Ferroelectric hafnium zirconium oxide (HZO) thin films show significant promise for applications in ferroelectric random-access memory devices, ferroelectric field-effect transistors, and ferroelectric tunneling junctions. However, there are shortcomings in understanding ferroelectric switching, which is crucial in the operation of these devices. Here a computational model based on the phase field method is developed to simulate the switching behavior of polycrystalline HZO thin films. Furthermore, we introduce a novel approach to optimize the effective Landau coefficients describing the free energy of HZO by combining the phase field model with a genetic algorithm. We validate the model by accurately simulating switching curves for HZO thin films with different ferroelectric phase fractions. The simulated domain dynamics during switching also shows amazing similarity to the available experimental observations. The present work also provides fundamental insights into enhancing the ferroelectricity in HZO thin films by controlling the grain morphology and crystalline texture. It can potentially be extended to improve the ferroelectric properties of other hafnia based thin films.