Mingqi Xu

Pan Du, Yongqi Li, Mingqi Xu et al.

Differentiable programming has emerged as a structural prerequisite for gradient-based inverse problems and end-to-end hybrid physics--machine learning in computational fluid dynamics. However, existing differentiable CFD platforms are confined to structured Cartesian grids, excluding the geometrically complex domains where body-conforming unstructured discretizations are indispensable. We present DiFVM, the first GPU-accelerated, end-to-end differentiable finite-volume CFD solver operating natively on unstructured polyhedral meshes. The key enabling insight is a structural isomorphism between finite-volume discretization and graph neural network message-passing: by reformulating all FVM operators as static scatter/gather primitives on the mesh connectivity graph, DiFVM transforms irregular unstructured connectivity into a first-class GPU data structure. All operations are implemented in JAX/XLA, providing just-in-time compilation, operator fusion, and automatic differentiation through the complete simulation pipeline. Differentiable Windkessel outlet boundary conditions are provided for cardiovascular applications, and DiFVM accepts standard OpenFOAM case directories without modification for seamless adoption in existing workflows. Forward validation across benchmarks spanning canonical flows to patient-specific hemodynamics demonstrates close agreement with OpenFOAM, and end-to-end differentiability is demonstrated through inference of Windkessel parameters from sparse observations. DiFVM bridges the critical gap between differentiable programming and unstructured-mesh CFD, enabling gradient-based inverse problems and physics-integrated machine learning on complex engineering geometries.

Pan Du, Mingqi Xu, Xiaozhi Zhu et al.

Accurate characterization of vascular geometry is essential for cardiovascular diagnosis and treatment planning. Traditional statistical shape modeling (SSM) methods rely on linear assumptions, limiting their expressivity and scalability to complex topologies such as multi-branch vascular structures. We introduce HUG-VAS, a Hierarchical NURBS Generative model for Vascular geometry Synthesis, which integrates NURBS surface parameterization with diffusion-based generative modeling to synthesize realistic, fine-grained aortic geometries. Trained with 21 patient-specific samples, HUG-VAS generates anatomically faithful aortas with supra-aortic branches, yielding biomarker distributions that closely match those of the original dataset. HUG-VAS adopts a hierarchical architecture comprising a denoising diffusion model that generates centerlines and a guided diffusion model that synthesizes radial profiles conditioned on those centerlines, thereby capturing two layers of anatomical variability. Critically, the framework supports zero-shot conditional generation from image-derived priors, enabling practical applications such as interactive semi-automatic segmentation, robust reconstruction under degraded imaging conditions, and implantable device optimization. To our knowledge, HUG-VAS is the first SSM framework to bridge image-derived priors with generative shape modeling via a unified integration of NURBS parameterization and hierarchical diffusion processes.