Computational thermo-microstructural modelling has become a powerful tool for understanding the process- microstructure linkage in the Laser Powder Bed Fusion (PBF-LB) technique. Developing models that accurately represent experimental results requires properly calibrating non-measurable model parameters through computationally intensive inverse analysis. This study details the calibration of a thermo-microstructural model based on observations from single-track PBF-LB experiments for Hastelloy X (HX) alloy. The calibration framework integrates physics-informed neural networks (PINNs) for thermal analysis and cellular automata (CA) for microstructure simulation. Initially, a PINNs model is trained in an unsupervised fashion and validated against finite element simulation results to serve as a parametric solution for predicting singletrack temperature profiles and melt pool dimensions under various PBF-LB process settings and heat source parameters. Due to the high computational efficiency of the PINNs model and its ability to provide high-order derivatives through automatic differentiation, the model can be effectively used in the inverse calibration of the heat source parameters in the thermal model based on experimentally measured melt pool dimensions. The calibrated thermal model then supplies temperature data for subsequent CA microstructure modelling, where the nucleation parameters and the temperature dependence of the grain growth rate need to be determined. In addition, this study thoroughly discusses the challenges in calibrating the microstructural model, particularly based on experimental observations from single PBF-LB tracks. Ultimately, it identifies the optimal CA parameter set capable of representing the experimentally observed microstructures of PBF-LB HX under five different process conditions.