The promising outcomes of dynamic system identification techniques, such as Sparse Identification of Nonlinear Dynamical Systems (SINDy) [1], and their integration with Physics-Informed Neural Networks (PINN) [2], as demonstrated in PINN-SR [3], highlight the potential and applicability of these methods to address hybrid problems like real-time process monitoring. By incorporating both physics and noisy data, these approaches enable more accurate simulations. The data assist in identifying dynamic parameters, while the physics-based constraints guide neural network training, enhancing both robustness and generalization. However, these techniques face limitations in real-time applications due to the difficulty of updating models, especially when system parameters are likely to change during or between processes. The training data are embedded in the model but are not treated as inputs, meaning that once trained, the model becomes fixed for a single instance. If parameters such as initial conditions (IC), boundary conditions (BC), or dynamic system properties change, the model can no longer deliver accurate results, necessitating retraining. This retraining process is impractical for applications that demand rapid responses based on real-time data. We implemented a technique introduced by [4, 5] for online parameter identification of dynamic systems. This approach involves training a Set-Encoder model to perform parameter identification based on dynamic state variables with varying lengths. By leveraging this methodology, we extended the PINN-SR framework to integrate PINNs with Set-Encoders. In this integrated framework, the Set-Encoder efficiently identifies system parameters, including initial conditions (IC) and boundary conditions (BC), using real-time data. The PINN then utilizes the output from the Set-Encoder to simulate dynamic behavior without requiring additional training. We applied this method to various ordinary and partial differential equations (PDEs), such as 1D thermal diffusion and 2D flow around a cylinder, as well as other ODEs. The current results demonstrate a strong ability to provide accurate predictions, along with a confidence level for those predictions. Additionally, given the very short inference time, this method could be implemented for industrial process monitoring and control.