We introduce a thermo-optic phase shifter (TOPS) array architecture with independent phase control of each phase shifter for large-scale and high-density photonic integrated circuits with two different control schemes: pulse amplitude modulation (PAM) and pulse width modulation (PWM). We realize a compact spiral TOPS and a 288-element high-density row-column TOPS ar- ray with this architecture and drive TOPS with waveforms of both control schemes and of different array sizes. We present a thermal excitation model and a finite difference method-based simulation to simulate large-scale TOPS arrays and compare both schemes experimentally and theoretically. We also analyze the effects of thermal crosstalk in the realized TOPS array and implement a ther- mal crosstalk correction algorithm with the developed model. The high-density TOPS array architecture and the thermal crosstalk correction algorithm pave the way for high-density TOPS arrays with independent phase control in large-scale photonic integrated circuits interfaced with electronics limited in voltage swing and bandwidth.