CSD Seminar Series: Alessio Fumagalli
Associate Professor Alessio Fumagalli is coming to Bergen to visit Professor Inga Berre and Dr. Eirik Keilegavlen. During his stay, he will give a talk in the CSD Seminar series.
Main content
Alessio Fumagalli is an associate professor from Politecnico di Milano. He completed his PhD in 2012 at Politecnico di Milano, after which he did successive post-docs at Inria, Institut français du pétrole, the University of Bergen, and Politecnico di Milano.
Title of talk: Consistent reduced models techniques for subsurface simulations
Abstract:
We introduce a novel approach to address parametrized Darcy-type models with linear constraints (conservation of mass) through a new reduced order modeling strategy. Our method utilizes traditional neural network architectures and supervised learning, yet it is designed to ensure that the resulting Reduced Order Model precisely adheres to the linear constraints.
The methodology involves partitioning the PDE solution into a homogeneous component and a non-homogeneous component, specifically a particular solution that satisfies the constraint. The homogeneous part is approximated by mapping a suitable potential function generated by a neural network model, onto the kernel of the constraint operator, while the particular solution is efficiently computed using a spanning tree algorithm. Building upon this framework, we present three alternative approaches that illustrate this methodology, varying from empirical spaces obtained through Proper Orthogonal Decomposition (POD) to more abstract spaces based on differential complexes. Each of these proposed approaches combines computational efficiency with rigorous mathematical interpretation, ensuring the interpretability of the model outputs.
To showcase the effectiveness of our strategies and underscore their advantages over standard blackbox methods, we conduct a series of numerical experiments on fluid flows in porous media, covering mixed-dimensional problems to nonlinear systems. This research establishes the groundwork for further exploration and advancement in the field of model order reduction, potentially unlocking new capabilities and solutions in computational geosciences and beyond.
We apply the same concepts to the linear elastic equation, resulting in a strategy to derive the stress, displacement, and rotation fields while ensuring the conservation of linear and angular momentum.
