Many problems in science and engineering require predicting how radiation, light, or particles move through and interact with complex media. These problems arise in areas such as atmospheric science, optical imaging, nuclear engineering, and astrophysics, where accurate predictions are essential to scientific discovery, engineering design, and decision-making. A central tool for making such predictions is numerical simulation based on partial differential equations, which provides a first-principles way to model the relevant physical processes. However, these simulations remain very expensive because of the high-dimensional and multiscale nature of the underlying problems. This project aims to address this barrier by developing a systematic computational framework that integrates efficient high-order adaptive numerical methods, substructure-based parallel computation, and localized machine-learning models. The substructure-based design makes the computation well-suited for modern parallel computing systems, including high-performance computing clusters and GPUs. It also allows machine-learning models to be trained locally and inexpensively at the substructure level, while keeping the overall solver grounded in reliable and theoretically justified classical numerical methods. This combination of low-cost machine learning and first-principles-based numerical computation is expected to broaden access to the interdisciplinary area of scientific machine learning and provide studen