This monograph develops a unified, application-driven framework for kernel methods grounded in reproducing kernel Hilbert spaces and optimal transport. The primary goal is to tackle industrial cases from computational physics and mathematical finance and discuss applications across various areas, such as statistics, or artificial intelligence (physics-informed systems, reinforcement learning, machine learning, generative methods, etc.). Reproducing Kernel Methods for Machine Learning, PDEs, and Statistics is divided into two parts, theoretical principles and the techniques employed in their applications; contains numerous applications in engineering, finance, and machine learning; and provides a framework for designing numerically efficient, large-scale dataset strategies.
