Objective To address the limitations of conventional physics-informed neural network(PINN)in handling hemodynamic boundary constraints,an improved hard boundary-constrained PINN(HBC-PINN)framework was proposed to achieve precise prediction of blood flow fields within stenotic arteries.Methods An idealized stenosed vessel geometry model was established and computational fluid dynamic simulation was performed to obtain a validation dataset.Appropriate boundary dependent trial functions were designed according to the hard constraint method to embed the flow boundary conditions into the network output.Thus,an HBC-PINN model with the hard boundary constraint method was constructed to predict the velocity field and pressure field of stenosed blood flow.Meanwhile,an original PINN model with the soft constraint method was also built for comparison.By evaluating the accuracy of the two models on the validation dataset,the capability of the HBC-PINN model to simulate hemodynamics without using any labeled data for training was verified.Results The effectiveness of the HBC-PINN method in predicting hemodynamic parameters in stenosed blood flow tasks was validated.The relative L2 errors of the flow velocity and pressure predicted by the HBC-PINN in two different stenosis scenarios were both lower than 0.5％,representing an improvement of over 48.8％in accuracy compared to the original PINN model.Additionally,the prediction accuracy of the transverse velocity also increased by more than 35.4％.Conclusions Implementing hard constraints on boundary conditions in the PINN modeling process can effectively improve the prediction accuracy of hemodynamic parameters and the efficiency of model solving.

Objective To address the limitations of conventional physics-informed neural network(PINN)in handling hemodynamic boundary constraints,an improved hard boundary-constrained PINN(HBC-PINN)framework was proposed to achieve precise prediction of blood flow fields within stenotic arteries.Methods An idealized stenosed vessel geometry model was established and computational fluid dynamic simulation was performed to obtain a validation dataset.Appropriate boundary dependent trial functions were designed according to the hard constraint method to embed the flow boundary conditions into the network output.Thus,an HBC-PINN model with the hard boundary constraint method was constructed to predict the velocity field and pressure field of stenosed blood flow.Meanwhile,an original PINN model with the soft constraint method was also built for comparison.By evaluating the accuracy of the two models on the validation dataset,the capability of the HBC-PINN model to simulate hemodynamics without using any labeled data for training was verified.Results The effectiveness of the HBC-PINN method in predicting hemodynamic parameters in stenosed blood flow tasks was validated.The relative L2 errors of the flow velocity and pressure predicted by the HBC-PINN in two different stenosis scenarios were both lower than 0.5％,representing an improvement of over 48.8％in accuracy compared to the original PINN model.Additionally,the prediction accuracy of the transverse velocity also increased by more than 35.4％.Conclusions Implementing hard constraints on boundary conditions in the PINN modeling process can effectively improve the prediction accuracy of hemodynamic parameters and the efficiency of model solving.