221 citations · 2.9k across the 217 of their papers we have counts for
232 papers
Cluster Attention Neural Operators for Solving Parametric Partial Differential Equations
Ming Zhong, Antonio Colanera, Gianluigi Rozza +1
Traditional simulations of parametric partial differential equations (PDEs) rely on repetitive computations for each parameter, which makes high-fidelity design impractical. Neural…
Active Subspace-Guided Free-Form Deformation with Sinkhorn Autoencoders for Reduced-Order Modelling of Parametrised Shape Problems
G. Padula, C. Giovannini, G. Rozza +1
Geometrically parametrised PDEs arise in shape optimisation, where solving a PDE over many deformed domains at manageable cost is a central challenge. Free-form Deformation (FFD) p…
A Comparative Study of Finite-Volume-based Coupled and Segregated Reduced-Order Models for Incompressible Flows in Parametrized Domains
Andrea Buffolini, Davide Oberto, Gianluigi Rozza
This work presents a comparative analysis of Reduced-Order Models (ROMs) applied to incompressible fluid dynamics within geometrically parametrized domains. Two distinct reduced-or…
A Dynamical Approximation Scheme on the Stiefel manifold for Wasserstein Gradient Flows
Isabella Carla Gonnella, Olga Mula, Federico Pichi +1
We propose a meshless Lagrangian dynamical method for approximating Wasserstein gradient flows (WGFs). The evolving measure is represented as the pushforward of the initial measure…
Trainable Spline Representations for Physics-Informed Learning
Giovanni Canali, Nicola Demo, Gianluigi Rozza
This work introduces Physics-Informed Splines (PI-Splines), a structured spline-based architecture for physics-informed learning. Instead of representing the solution of a differen…
A Generative Model-Free Form Deformation Approach for the Generation of Mesh Motions with Applications to PDE
Gugliemo Padula, Artem Sinitsa, Gianluigi Rozza
We introduce a topology-agnostic framework for matching deformations of three-dimensional shapes with non-isomorphic mesh graphs by modelling the deformation as the flow of an Ordi…