PINNs for the time-domain Maxwell equations - Preliminary results
Résumé
The Physics-Informed Neural Network (PINN) corresponds to a machine
learning strategy to approximate the solution of partial
differential equations by in- cluding the residual PDE in the loss
function. In a previous work, we found that adding physical
coefficients as predictor variables in a PINN for boundary layer
linear problems improves the accuracy of the approximation when com-
paring it with the approximate solution obtained from PINNs that use
only spatio-temporal inputs. This work explores this same strategy
for the time-dependent Maxwell linear equations in case electric and
magnetic fields present highly oscillatory behavior. Extensive
numerical experiments assess this strategy by simulating electromagnetic
fields in heterogeneous media with high permittivity variability
in small spatiotemporal regions of the domain
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