Fig. 1: Wave-based time-Floquet extreme learning machine.

a Schematic of a neural network including a time-Floquet layer made from neurons whose properties are modulated periodically in time, and traditional random layers. Only the last layer (output) is trainable. b Concrete implementation with electromagnetic waves. The input signals \({\zeta }_{n}^{{{{{{\mathrm{in}}}}}}}\) are modulated at ω₁ and ω₂. The sums of these frequency components forms input signals that are independently radiated into the surrounding space by an array of source antennas (black disks). As the waves propagates in the green region, they encounter a thin dielectric slab whose index of refraction is modulated at the frequency ω_m = ∣ω₁ − ω₂∣/2, as well as five sub-wavelength scatterers, randomly located in the domain. The modulation phase depends on the input vector \({\zeta }_{n}^{{{{{{\mathrm{in}}}}}}}(t)\). The gray rectangle represents an absorbing boundary layer. The outputs \({\zeta }_{n}^{{{{{{\mathrm{out}}}}}}}(t)\) are fed into an adaptable blue dense layer, and used for regression and classification. c Nonlinear phase entanglement. The modulated slab mixes signals at ω₁ and ω₂ into Floquet harmonics spaced by ω_m, whose interferences depend non-linearly on the input vector.