This thesis investigates hybrid neural network frameworks for developing reliable digital twins in process systems engineering. The overall aim is to combine physics-based knowledge with data-driven models to obtain predictive tools that are accurate, computationally efficient, and robust enough for use in real-time decision making. Particular emphasis is placed on addressing limitations of purely mechanistic and purely black-box models with respect to extrapolation capability, adaptability to changing conditions, and model trustworthiness from the perspective of process operators and other stakeholders. The first part of the work focuses on the development of a novel hybrid neural network framework based on physics-informed regularization for modeling nonlinear dynamic systems. In this approach, neural networks are trained simultaneously on historical and simulation data and on soft constraints derived from underlying first-principles models. The physics-informed loss terms act as a learning bias that improves extrapolation capability and reduces the risk of physically inconsistent predictions, especially when only limited data are available. The methodology is applied to representative dynamic processes and benchmarked against conventional black-box neural networks and purely mechanistic models. The results demonstrate that physics-informed regularization can significantly improve predictive accuracy in extrapolative regimes, while preserving flexibility in capturing unmodeled dynamics. The next part investigates the problem of online parameter estimation and model maintenance for hybrid neural models intended for use as digital twins. In practical applications, model parameters drift over time due to aging, fouling, catalyst deactivation, changes in feed quality, or other sources of model–plant mismatch. A key question is how to update hybrid models in a recursive and computationally efficient manner so that prediction quality is maintained without full retraining. In this work, strategies for online updating of model parameters and hyperparameters are developed and evaluated using representative case studies. The results show that appropriate maintenance schemes can preserve model performance over extended operating horizons, while keeping computational costs compatible with real-time deployment. The following part studies the integration of a physics-informed neural network with an Ensemble Kalman Filter for joint state and parameter estimation in an adaptive digital twin framework. Here, a PINN acts as a compact, physics-guided surrogate model that is sensitive to process parameters, while the EnKF provides recursive updates of states and parameters using plant measurements. The integrated framework is applied to a continuous polymerization reactor producing polymethyl methacrylate (PMMA), under scenarios involving model-plant mismatch, step and ramp changes in parameters, and varying levels of measurement availability. The proposed adaptive digital twin is shown to maintain high predictive accuracy under changing operating conditions, while reducing computational effort relative to an EnKF implementation that relies directly on a high-fidelity mechanistic model. The final part extends the methodology to adsorption-based separation processes using dynamic column breakthrough experiments. In this setting, accurate characterization of equilibrium and kinetic parameters is essential but often expensive and time-consuming. A physics-informed neural network framework is developed that learns the spatio-temporal evolution of concentration profiles in a packed bed directly from limited breakthrough data, while implicitly capturing unmodeled equilibrium effects. The trained PINN is used as a digital twin of the dynamic column breakthrough experiment and evaluated under extrapolative operating conditions. The results show that the PINN-based hybrid model provides substantial improvements in profile prediction compared to conventional neural networks and can reliably predict behavior outside the training domain, thereby reducing the need for extensive equilibrium experiments. Overall, the thesis demonstrates that hybrid neural network frameworks based on physics-informed regularization, adaptive state and parameter estimation, and dynamic column breakthrough characterization can significantly enhance the fidelity, robustness and adaptability of digital twins in process systems engineering. By embedding physical structure and constraints into neural network models, the proposed approaches improve interpretability and reduce the incidence of unrealistic predictions, which is critical for building trust among chemical process operators and decision makers who rely on these models for safety-, environment- and quality-critical tasks. The results highlight the potential of such hybrid digital twins to reduce experimental and modeling effort, support real-time monitoring and control under evolving process conditions, and provide a pathway toward more reliable and sustainable operation of complex chemical and adsorption-based separation processes.