The first direct gravitational wave detection by LIGO and Virgo in 2015 marked the beginning of the gravitational wave astronomy era. Gravitational waves are an excellent tool to prove general relativity and unveil compact objects' dynamics in the universe. Over the years, we observe more signals from coalescing black hole binaries. Signals from the detectors are filtered through numerous waveform templates coming from theoretical predictions. Some models are more accurate but slow, and the others are less accurate but fast. We face ever-increasing demands for accuracy, speed, and parameter coverage of waveform models with more detections. Thus, we investigate strategies to speed up waveform generation without losing much accuracy for future signal analysis. In this dissertation, we present our approach as follows: 1. developing a method to dynamically tune less accurate (but fast) models with a more accurate (but slow) models through an iterative dimensionality reduction technique, 2. investigating the performance of regression methods, including machine learning for higher dimensions, 3. adding eccentricity to quasicircular analytical models through fitting technique. We analyze our results' faithfulness and prospects to speed up waveform generation. Our methods can readily be applied to reduce the complexity and time of building a new waveform model. Additionally, we build a python package pyrex to carry out the quasicircular turned eccentric computation. This study is crucial for the development of models which include more parameters.