This workshop aims to bring together researchers from diverse fields of applied mathematics to explore the critical role of variational methods in both physical sciences and data sciences. Variational problems are fundamental in modeling natural phenomena and optimizing complex systems. This interdisciplinary workshop will focus on the latest advances in the analysis of physical problems, mathematical aspects of data science, optimization techniques, and computational mathematics, and at the same time celebrate the important contributions of Rustum Choksi at the occasion of his 60th birthday. By bringing together a diverse group of scholars, the workshop will also create a venue for new research directions, innovative solutions, and enhanced computational methods.