Multivariate flow dynamics-conditioned diffusion for automated structural optimization of semi-filled micro gas...

Semi-filled microcolumns in micro gas chromatography (μGC) demand precise structural optimization to balance separation efficiency and backpressure, a task complicated by the multivariate coupling of micro-post geometries, flow uniformity, and analyte dispersion dynamics. Conventional approaches, including computational fluid dynamics (CFD) parameter sweeps and existing generative models, often neglect spatial heterogeneity and fail to preserve covariance structures in flow behavior. This work introduces a Multi-dimensional Continuous Conditional Diffusion Model (M-CCDM) to address these challenges. Unlike traditional theoretical frameworks reliant on idealized assumptions such as uniform porosity or homogenized permeability, M-CCDM directly learns the high-dimensional relationship between micro-post architectures and CFD-derived velocity descriptors through Mahalanobis-distance-aligned denoising. By explicitly encoding the covariance structure of velocity differences across diagnostic cross-sections, the model generates designs that inherently satisfy coupled fluid-dynamic constraints without resorting to analytical simplifications. Experimental validations confirm that M-CCDM bridges data-driven optimization with manufacturable microfluidic architectures, establishing a paradigm for automated design of high-performance μGC columns in environmental sensing and lab-on-a-chip systems.