3 papers
math.NA2025
Numerical Solution of Mixed-Dimensional PDEs Using a Neural Preconditioner
Nunzio Dimola, Nicola Rares Franco, Paolo Zunino
Mixed-dimensional partial differential equations (PDEs) are characterized by coupled operators defined on domains of varying dimensions and pose significant computational challenge…
math.NA2024
A practical existence theorem for reduced order models based on convolutional autoencoders
Nicola Rares Franco, Simone Brugiapaglia
In recent years, deep learning has gained increasing popularity in the fields of Partial Differential Equations (PDEs) and Reduced Order Modeling (ROM), providing domain practition…
math.NA2024
Deep orthogonal decomposition: a continuously adaptive data-driven approach to model order reduction
Nicola Rares Franco, Andrea Manzoni, Paolo Zunino +1
We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial diffe…