We demonstrate an ultra-low loss single-mode silicon waveguide crossing and an ultra-compact and ultra-low loss polarization-insensitive silicon waveguide crossing using a hybrid global optimizer based on a physics-informed generative adversarial network with a direct binary search refinement. By adopting this method, a parallel waveguide crossing structure with a footprint of 3 × 4 μm2 for transverse electric(TE) mode which has an insertion loss better than 0.03 dB and has crosstalk lower than −27 dB in 1500∼1600 nm bands is designed. A polarization-insensitive waveguide crossing with the same footprint is also designed in 1530∼1570 nm bands, which can provide insertion loss lower than 0.2 dB and crosstalk lower than −26.3 dB for TE mode and insertion loss lower than 0.1 dB and crosstalk lower than −27.8 dB transverse magnetic(TM) mode. The results show that this global optimizer produced high-efficiency devices while avoiding being trapped in the local optimal solutions compared to the traditional stochastic inverse design algorithm.