8 papers · 1 filter
Symplectic Neural Flows for Modeling and Discovery
Priscilla Canizares, Davide Murari, Carola-Bibiane Schönlieb +2
Hamilton's equations are fundamental for modeling complex physical systems, where preserving key properties such as energy and momentum is crucial for reliable long-term simulation…
Approximation Theory for Lipschitz Continuous Transformers
Takashi Furuya, Davide Murari, Carola-Bibiane Schönlieb
Stability and robustness are critical for deploying Transformers in safety-sensitive settings. A principled way to enforce such behavior is to constrain the model's Lipschitz const…
Deep Network Trainability via Persistent Subspace Orthogonality
Alex Massucco, Davide Murari, Carola-Bibiane Schönlieb
Training neural networks via backpropagation is often hindered by vanishing or exploding gradients. In this work, we design architectures that mitigate these issues by analyzing an…
Approximation theory for 1-Lipschitz ResNets
Davide Murari, Takashi Furuya, Carola-Bibiane Schönlieb
1-Lipschitz neural networks are fundamental for generative modelling, inverse problems, and robust classifiers. In this paper, we focus on 1-Lipschitz residual networks (ResNets) b…
Enhancing Fourier Neural Operators with Local Spatial Features
Chaoyu Liu, Davide Murari, Lihao Liu +3
Partial Differential Equation (PDE) problems often exhibit strong local spatial structures, and effectively capturing these structures is critical for approximating their solutions…
Hamiltonian Matching for Symplectic Neural Integrators
Priscilla Canizares, Davide Murari, Carola-Bibiane Schönlieb +2
Hamilton's equations of motion form a fundamental framework in various branches of physics, including astronomy, quantum mechanics, particle physics, and climate science. Classical…