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SUMMARY:Constrained Neural Flows - Chandan Gupta
DTSTART:20241129T170000Z
DTEND:20241129T174500Z
UID:TALK224980@talks.cam.ac.uk
CONTACT:Pietro Lio
DESCRIPTION:Modelling dynamical systems with explicit constraints has beco
 me a key focus within the machine learning community\, particularly in tim
 e series analysis. Neural Ordinary Differential Equations (Neural ODEs) ha
 ve emerged as a popular approach for modelling continuous-time data. Howev
 er\, the standard NODE framework struggles when faced with explicit constr
 aints critical to many real-world applications. To address this\, Stabiliz
 ed Neural Differential Equations (SNDEs) were developed to incorporate the
 se constraints by modifying the original dynamics. Despite these advanceme
 nts\, SNDEs inherit several limitations from Neural ODEs\, including chall
 enges with stiff systems\, dependence on hyperparameter-sensitive numerica
 l solvers\, and inefficiencies in solving the adjoint system for gradient 
 computation. Recently\, Neural Flows have been\nintroduced as an alternati
 ve\, bypassing the need for solvers by directly learning the flow of the u
 nderlying system\, which simplifies training and inference. In this work\,
  we extend this concept by learning the flow of a constrained dynamical sy
 stem. Specifically\, we split the constrained ODEs\, as formulated in SNDE
 s\, and employ techniques like Lie-Trotter splitting to combine the flows 
 of the individual ODEs effectively. This approach maintains the benefits o
 f constraint-aware learning while mitigating the solver-related challenges
  faced by traditional Neural ODEs and SNDEs.
LOCATION:Venue to be confirmed
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