Abstract: Leveraging large-scale data and systems of computing accelerators, statistical learning has led to significant paradigm shifts in many scientific disciplines. Grand challenges in science have been tackled with exciting synergy between disciplinary science, physics-based simulations via high-performance computing, and powerful learning methods. In this talk, I will describe several vignettes of our research in the theme of modeling complex dynamical systems characterized by partial differential equations with turbulent solutions. I will also demonstrate how machine learning technologies, especially advances in generative AI technology, are effectively applied to address the computational and modeling challenges in such systems, exemplified by their successful applications to weather forecast and climate projection. I will also discuss what new challenges and opportunities have been brought into future machine learning research. The research work presented in this talk is based on joint and interdisciplinary research work of several teams across multiple institutions.