  Ultrafast lasers ($< 500$ fs) have enabled laser-matter interactions at
intensities exceeding $10^{18} \rm{Wcm}^{-2}$ with only millijoules of laser
energy. However, as pulse durations become shorter, larger spectral bandwidths
are required. Increasing the bandwidth causes the temporal structure to be
increasingly sensitive to spectral phase, yet measuring the spectral phase of a
laser pulse is nontrivial. While direct measurements of the spectral phase
cannot be done using square-integrable detectors, phase information can be
reconstructed by measuring the spectral response of a nonlinear optical effect.
We introduce a new deep learning approach using the generalized nonlinear
Schr\"{o}dinger equation and self-phase modulation, a $\chi_3$ nonlinearity
occurring from material propagation. By training a neural network on numerical
simulations of pulses propagating in a known material, the features of spectral
change can be use to reconstruct the spectral phase. The technique is also
sensitive to the local fluence of the pulse, enabling the full temporal
intensity profile to be calculated. We demonstrate our method on a simulated
large bandwidth pulse undergoing moderate material dispersion, and an
experimentally produced broadband spectrum with substantial material
dispersion. Error rates are low, even when modest amounts of noise introduced.
With a single plate of glass and an optical spectrometer, single shot phase and
fluence measurements are possible in real-time on intense ultrafast laser
systems.
