In this dissertation, an exploration of nematic liquid crystal (LC) systems is conducted, encompassing various conditions such as confinement, chirality, and colloidal interactions. Employing a mean-field approach and innovative simulation techniques, the research aims to unravel the intricate interplay between elasticity, confining geometries, and computational efficiency in the realm of soft matter materials. To efficiently navigate the vast parameter space, a rigorous framework augmented with stochastic elements is employed. The initial part of the dissertation delves into the fascinating realm of geometrical frustration in LC systems. Through meticulous investigation, it unveils the emergence of hybrid morphologies resulting from the delicate interplay between chirality and confinement. Notably, the pivotal role of surface defects in stabilizing equilibrium configurations is elucidated. Furthermore, the deformation of LC spheroids is examined, shedding light on its profound influence on the growth and thermal stability of blue phases. Analogous effects are observed in cylindrical and toroidal confinement, leading to the discovery of tunable chiral ribbon-like defects. The subsequent section of this work centers around the intriguing interaction between liquid crystals and colloidal particles. The research uncovers the formation of stable configurations characterized by intricate defect structures at interfaces, thereby offering exciting prospects for the design of stimuli-responsive emulsions. Moreover, it investigates the assembly of nanoparticle clusters on bipolar droplets, revealing the presence of kinetic traps through the application of advanced simulation techniques. To simplify the complex energy landscape, a novel simplified model is developed based on mean-field results, providing valuable insights into the construction of the free energy surface. The final study within this dissertation focuses on the optimization of phenomenological parameters in continuum simulations through comparisons with experimental microscopy images. The research showcases an efficient simulation methodology capable of accurately capturing the complexities of intricate geometries and nonlinear behavior. The integration of stochastic elements prevents configurations from becoming trapped in local minima, while Bayesian optimization facilitates thorough exploration of the parameter space. In summary, this dissertation presents a comprehensive investigation into soft matter materials, merging conventional continuum methods with molecular simulation elements. It highlights the profound impact of geometric effects, particularly the role of frustration, in engineering unique defect morphologies and driving colloidal assembly. The findings of this research open up exciting possibilities for the design and manipulation of soft matter materials, paving the way for future advancements in the field.