Cerebrovascular flow field reconstruction method based on residual network of physical information

Abstract

Accurate characterization of the hemodynamic environment within intracranial aneurysms is important for rupture‐risk assessment and interventional treatment planning. Although computational fluid dynamics (CFD) provides high‐fidelity flow‐field data, its computational cost limits parametric analyses across multiple vascular geometries and inlet flow conditions. Existing physics‐informed neural‐network surrogates are predominantly trained for individual geometries and single flow conditions. Systematic comparisons of performance degradation under geometric and flow‐rate distribution shifts across different architectures remain lacking, and the distinct roles of physics‐based constraints under in-distribution versus out‐of‐distribution conditions have not been thoroughly examined. This study proposes PIReN, a physics‐informed residual network that decomposes the velocity‐pressure field into a learnable baseline field and a gated residual correction. The training objective incorporates continuity and steady, incompressible Navier‐Stokes momentum residuals. Training and in‐domain evaluation employ seven geometries; zero‐shot testing uses 16 fully held‐out geometries, and flow‐rate generalization is evaluated via five leave‐one‐flow‐rate‐out folds. These two protocols withhold complete geometries or flow conditions and avoid spatial-correlation leakage. In the pointwise‐random in‐domain test, PIReN achieves an aggregate relative L 2 error of 11.34% ± 0.65%, outperforming a standard PINN (16.57% ± 1.04%) and purely supervised MLP (14.74% ± 0.72%). These optimistic values describe spatial‐interpolation accuracy. Using a contiguous axial held‐out block while fixing model weights, PIReN still delivers superior accuracy: under the pooled configuration, its aggregate relative L 2 error is 30.35%± 2.55% versus 39.27%±2.85% for PINN. PIReN dominates across all four metrics, both partitions and five configurations, with a larger absolute performance margin under the stricter block partition. On geometry set B, the corresponding errors for PIReN and the PINN are 42.71% and 121.92%, respectively. Ablation studies show that removing the residual decoder produces the largest increase in prediction error, whereas the physics‐informed loss terms primarily reduce governing‐equation residuals. These results indicate that PIReN reduces performance degradation under changes in vascular geometry and inlet flow rate and provides a promising framework for steady‐state cerebrovascular flow‐field surrogate modeling.