Controlling the orientation of block copolymer (BCP) morphologies in thin films is essential for their use as nanostructured coatings, yet remains a significant challenge across diverse block chemistries. In this work, we develop a parametric, coarse-grained molecular dynamics (MD) model and use it to systematically investigate the ordering of di-block copolymers in thin films, examining the roles of chain composition, substrate surface energy, and surface tension differences between blocks. To efficiently map the complex parameter space associated with parameters of the model, we integrate a machine-learning framework based on a Gaussian process (GP) control algorithm, which autonomously identifies and prioritizes simulations of greatest value. The GP kernel is specifically designed to encode relevant physical symmetries, enabling the trained model to serve both as a comprehensive system response map and a tool for extracting key material insights. Our results reveal that achieving vertical orientation of BCP domains is governed by a balance of competing energetic factors, including entropic and enthalpic enrichment at interfaces, morphological distortions through the film thickness, and interfacial energies. Notably, lamellar BCP phases exhibit greater resilience to these competing effects, consistently forming vertically oriented structures across a wide range of conditions. In contrast, cylindrical BCP morphologies are highly sensitive to surface tension disparities, leading to less robust vertical alignment. These findings provide new guidance for the design and processing of BCP thin films with targeted orientations. [References] [1] Bae, S., Noack, M.M., Yager, K.G., “Surface Enrichment Dictates Block Copolymer Orientation”, Nanoscale, 2023, 15, 6901-6912