Integrating physical knowledge and machine learning is a cost-efficient solution to modelling complex biochemical processes when the underlying mechanisms are not fully understood. However, hybrid model structure identification is still time-consuming for new processes, ruiring iteration over different hypotheses to explain the observed process dynamics while minimizing over-parameterization. Unfortunately, conventional approaches to automatic model structure identification do not always converge for highly nonlinear models and cannot estimate time-varying model parameters. To address this and accelerate the design of new biochemical processes, a Reinforcement Learning (RL) based framework recently reformulated synchronous hybrid model structure-parameter identification into a process optimal control problem. To further investigate other possible solutions, in this study, a novel Physics Informed Neural Network (PINN) based framework was proposed for the first time to infer time-varying kinetic parameters. This framework first combines possible kinetic structures from phenomenological knowledge, then simultaneously identifies the most likely hybrid model structure and time-varying parameter trajectories. To demonstrate the performance of the PINN based framework, several in-silico case studies were conducted using a known ground truth bioprocess. We thoroughly examined the advantages and limitations of the framework, elucidating its potential for high-fidelity hybrid model construction in biochemical engineering research.