Nonlinear frequency modulated (NLFM) pulse compression waveforms have become a mainstream methodology for radars across multiple sectors and missions, including weather observation, target tracking, and target detection. NLFM affords the ability to generate a low-sidelobe autocorrelation function and matched filter while avoiding aggressive amplitude modulation, resulting in more power incident on the target. This capability can lead to significantly lower system design costs due to the possibility of sensitivity gains on the order of 3 dB or more compared with traditional, amplitude-modulated linear frequency modulated (LFM) waveforms. Generation of an optimal NLFM waveform, however, can be an arduous task, and may involve complex optimization and non-closed-form solutions. For a multimission or cognitive radar, which may utilize a wide combination of frequencies, pulse lengths, and amplitude modulations (among other factors), this could lead to an extremely large waveform table for selection. This paper takes a neural network approach to this problem by optimizing a set of over 100 waveforms spanning a wide space and using the results to interpolate the waveform possibilities to a higher resolution. A modified form of a previous NLFM method is combined with a four-hidden-layer neural network to show the integrated and peak range sidelobes of the generated waveforms across the model training space. The results are applicable to multi-mission and cognitive radars that need precise waveform specifications in rapid succession. The expected waveform generation times are addressed and quantified, and the potential applicability to multi-mission and cognitive radars is discussed.