A Flow-rate-conserving CNN-based Domain Decomposition Method for Blood Flow Simulations

This work aims to predict blood flow with non-Newtonian viscosity in stenosed arteries using convolutional neural network (CNN) surrogate models. An alternating Schwarz domain decomposition method is proposed which uses CNN-based subdomain solvers. A universal subdomain solver (USDS) is trained on a single, fixed geometry and then applied for each subdomain solve in the Schwarz method. Results for two-dimensional stenotic arteries of varying shape and length for different inflow conditions are presented and statistically evaluated. One key finding, when using a limited amount of training data, is the need to implement a USDS which preserves some of the physics, as, in our case, flow rate conservation. A physics-aware approach outperforms purely data-driven USDS, delivering improved subdomain solutions and preventing overshooting or undershooting of the global solution during the Schwarz iterations, thereby leading to more reliable convergence.

Generating observation guided ensembles for data assimilation with denoising diffusion probabilistic model

This paper presents an ensemble data assimilation method using the pseudo ensembles generated by denoising diffusion probabilistic model. Since the model is trained against noisy and sparse observation data, this model can produce divergent ensembles close to observations. Thanks to the variance in generated ensembles, our proposed method displays better performance than the well-established ensemble data assimilation method when the simulation model is imperfect.