Semi-parameterized Nonlinear Optical Operator Predict Ultrafast Spectral across Multiple Power Domains

Ultrafast laser spectroscopy is a central tool in ultrafast optics. However the evolution of intracavity pulses is governed by strongly coupled multiphysics processes on sub-nanosecond time scales, making their behavior difficult to predict and control. Existing deep learning approaches are typically limited to modeling a single pump power or simulated spectra, and fail to capture transient spectral dynamics under varying operating conditions. Here we propose a semi-parameterized approach that embeds the dispersion and nonlinear structure of the generalized nonlinear Schrödinger equation into an intelligent computation framework, and we design a semi-parameterized nonlinear optical operator (SNOO) as a concrete realization of this idea. This study achieves for the first time multi-power ultrafast spectral prediction in lasers, reconstructing the spectral dynamics of Q-switched and microresonator soliton mode-locked pulses at 128 round trips intervals on sub-nanosecond timescales. Using only the initial 128 round trips, SNOO accurately predicts the spectral evolution over the subsequent 12800 round trips, precisely capturing the periodicity and amplitude of microcomb lines. Furthermore SNOO enables super-resolution spectral prediction across an eight-fold oscilloscope sampling-rate gap for four distinct classes of modelocked pulses, recovering high-speed sideband features unresolved by low-sampling-rate oscilloscopes. In all results, SNOO achieves state-of-the-art performance in relative error, similarity, and signal-to-noise ratio across nine models (five data-driven models and four neural operator models), while using fewer trainable parameters (as few as 10%). Our semi-parameterized structure provides a novel design paradigm for intelligent models in ultrafast optics, paving the way toward surpassing current instrumentation limits and enabling future terahertz-band spectral measurements.