3 papers
math.NA2025
Deep Symmetric Autoencoders from the Eckart-Young-Schmidt Perspective
Simone Brivio, Nicola Rares Franco
Deep autoencoders have become a fundamental tool in various machine learning applications, ranging from dimensionality reduction and reduced order modeling of partial differential…
math.NA2024
On latent dynamics learning in nonlinear reduced order modeling
Nicola Farenga, Stefania Fresca, Simone Brivio +1
In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework…
math.NA2024
Handling geometrical variability in nonlinear reduced order modeling through Continuous Geometry-Aware DL-ROMs
Simone Brivio, Stefania Fresca, Andrea Manzoni
Deep Learning-based Reduced Order Models (DL-ROMs) provide nowadays a well-established class of accurate surrogate models for complex physical systems described by parametrized PDE…