Explore a 58-minute lecture on data-driven information geometry for stochastic model reduction. Delve into the extension of least squares techniques from flat spaces to curvilinear manifolds of probability distributions. Learn about the data-driven construction of statistical manifolds using local normal distributions derived from singular value decomposition. Discover how reduced-order models are obtained through geodesic transport on curved manifolds. Examine applications in adaptive computation of rapidly varying stochastic phenomena, including wave propagation in stochastic media and inhomogeneous biomechanical systems. Gain insights from Professor Sorin Mitran of the University of North Carolina, Chapel Hill, an expert in mathematics and computational science with extensive research experience and numerous publications.