PINNs for the time-domain Maxwell equations - Preliminary results

International audienceThe Physics-Informed Neural Network (PINN) corresponds to a machinelearning strategy to approximate the solution of partialdifferential equations by in- cluding the residual PDE in the lossfunction. In a previous work, we found that adding physicalcoefficients as predictor variables in a PINN for boundary layerlinear problems improves the accuracy of the approximation when com-paring it with the approximate solution obtained from PINNs that useonly spatio-temporal inputs. This work explores this same strategyfor the time-dependent Maxwell linear equations in case electric andmagnetic fields present highly oscillatory behavior. Extensivenumerical experiments assess this strategy by simulating electromagneticfields in heterogeneous media with high permittivity variabilityin small spatiotemporal regions of the domai