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
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…
math.NA2023
Error estimates for POD-DL-ROMs: a deep learning framework for reduced order modeling of nonlinear parametrized PDEs enhanced by proper orthogonal decomposition
Simone Brivio, Stefania Fresca, Nicola Rares Franco +1
POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear parametrized partial differentia…