Project Grant 2245674

This $235,622 National Science Foundation Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) supports the development of scalable computational methods for large-scale stochastic optimization of partial differential equations with high-dimensional uncertainty. Key products include analysis of the intrinsic low-dimensionality of parameter-to-objective maps for stochastic PDE-constrained optimization problems. Methods to be developed include extension of local quadratic approximation using Hessian approximation as a translation invariant operator, higher-order Taylor approximation using hierarchical Tucker-tensor-train decomposition, and multi-point Taylor approximation based on Gaussian mixture models. These methods will be applied to optimization of subsurface flow control and implemented in an open-source Python library called SOUPY. The award is also supporting graduate students at the Georgia Institute of Technology and The University of Texas at Austin to work on these computational method developments and applications.