The present work proposes a framework for nonlinear model order reduction based on a
Graph Convolutional Autoencoder (GCA-ROM). In the reduced order modeling (ROM) …

Learning approximations to smooth target functions of many variables from finite sets of
pointwise samples is an important task in scientific computing and its many applications in …

Computational fluid dynamics (CFD) is an important tool for the simulation of the
cardiovascular function and dysfunction. Due to the complexity of the anatomy, the …

Recent years have witnessed a growth in mathematics for deep learning—which seeks a
deeper understanding of the concepts of deep learning with mathematics and explores how …

The past decade has seen increasing interest in applying Deep Learning (DL) to
Computational Science and Engineering (CSE). Driven by impressive results in applications …

Background Simulating the cardiac function requires the numerical solution of multi-physics
and multi-scale mathematical models. This underscores the need for streamlined, accurate …

Uncertainty quantification (UQ) tasks, such as sensitivity analysis and parameter estimation,
entail a huge computational complexity when dealing with input-output maps involving the …

Mesh-based simulations play a key role when modeling complex physical systems that, in
many disciplines across science and engineering, require the solution to parametrized time …

We propose a local, non-intrusive model order reduction technique to accurately
approximate the solution of coupled multi-component parametrized systems governed by …

Reducing the computational time required by high‐fidelity, full‐order models (FOMs) for the
solution of problems in cardiac mechanics is crucial to allow the translation of patient …