Time series prediction and simulation are crucial across various real-life applications. Our research specifically tackles the challenges of multivariate, multi-step forecasting which involves predicting future behavior over multiple time steps, a task where model uncertainty accumulates, complicating accuracy and interpretability. Unlike univariate models, multivariate analysis must handle complex interdependencies among multiple variables, which increases both the complexity and the computational demand.To manage these complexities, our work explores the development of predictive surrogates that integrate both data-driven machine learning techniques (such as LSTM) and hybrid methods incorporating physics-based enhancements (like physics-based constraints). Utilizing a process plant as our case study, we have constructed these surrogates using a blend of real, simulated, and synthetic data from the plant, a digital twin, and soft sensors. Our methodologies extend to crafting appropriate training and testing datasets from sparsely available real data.The results from our research project demonstrate the differences in forecasting accuracy between data-driven and hybrid models. We discuss the comparative benefits of each model and share insights gained from the integration of machine learning and physical models for multi-step prediction. Looking forward, we aim to refine these predictive surrogate models further to enhance their predictive performance and operational applicability in process control and optimization.