best target-driven objective score, reducing the relative target error by $3$--$22\%$ against seven baselines (DANTE, TuRBO, BAxUS, CMA-ES, DDOM, SEIKO, DDPO) on the same decoder.