There is a critical need for the development of cleaner and more efficient combustion technologies to limit their detrimental effects on the climate and the environment and reduce the world's dependence on fossil fuels. Predictive tools, such as computational fluid dynamics simulations (CFD), are essential for the design of future reacting combustion technologies. The ability to accurately predict the chemical kinetics in combustion technologies is critical to accurately describing the system's behavior. However, using a detailed representation of the chemistry is often computationally cost-prohibitive due to the high dimensionality and nonlinearity of the chemical kinetics. In this dissertation, I present frameworks to reduce the dimensionality of large chemical mechanisms with complex dynamics to enable simulations of next-generation combustion technologies at a reduced computational cost. First, a novel methodology for the reduction of large detailed plasma-assisted combustion mechanisms to smaller skeletal ones is presented and applied to an ethylene-air mechanism. The methodology extends a commonly used graph-based reduction technique, the Directed Relation Graph with Error Propagation (DRGEP), to consider the energy branching characteristics of plasma discharges during the reduction. The performance of the novel framework, named P-DRGEP, is assessed for the simulation of ethylene-air ignition by nanosecond repetitive pulsed discharges at conditions relevant to supersonic combustion and flame holding in scramjet cavities. The generated skeletal mechanism is capable of simulating ignition with a computational speed-up of 84% and with ignition delay time errors below 10%. Next, a novel empirical manifold framework is presented with the goal of enabling a posteriori CFD simulations with a very low-dimensional representation of the thermochemical state. The presented framework uses an autoencoder (AE) to learn the low-dimensional manifold and the Neural Ordinary Differential Equations (NODE) training framework to learn a source term approximation of the low-dimensional variables. The framework is validated by simulating ignition in an a posteriori framework with only 6 latent variables relative to the skeletal mechanism of a sustainable aviation fuel containing 152 species. The AE-NODE framework is able to capture the time to ignition and the equilibrium temperature and composition and exhibits a 96% reduction in memory relative to the thermochemical state vector and approximately 96% reduction in the time associated with the direct integration.