Hessian Preconditioning of Adaptive Tabulation for Reactive Flow Applications

October 4, 2024

TIME: 3:30 PM

LOCATION: GMCS 314

SPEAKER: Pavel Popov

ABSTRACT:

This work tackles the problem of fast estimation of a function whose direct evaluation is computationally costly. In an application such as simulation of reactive flow, can be the composition and temperature at a point, and is the increment of that composition after a single time step. Over the course of a simulation, there is a query for at every grid cell and time step, with the total number of queries exceeding . Thus, a fast approximation is preferable to a slow, albeit machine precision-accurate, direct evaluation. The present method builds on the In Situ Adaptive Tabulation (ISAT) method of Pope [1], which spans the domain with a set of ellipsoids, each of which provides a linearization of its interior. For a user-specified estimation accuracy, the size of the ellipsoids comprising the ISAT table is inversely proportional to the Hessian, , of . Thus, minimizing the Hessian allows the same accuracy to be achieved with a lower number of ellipsoids, hence less memory and computational cost of building the table. Hessian minimization is achieved via subtraction of a computationally inexpensive function , leaving the remainder, , to be estimated by ISAT. The preconditioning function is implemented via a small fully-connected neural network with smooth activation functions. The network can be trained to minimize a standard RMS loss function, which estimates the Hessian implicitly. Alternatively, the Hessian can be estimated explicitly via a newly developed loss function based on distance to a local linearization on a set of points selected with K-means clustering. The ISAT with Hessian preconditioning implementation is compared to standalone ISAT, using both user-specified analytic functions and a hydrogen-burning partially-stirred reactor (PaSR) test case. For a fixed ISAT accuracy, reductions of the table size by more than a factor of are observed. Several alternative smooth activation functions are tested, with the aim of minimizing both the Hessian estimation error and the computational cost of evaluating the preconditioner . [1] S.B. Pope, Computationally Efficient Implementation of Combustion Chemistry Using In Situ Adaptive Tabulation, Combustion Theory and Modelling, 1, 44-63

HOST: Jose Castillo

VIDEO: