This work demonstrates a method to design photonic surfaces by combining femtosecond laser processing with the inverse design capabilities of tandem neural networks that directly link laser fabrication parameters to their resulting textured substrate optical properties. High throughput fabrication and characterization platforms are developed that generate a dataset comprising 35280 unique microtextured surfaces on stainless steel with corresponding measured spectral emissivities. The trained model utilizes the nonlinear one-to-many mapping between spectral emissivity and laser parameters. Consequently, it generates predominantly novel designs, which reproduce the full range of spectral emissivities (average root-mean-squared-error < 2.5%) using only a compact region of laser parameter space 25 times smaller than what is represented in the training data. Finally, the inverse design model is experimentally validated on a thermophotovoltaic emitter design application. By synergizing laser-matter interactions with neural network capabilities, the approach offers insights into accelerating the discovery of photonic surfaces, advancing energy harvesting technologies.