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

2026-03-16

AI Summary

针对非结构网格CFD不可微问题，提出DiFVM方法，将有限体积法算子转化为图神经网络消息传递操作，实现端到端可微与GPU加速。

Technology Category

• Machine Learning: Graph-based Machine Learning
• Computer Vision: Diffusion Models for Vision
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Content-based information diffusion
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

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.

Problem

• differentiable CFD
• unstructured meshes
• gradient-based inverse problems
• computational fluid dynamics
• complex geometries

Innovation

• differentiable CFD
• unstructured meshes
• finite volume method
• graph neural networks
• GPU acceleration