Research Summary: Efficient and reliable performance predictions are essential for improving reservoir management and making informed business decisions. Optimizing the production and understanding geological uncertainty require exploration of the parameter space using multiple high-fidelity simulations. However, the inherent large computing time of these high-fidelity simulations limits the number of different scenarios that can be simulated. This limitation motivates my research wherein I study the use of proxy simulators, also known as reduced-order models (ROM), to rapidly explore the parameter space. I focus on the development of ROM (both invasive and non-invasive) under non-linear effects for reservoir simulation applications.