Extended Data Fig. 4: Generalization of RNN applicability to modelling GNLSE dynamics.

Training data were generated using the normalized form of the GNLSE including Raman effect, self-steepening and third-order dispersion (see Methods). The results are plotted in dimensional units. The network was trained using 11800 normalized GNLSE realizations where the soliton number, normalized third-order dispersion parameter, and pulse duration were respectively randomly varied in the range 2 to 8, 1 to 9 and 30 and 130 fs (FWHM). (a) shows the results for a transform-limited N = 4 input pulse centered at 830 nm with 7.6 kW peak power and 40 fs duration. Corresponding fibre parameters are γ = 0.1 W⁻¹m⁻¹, β₂ = − 8 × 10⁻²⁷ s²m⁻¹ and β₃ = 9 × 10⁻⁴¹ s³m⁻¹. (b) shows the results for a transform-limited N = 7 input pulse with 2.9 kW peak power and 120 fs duration. Corresponding fibre parameters are γ = 0.0184 W⁻¹m⁻¹, β₂ = − 5.1 × 10⁻²⁷ s²m⁻¹ and β₃ = 4.3 × 10⁻⁴¹ s³m⁻¹. (c) shows the results for a transform-limited N = 4.5 input pulse with 3.0 kW peak power and 60 fs duration. Corresponding fibre parameters are γ = 0.01 W⁻¹m⁻¹, β₂ = − 1.7 × 10⁻²⁷ s²m⁻¹ and β₃ = 6.5 × 10⁻⁴² s³m⁻¹. In each panel, we show the evolution map directly obtained from the numerical GNLSE simulations and that obtained from the RNN network model. The r.m.s. error computed over 200 test realizations is R = 0.092.