Enhancing lattice kinetic schemes for fluid dynamics with Lattice-Equivariant Neural Networks

no code implementations • 22 May 2024 • Giulio Ortali, Alessandro Gabbana, Imre Atmodimedjo, Alessandro Corbetta

We present a new class of equivariant neural networks, hereby dubbed Lattice-Equivariant Neural Networks (LENNs), designed to satisfy local symmetries of a lattice structure.

Towards a Numerical Proof of Turbulence Closure

no code implementations • 18 Feb 2022 • Giulio Ortali, Alessandro Corbetta, Gianluigi Rozza, Federico Toschi

The development of turbulence closure models, parametrizing the influence of small non-resolved scales on the dynamics of large resolved ones, is an outstanding theoretical challenge with vast applicative relevance.

Gaussian process approach within a data-driven POD framework for fluid dynamics engineering problems

no code implementations • 3 Dec 2020 • Giulio Ortali, Nicola Demo, Gianluigi Rozza

This work describes the implementation of a data-driven approach for the reduction of the complexity of parametrical partial differential equations (PDEs) employing Proper Orthogonal Decomposition (POD) and Gaussian Process Regression (GPR).

GPR Numerical Analysis Numerical Analysis