Controlling nonlinear pulse propagation in optical fibers is paramount for applications spanning spectroscopy and optical communication networks. However, the inherent complexity of laser pulse evolution in matter, shaped by the interplay of nonlinearity and dispersion, poses significant challenges in experimental situations. Modulation instability, a fundamental process in nonlinear fiber optics, illustrates such experimental issues due to its noise-driven nature, leading to unpredictable dynamics and thus requiring advanced control strategies. Here, we investigate noise-driven modulation instability during nonlinear fiber propagation, underlining the potential of coherent optical seeding and machine learning to jointly control incoherent spectral broadening dynamics. By introducing weak coherent seeds into an initial laser pulse, we demonstrate the ability to tailor noise-driven MI properties through fine adjustments of the seed parameters driven by evolutionary algorithms. In particular, real-time spectral characterization is achieved via time-stretch dispersive Fourier transform, enabling optimized control of spectral intensity correlations. Our experimental results highlight the effectiveness of combining coherent optical seeding with optimization techniques such as genetic algorithms, to tailor incoherent spectral fluctuations arising from the competition between coherent and incoherent nonlinear frequency conversion processes. Specifically, we show that the proposed approach can be leveraged on-demand, to shape specific correlation features in the output spectrum. The implications of our research extend beyond the sheer process of modulation instability, offering promising applications in advanced optical information processing. By demonstrating simple yet robust and flexible management strategies, this work paves the way for next-generation nonlinear photonic technologies, exploiting incoherent processes in practical optical fiber architectures.
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