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UID:submissions.pasc-conference.org_PASC24_sess156_pos118@linklings.com
SUMMARY:P18 - Exact Conservation Laws for Neural Network Integrators of Dy
 namical Systems
DESCRIPTION:Poster\n\nEike Mueller (University of Bath)\n\nWe consider the
  construction of neural network surrogates for the solution of differentia
 l equations that describe the time evolution of physical systems. In contr
 ast to other problems that are tackled by machine learning, in this case u
 sually a lot is known about the system at hand: for many dynamical systems
  physical quantities such as (angular) momentum and energy are conserved. 
 Learning these fundamental conservation laws from data is inefficient and 
 will only lead to the approximate conservation of these quantities. We des
 cribe an alternative approach for incorporating inductive biases into the 
 surrogate model. For this we use Noether's Theorem which relates conservat
 ion laws to continuous symmetries of the system and we incorporate the rel
 evant symmetries into the architecture of the neural network Hamiltionian.
  We demonstrate that this leads to the exact conservation of (angular) mom
 entum for a range of model systems that include the motion of a particle u
 nder Newtonian gravity, orbits in the Schwarzschild metric and two interac
 ting particles in four dimensions. Our numerical results show that the sol
 ution conserves the relevant quantities exactly, is more accurate and does
  not suffer from instabilities that arise when using naive neural network 
 surrogates.\n\nSession Chair: Erik W. Draeger (Lawrence Livermore National
  Laboratory)
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