2 citations · 3 across the 16 of their papers we have counts for
6 papers · 1 filter
Constructive interpolation and generalization rates for neural ODEs: a control perspective
Antonio Álvarez-López, Lorenzo Liverani, Enrique Zuazua
We study supervised regression with neural ODEs (NODEs) from a control-theoretic perspective to derive explicit population-risk bounds. We focus on a widely used class of non-auton…
HYCO: A Formalism for Hybrid-Cooperative PDE Modelling
Lorenzo Liverani, Enrique Zuazua
We present Hybrid-Cooperative Learning (HYCO), a hybrid modeling framework that integrates physics-based and data-driven models through mutual regularization. Unlike traditional ap…
A PDE Perspective on Generative Diffusion Models
Kang Liu, Enrique Zuazua
Score-based diffusion models have emerged as a powerful class of generative methods, with successful applications across diverse domains. Despite their empirical success, their mat…
HYCO: Hybrid-Cooperative Learning for Data-Driven PDE Modeling
Lorenzo Liverani, Enrique Zuazua
We introduce Hybrid-Cooperative Learning (HYCO), a framework for data-driven PDE modeling in which a physics-based solver and a flexible synthetic model are trained as two independ…
Interplay between depth and width for interpolation in neural ODEs
Antonio Álvarez-López, Arselane Hadj Slimane, Enrique Zuazua
Neural ordinary differential equations (neural ODEs) have emerged as a natural tool for supervised learning from a control perspective, yet a complete understanding of their optima…
Cluster-based classification with neural ODEs via control
Antonio Álvarez-López, Rafael Orive-Illera, Enrique Zuazua
We address binary classification using neural ordinary differential equations from the perspective of simultaneous control of data points. We consider a single-neuron architect…