5 papers
Constructive interpolation and generalization rates for neural ODEs: a control perspective
Antonio Ãlvarez-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…
Universal Approximation of Dynamical Systems by Semi-Autonomous Neural ODEs and Applications
Ziqian Li, Kang Liu, Lorenzo Liverani +1
In this paper, we introduce semi-autonomous neural ordinary differential equations (SA-NODEs), a variation of the vanilla NODEs, employing fewer parameters. We investigate the univ…
HYCO: Hybrid-Cooperative Learning for Data-Driven PDE Modeling
Lorenzo Liverani, Matthys Steynberg, 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…
Large-Time Asymptotics for Hyperbolic Systems with Non-Symmetric Relaxation: An Algorithmic Approach
Timothée Crin-Barat, Lorenzo Liverani, Ling-Yun Shou +1
We study the stability of one-dimensional linear hyperbolic systems with non-symmetric relaxation. Introducing a new frequency-dependent Kalman stability condition, we prove an abs…