Fig. 1. Principle of CE-ORC. The complex-valued encoding strategy converts the input state Ut defined in the real space, with the previous state Rt−1, to a complex optical field. The scattering medium as the reservoir transforms this field to the current state Rt that is captured by the detector. Based on the captured image, a trained program generates the current output Yt.

Fig. 2. Experimental setup and characterization of CE-ORC system. (a) Schematic illustration and physical demonstration of the CE-ORC implementation. M, mirror; L1 and L2, lenses; PF, pinhole filter; SM, scattering medium. (b) CE-ORC processing unit and dedicated FPGA board. (c) Distance matrix of the CE-ORC system with the encoding dimension of 10. (d) Correlation matrix of the responses in different ORC systems.

Fig. 3. The horizontal coordinate representing time has been normalized with respect to the Lyapunov exponent Λmax. (a) Example of free-running prediction made by CE-ORC at optimal configuration (si=0.95 and sr=0.9). (b) Comparison of NMSE in the free-running predictions given by the conventional basket-encoding ORC, and CE-ORC with different configurations of the scale factors. (c) Example of one-step prediction made by CE-ORC at si=0.95 and sr =0.9. (d) Comparison of errors in the one-step predictions given by the conventional basket-encoding ORC and CE-ORC. Note: Free-running prediction [(a), (b)] and one-step prediction [(c), (d)] are different prediction modes and should not be directly compared.

Fig. 4. Test of CE-ORC for weather forecast. (a) Predictions of temperature made by the CE-ORC and conventional basket-encoding ORC in the free-running prediction mode. (b) Predictions of humidity made by the CE-ORC and conventional basket-encoding ORC in the free-running prediction mode. (c) Predictions of temperature made by the CE-ORC in the one-step prediction mode. (d) Errors in the predictions of humidity made by the CE-ORC in the one-step prediction mode.