2024/01/13 by Nicola Parolini, Andrea Poiatti, Parolini, Nicola +5 · 2 citations
Chemical Engineering · Engineering · Physics and Astronomy · #41A46 #76A05 #76D03 #76M10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Lattice Boltzmann Simulation Studies #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Rheology and Fluid Dynamics Studies
paper · pdf · doi:10.48550/arxiv.2401.07121
openalex publication_date 2024/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we address the importance and the impact of employing structure preserving neural networks as surrogate of the analytical physics-based models typically employed to describe the rheology of non-Newtonian fluids in Stokes flows. In particular, we propose and test on real-world scenarios a novel strategy to build data-driven rheological models based on the use of Input-Output Convex Neural Networks (ICNNs), a special class of feedforward neural network scalar valued functions that are convex with respect to their inputs. Moreover, we show, through a detailed campaign of numerical experiments, that the use of ICNNs is of paramount importance to guarantee the well-posedness of the associated non-Newtonian Stokes differential problem. Finally, building upon a novel perturbation result for non-Newtonian Stokes problems, we study the impact of our data-driven ICNN based rheological model on the accuracy of the finite element approximation.