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

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 L₂ 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 L₂ 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.