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Many phenomena in physics, including light, water waves, and sound, aredescribed by wave equations. Given their coefficients, wave equations can besolved to high accuracy, but the presence of the wavelength scale often leadsto large computer simulations for anything beyond the simplest geometries. Theinverse problem, determining the coefficients from a field on a boundary, iseven more demanding, since traditional optimization requires a large number offorward problems be solved sequentially. Here we show that the free-forminverse problem of wave equations can be solved with machine learning. First weshow that deep neural networks can be used to predict the optical properties ofnanostructured materials such as metasurfaces. Then we demonstrate thefree-form inverse design of such nanostructures and show that constraintsimposed by experimental feasibility can be taken into account. Our neuralnetworks promise automated design in several technologies based on the waveequation.

Deep neural networks for the prediction of the optical properties and the free-form inverse design of metamaterials