From the 1 of 56 linked papers with an AI index.
39 papers · 1 filter
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…
A Generative Model-Free Form Deformation Approach for the Generation of Mesh Motions with Applications to PDE
Gugliemo Padula, Artem Sinitsa, Gianluigi Rozza
The paper presents a topology‑agnostic framework that models 3D shape deformations as an ODE flow parameterized by a time‑dependent free‑form deformation lattice, and couples it wi…
Bifurcation curve detection with deflation for multiparametric PDEs
Nitin Kumar, Federico Pichi, Gianluigi Rozza
This work presents a comprehensive framework for capturing bifurcating phenomena and detecting bifurcation curves in nonlinear multiparametric partial differential equations, where…
Convolutional Symmetric AutoEncoders: enhancing latent stability via differential geometry
G. Li Causi, N. Tonicello, L. Magri +1
Autoencoders (AEs) have emerged as powerful tools for non-linear dimensionality reduction, often surpassing traditional linear methods such as Proper Orthogonal Decomposition (POD)…
An isotropic recovery-based error estimator algorithm for mesh adaptation in a finite volume environment with application to atmospheric flows
Lander Besabe, Michele Girfoglio, Simona Perotto +2
We develop an Isotropic Recovery-based Error Estimator (IREE) to drive mesh adaptation within a finite volume framework. Recovery-based error estimators are widely used in practice…
A Quadratic Order Reduction -- Gaussian Process Ordinary Differential Equation framework for the inference of Large Continuous Dynamical Systems
Guglielmo Padula, Michele Girfoglio, Gianluigi Rozza
Forecasting the evolution of complex dynamical systems remains a fundamentally challenging task, primarily due to pronounced nonlinear interactions, high-dimensional state spaces,…