“Modeling and simulation of vascular flows: Reduced order modeling and physics based neural network”
Prof. Simone Deparis is Adjunct Professor in Mathematics and deputy director of the Section of Mathematics
Monday, 5th Oct 2020
We are interested in the approximation of vascular flows modeled by parametrized partial differential equations, when the value of the physical parameters is unknown or difficult to be directly measured. We aim at estimating the flows field or other quantities of clinical interest by combining reduced order modeling with neural networks.
The reduced order model accounts for the underlying physical phenomenon and allows for generating a large test set for the training of the neural network. The snapshots are obtained from randomly selected values of the physical parameters during an expensive offline phase. The chosen DNN architecture resembles an asymmetric autoencoder in which the decoder is the reduced orde model solver and it does not contain trainable parameters.
We present few examples of our method in applications related to vascular flows and electrophysiology, where the neural network is able to approximately identify the physical parameters or clinical indices.
Simone Deparis is Adjunct Professor in Mathematics and deputy director of the Section of Mathematics. His research focuses on scientific computing and numerical analysis applied to haemodynamics, but he also studies reduced order models for the Navier-Stokes equations and blood flow. Recently he has begun to investigate the interplay between reduced basis and neural network approaches for parametrised PDEs.