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Data-Driven Model Reduction, Scientific Frontiers, and Applications ()

Rami Younis, Harold Vance Department of Petroleum Engineering
Two Cases of Leveraging Solution Character to Expedite Computation


Subsurface energy systems are inherently complex. Pressing needs to advance certain aspects of their efficient and prudent operation require experimentation at prohibitive scales. Numerical simulation is a promising pathway for scientific discovery and engineering by virtual experimentation. To deliver good on this promise, however, numerical models must cope with unprecedented physical complexity and a vast range of scales. This talk develops two advances to cope with such nonlinear complexity.

Over finite increments in time, changes to state often occur locally in space. I will outline another kind of locality that occurs across iterations for the solution of nonlinear algebraic systems that approximate physical phenomena. This characterization leads to the development of adaptive solution methods that compute full resolution iterates using local computations.

Along a parallel track, I will develop nonlinear solution methods for such systems by leveraging a statistical approximator to solve scalar problems. In an amortized offline regression stage, the single-element equation is solved over a sampling of possible neighboring states and parameters (e.g., cell volume and timestep size). An equivalent preconditioned algebraic system is posed using the approximator, and an incomplete elemental Seidel iteration is used to solve it.