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VERSION:2.0
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CATEGORIES:Academics,Lectures/Seminars
DESCRIPTION:Motivated by finite volume scheme\, a cell-average based neural
network method is proposed. The method is\nbased on the integral or weak f
ormulation of partial differential equations. A simple feed forward network
is forced to learn the solution average evolution between two neighboring
time steps. Offline supervised training is carried out to obtain the optima
l network parameter set\, which uniquely identifies on finite volume like n
eural network method. Once well trained\, the network method is implemented
as an explicit finite volume scheme\, thus is mech dependent. Different to
traditional numerical methods\, our method can be relieved from the explic
it scheme CFL restriction and can adapt to any time step size for solution
evolution. For second order and fourth PDEs\, first order of convergence is
observed and the errors are related to the spatial mesh size but are obser
ved being independent of the mesh size in time. The cell-average based neur
al\nnetwork method can sharply evolve contact discontinuity with almost zer
o numerical diffusion introduced. Shock and rarefaction waves are well capt
ured for nonlinear hyperbolic conversion laws. The method is further applie
d to solve kdV equations\, and higher order PDEs.
DTEND:20211006T180000Z
DTSTAMP:20220516T225242Z
DTSTART:20211006T170000Z
LOCATION:
SEQUENCE:0
SUMMARY:Cell-average based neural network method for time dependent partial
differential equations
UID:tag:localist.com\,2008:EventInstance_38084504134366
URL:https://events.mtu.edu/event/cell-average_based_neural_network_method_f
or_time_dependent_partial_differential_equations
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