Recent years have seen the rapid growth and development of the field of smart photonics, where machine learning algorithms are being matched to optical systems to add new functionalities and to enhance performance. An area where machine learning shows particular potential to accelerate technology is the field of ultrafast photonics -the generation and characterization of light pulses, the study of light-matter interactions on short timescales, and high-speed optical measurements. Our aim here is to highlight a number of specific areas where the promise of machine learning in ultrafast photonics has already been realized, including the design and operation of pulsed lasers, and the characterization and control of ultrafast propagation dynamics. We also consider challenges and future areas of research.

A central research area in nonlinear science is the study of instabilities that drive extreme events. Unfortunately, techniques for measuring such phenomena often provide only partial characterisation. For example, real-time studies of instabilities in nonlinear optics frequently use only spectral data, limiting knowledge of associated temporal properties. Here, we show how machine learning can overcome this restriction to study time-domain properties of optical fibre modulation instability based only on spectral intensity measurements. Specifically, a supervised neural network is trained to correlate the spectral and temporal properties of modulation instability using simulations, and then applied to analyse high dynamic range experimental spectra to yield the probability distribution for the highest temporal peaks in the instability field. We also use unsupervised learning to classify noisy modulation instability spectra into subsets associated with distinct temporal dynamic structures. These results open novel perspectives in all systems exhibiting instability where direct time-domain observations are difficult.

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Supercontinuum generation is a highly nonlinear process that exhibits unstable and chaotic characteristics when developing from long pump pulses injected into the anomalous dispersion regime of an optical fiber. A particular feature associated with this regime is the long-tailed "rogue wave"like statistics of the spectral intensity on the long-wavelength edge of the supercontinuum, linked to the generation of a small number of "rogue solitons" with extreme red-shifts. Whilst the statistical properties of rogue solitons can be conveniently measured in the spectral domain using the real-time dispersive fourier transform technique, we cannot use this technique to determine any corresponding temporal properties since it only records the spectral intensity and one loses information about the spectral phase. And direct temporal characterization using methods such as the time-lens has resolution of typically 100's of fs, precluding the measurement of solitons which possess typically much shorter durations. Here, we solve this problem by using machine learning. Specifically, we show how supervised learning can train a neural network to predict the peak power, duration, and temporal walk-off with respect to the pump pulse position of solitons at the edge of a supercontinuum spectrum from only the supercontinuum spectral intensity without phase information. Remarkably, the network accurately predicts soliton characteristics for a wide range of scenarios, from the onset of spectral broadening dominated by pure modulation instability to near octave-spanning supercontinuum with distinct rogue solitons.

The nonlinear propagation of ultrashort pulses in optical fibers depends sensitively on the input pulse and fiber parameters. As a result, the optimization of propagation for specific applications generally requires time-consuming simulations based on the sequential integration of the generalized nonlinear Schrödinger equation (GNLSE). Here, we train a feed-forward neural network to learn the differential propagation dynamics of the GNLSE, allowing emulation of direct numerical integration of fiber propagation, and particularly the highly complex case of supercontinuum generation. Comparison with a recurrent neural network shows that the feed-forward approach yields faster training and computation, and reduced memory requirements. The approach is generic and can be extended to other physical systems.