In_situ_adaptive_tabulation
In situ adaptive tabulation
Algorithm for approximating nonlinear relationships
In situ adaptive tabulation (ISAT) is an algorithm for the approximation of nonlinear[disambiguation needed] relationships. ISAT is based on multiple linear regressions that are dynamically added as additional information is discovered. The technique is adaptive as it adds new linear regressions dynamically to a store of possible retrieval points. ISAT maintains error control by defining finer granularity in regions of increased nonlinearity. A binary tree search transverses cutting hyper-planes to locate a local linear approximation. ISAT is an alternative to artificial neural networks that is receiving increased attention for desirable characteristics, namely:
- scales quadratically with increased dimension
- approximates functions with discontinuities
- maintains explicit bounds on approximation error
- controls local derivatives of the approximating function
- delivers new data training without re-optimization
ISAT was first proposed by Stephen B. Pope for computational reduction of turbulent combustion simulation[1] and later extended to model predictive control.[2] It has been generalized to an ISAT framework that operates based on any input and output data regardless of the application. An improved version of the algorithm[3] was proposed just over a decade later of the original publication, including new features that allow you to improve the efficiency of the search for tabulated data, as well as error control.