Fast and realistic coupling of blood flow and vessel wall is of great importance to virtual surgery. In this paper, we propose a novel data-driven coupling method that formulates physics-based blood flow simulation as a regression problem, using an improved periodic-corrected neural network (PcNet), estimating the acceleration of every particle at each frame to obtain fast, stable and realistic simulation. We design a particle state feature vector based on smoothed particle hydrodynamics (SPH), modeling the mixed contribution of neighboring proxy particles on the blood vessel wall and neighboring blood particles, giving the extrapolation ability to deal with more complex couplings. We present a semi-supervised training strategy to improve the traditional BP neural network, which corrects the error periodically to ensure long term stability. Experimental results demonstrate that our method is able to implement stable and vivid coupling of blood flow and vessel wall while greatly improving computational efficiency.
@cite_9: Physically based fluid simulation requires much time in numerical calculation to solve Navier-Stokes equations. Especially in grid-based fluid simulation, because of iterative computation, the projection step is much more time-consuming than other steps. In this paper, we propose a novel data-driven projection method using an artificial neural network to avoid iterative computation. Once the grid resolution is decided, our data-driven method could obtain projection results in relatively constant time per grid cell, which is independent of scene complexity. Experimental results demonstrated that our data-driven method drastically speeded up the computation in the projection step. With the growth of grid resolution, the speed-up would increase strikingly. In addition, our method is still applicable in different fluid scenes with some alterations, when computational cost is more important than physical accuracy. Copyright © 2016 John Wiley & Sons, Ltd.
@cite_10: Traditional fluid simulations require large computational resources even for an average sized scene with the main bottleneck being a very small time step size, required to guarantee the stability of the solution. Despite a large progress in parallel computing and efficient algorithms for pressure computation in the recent years, realtime fluid simulations have been possible only under very restricted conditions. In this paper we propose a novel machine learning based approach, that formulates physics-based fluid simulation as a regression problem, estimating the acceleration of every particle for each frame. We designed a feature vector, directly modelling individual forces and constraints from the Navier-Stokes equations, giving the method strong generalization properties to reliably predict positions and velocities of particles in a large time step setting on yet unseen test videos. We used a regression forest to approximate the behaviour of particles observed in the large training set of simulations obtained using a traditional solver. Our GPU implementation led to a speed-up of one to three orders of magnitude compared to the state-of-the-art position-based fluid solver and runs in real-time for systems with up to 2 million particles.
@cite_6: 
In recent years, data-driven methods are increasingly proposed in the field of fluid simulation. generated a large number of fluid simulations by interpolating the existing fluid simulation results. @cite_6 used neural network prediction instead of the diffusion projection in the gridding method to achieve a speed increase of about 10 times. @cite_9 used regression forests to simulate fluid particle state changes, which can achieve 10-1000 times faster operation on the GPU. @cite_10 At present, there are few studies that combine data-driven methods with blood flow simulation and even virtual surgery.