Algorithm for approximating nonlinear relationships
In situadaptive 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.
^Pope, S. B. (1997). "Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation" (PDF). Combustion Theory and Modelling. 1 (1): 44–63. Bibcode:1997CTM.....1...41P. doi:10.1080/713665229.
^Hedengren, J. D. (2008). "Approximate Nonlinear Model Predictive Control with In Situ Adaptive Tabulation" (PDF). Computers and Chemical Engineering. 32 (4–5): 706–714. doi:10.1016/j.compchemeng.2007.02.010.
^Lu, L. (2009). "An improved algorithm for in situ adaptive tabulation" (PDF). Journal of Computational Physics. 228 (2): 361–386. Bibcode:2009JCoPh.228..361L. doi:10.1016/j.jcp.2008.09.015.
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