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Two major challenges in modern cosmology involve understanding the origin and growth of Cosmic structure and the progenitors of Gravitational Waves. Both scenarios currently require heavy computational resources to perform simulations and inference. In this work, we adopt simple Machine Learning methods to alleviate these requirements, to enable significantly faster sampling and inference. We show that using Dimensionality Reduction and simple Supervised Learning methods, it is possible to generate high-precision emulations of density fields given a set of parameters (such as the Dark Matter density parameter and redshift). Our method provides orders of magnitude improvement of CPU run times and much less computational resources when compared with N-Body simulations or more complex supervised learning approaches. We also show that it is possible to generate fast inference of gravitational wave parameters (such as the Chirp Mass) from Binary Black Hole systems using the same method. This method provides a promising approach to fast emulation and parameter inference to further explore in the context of upcoming large surveys like Euclid, LSST/Rubin, and LISA.