Fig. 3: Simulation results of solving time-dependent Navier-Stokes and Maxwell’s equations.
From: Optical neural engine for solving scientific partial differential equations
Illustrations of (a) Navier-Stokes equation for solving the time evolution of the vorticity field in a viscous, incompressible fluid in vorticity form on the unit torus and (b) Maxwell’s equations for solving the time evolution of the electric field in a dielectric metasurface. Validation loss curves for (c) solving the Navier-Stokes equation and (d) Maxwell’s equations with 10, 20, and 30 additional time steps using the optical neural engine architecture. The expected ground truth field, the predicted field, and the absolute and relative errors between these two fields for (e) the Navier-Stokes equation and (f) Maxwell’s equations, respectively.
