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UID:716074288c83027daff98c26c9870164
DTSTAMP:20260719T110057Z
SUMMARY:LC2 Seminar – Carlos Esteve Yagüe (University of Alicante)
DESCRIPTION:Title: Solving Hamilton-Jacobi PDEs by minimizing residuals of 
 monotone discretizations using neural networks\nAbstract: In recent years\
 , advancements in deep learning and new optimisation algorithms have motiv
 ated the use of artificial neural networks to solve non-linear problems in
  high-dimensional setups. One of the crucial steps during the implementati
 on of any deep learning method is the choice of the loss functional\, whic
 h is used to train the neural network parameters\, typically through a gra
 dient-based method. In this talk\, I will consider the approximation of th
 e viscosity solution for Hamilton-Jacobi equations by means of an artifici
 al neural network. I will present some recent results concerning loss func
 tionals involving a consistent and monotone numerical Hamiltonians. Using 
 the numerical diffusion built in the numerical Hamiltonian\, we are able t
 o prove that any critical point solves the associated finite-difference pr
 oblem and\, therefore\, approximates the viscosity solution. Moreover\, I 
 will show that by using discretizations with strong monotonicity propertie
 s\, one can speed up the training process.
URL:https://www.imperial.ac.uk/events/208995/lc2-seminar-carlos-esteve-yagu
 e-university-of-alicante/
DTSTART;TZID=Europe/London:20260506T130000
DTEND;TZID=Europe/London:20260506T140000
LOCATION:340\, Huxley Building\, South Kensington Campus\, Imperial College
  London\, London\, SW7 2AZ\, United Kingdom
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