We have designed a polarization-splitting grating coupler (PSGC) in silicon-on-insulator (SOI) that has 1.2 dB peak loss in numerical simulations, which is the best simulated performance of PSGCs without a bottom reflector to the best of our knowledge. Adjoint method-based shape optimization enables us to explore complex geometries that are intractable with conventional design approaches. Physics-based process-independent knowledge of PSGCs is extracted from the adjoint optimization and can be transferred to other platforms with a minimum of effort.