PGMODAYS 2024: Universal Approximation of Dynamical Systems by Semi-Autonomous Neural ODEs
On Tue. November 19, 2024, Kang Liu will talk on “Universal Approximation of Dynamical Systems by Semi-Autonomous Neural ODEs” at the PGMODAYS 2024 (Session 9B) at the FMJH – Fondation Mathématique Jacques Hadamard organized on November 19 – 20, 2024 at University of Paris-Saclay in France.
Session 9B: Invited Session: Differential equations in machine learning
Kang Liu, Ziqian Li, Lorenzo Liverani and Enrique Zuazua
Universal Approximation of Dynamical Systems by Semi-Autonomous Neural ODEs
PRESENTER: Kang Liu
https://easychair.org/smart-program/PGMODAYS2024/2024-11-19.html#talk:270414
Abstract. In this presentation, we introduce semi-autonomous neural ordinary differential equations (SA-NODEs), a variation of the classical NODEs, employing fewer parameters. We investigate the universal approximation properties of SA-NODEs for dynamical systems from both a theoretical and a numerical perspective. Within the assumption of a finite-time horizon, under general hypotheses we establish an asymptotic approximation result, demonstrating that the error vanishes as the number of parameters goes to infinity. Under additional regularity assumptions, we further specify this convergence rate in relation to the number of parameters, utilizing quantitative approximation results in the Barron space. Based on the previous result, we prove an approximation rate for transport equations by their neural counterparts. Our numerical experiments validate the effectiveness of SA-NODEs in capturing the dynamics of various ODE systems and transport equations. Additionally, we compare SA-NODEs with classical NODEs, highlighting the superior performance and reduced complexity of our approach.
Invited plenary speakers
• Paola Goatin (Inria Sophia-Antipolis. France)
• Edouard Graves (LLM, Kyutai. France)
• Huseyin Topaoglou (Cornell University. USA)
• Enrique Zuazua (FAU, Erlangen. Germany)
Registration
Registration and abstract submission deadline date: September 13, 2024.
See about submission details
Conference fees may apply. See more at the official page of the event.
WHEN
Tue. November 19, 2024 at 16:30H
WHERE
EDF Lab Paris-Saclay, Palaiseau, France
Check the official page of the event
