DiFVM: A Vectorized Graph-Based Finite Volume Solver for Differentiable CFD on Unstructured Meshes

Differentiable programming has emerged as an important tool for gradient-based inverse problems and end-to-end hybrid physics-machine learning in computational fluid dynamics. Existing differentiable CFD platforms predominantly rely on structured Cartesian grids, limiting their direct application to geometrically complex domains where body-conforming unstructured discretizations are essential. We present DiFVM, the first GPU-native, end-to-end differentiable finite-volume (FV) CFD solver for incompressible flow on unstructured polyhedral meshes. The central methodological contribution is a graph-based computational reformulation of the complete unstructured FV/PISO solution procedure: by expressing FV operators as static scatter/gather primitives on the mesh connectivity graph, DiFVM transforms irregular unstructured connectivity into a GPU-compatible computational representation. 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 accuracy is assessed through analytical and canonical benchmark problems, comparisons with published reference data, and independent solver comparisons, while end-to-end differentiability is demonstrated through proof-of-concept inverse modeling examples. DiFVM provides a differentiable CFD framework for gradient-based optimization, inverse modeling and future physics-integrated machine learning on complex unstructured geometries.