Artificial intelligence (AI), specifically machine learning (ML) and deep learning (DL) tools, have revolutionized numerous facets of our lives. Their capacity to manage high-dimensional and large data sets has facilitated solutions to various scientific and engineering challenges, from nanotechnology development to intricate medical data analysis. However, there are still obstacles in fully harnessing the potential of ML algorithms for certain specific scientific or engineering tasks. This research concentrates on addressing these issues, focusing on two critical domains: 1) ML-assisted optimization and knowledge discovery in nanophotonics, and 2) ML-assisted pneumonia diagnosis and prognosis using chest X-rays. This study introduces a novel dimensionality reduction (DR) technique that enables inverse design and optimization in nanophotonics, requiring significantly less computation than existing methods. Moreover, a new method combining DR and manifold learning has been developed to study the feasibility of responses in certain nanostructures and offer invaluable insight into the underlying physics. Importantly, this work pioneers a new method to establish physics-friendly similarity measures and metrics tailored to the design needs in nanophotonics. In the context of ML-assisted radiology, a confidence-aware model has been developed for assessing disease severity from chest X-rays. A user-friendly labeling tool has been created to study the variability in human labeling and the influence of AI decision-making on human readers. Further, a unique visualization technique combining pruning and manifold learning has been introduced to enhance model reliability and interpretability. This comprehensive exploration of machine learning applications across nanophotonics and medical diagnostics not only offers novel techniques and tools for these fields but also provides a framework that could guide future research in utilizing AI for problem-specific solutions. This work marks a significant step towards maximizing the transformative potential of AI in both scientific and engineering contexts, promising advancements in technology, medicine, and beyond.