This comprehensive study delves into the transformative evolution of photonic feature prediction and design, where traditional methods, deeply rooted in theory-driven computational approaches, have shaped our understanding of optical phenomena and advanced photonic structures. Integrating machine learning (ML) in photonics marks a fundamental departure from conventional predictive modeling, driven by the acknowledgment of its vast potential to deliver ingenious solutions, optimize designs, and accelerate the advancement of cutting-edge optical technologies. The article introduces a practical application of machine learning, specifically regression, to address optical engineering problems. The focal point is hexagonal photonic crystal fiber (PCF), an important photonic device with crucial input parameters such as wavelength, diameter, and pitch guiding the analysis. This hands-on application of ML showcases the adaptability of machine learning techniques. It underscores the pivotal role of creating a robust dataset as the foundational step for effective model training and application in the problem-solving of optical systems. The synergy between theory-driven computational models and data-driven machine learning approaches is explored, revealing a promising era for unlocking novel insights and driving innovation in photonics, revealing important features of photonics devices. The shift towards data-driven methodologies addresses prevailing limitations of theory-driven computational methods when navigating the intricate complexities inherent in photonic systems. Research into the dynamic interplay between established theories and emerging machine learning methodologies is poised to uncover novel insights, ultimately driving the field towards efficiently solving complex photonic systems by deploying effectively optimized neural networks to predict specific outputs for given inputs.