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Conference Papers Year : 2022

PINNs for the time-domain Maxwell equations - Preliminary results

Abstract

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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Dates and versions

hal-03933994 , version 1 (11-01-2023)

Identifiers

  • HAL Id : hal-03933994 , version 1

Cite

Amine Bennini, Séphane Lanteri, Frédéric Valentin, Tadeu A Gomes, Larissa Miguez da Silva. PINNs for the time-domain Maxwell equations - Preliminary results. CARLA 2022 - Latin America High Performance Computing Conference, Sep 2022, Porto Alegre, Brazil. ⟨hal-03933994⟩
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