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''''''In situ''''' '''adaptive tabulation''' ('''ISAT''') is an [[algorithm]] for the approximation of [[nonlinear]] relationships. ISAT is based on [[multiple linear regression]]s 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 network]]s that is receiving increased attention for desirable characteristics, namely: * scales [[quadratic function|quadratically]] with increased dimension * approximates functions with [[discontinuity (mathematics)|discontinuities]] * maintains explicit bounds on [[approximation error]] * controls local [[derivative]]s 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]]<ref>{{cite journal | last=Pope | first=S. B. | title=Computationally efficient implementation of combustion chemistry using ''in situ'' adaptive tabulation | journal=Combustion Theory and Modelling | year=1997 | url=http://tcg.mae.cornell.edu/pubs/Pope_CTM_97.pdf | volume=1 | pages=44–63}}</ref> and later extended to model predictive control.<ref>{{cite journal | last=Hedengren | first=J. D. | title=Approximate Nonlinear Model Predictive Control with In Situ Adaptive Tabulation | journal=Computers and Chemical Engineering | year=2008 | url=http://hedengren.net/research/Publications/CACE/hedengren_cace_2006.pdf | volume=32 | pages=706–714}}</ref> It has been generalized to an [http://hedengren.net/research/isat.htm ISAT framework] that operates based on any input and output data regardless of the application. An improved version of the algorithm<ref>{{cite journal | last=Lu | first=L. | title=An improved algorithm for in situ adaptive tabulation | journal=Journal of Computational Physics | year=2009 | url=https://tcg.mae.cornell.edu/pubs/Lu_LRP_JCP_09.pdf | volume=228 | pages=361–386}}</ref> 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. ==See also== *[[Predictive analytics]] *[[Radial basis function network]] *[[Recurrent neural networks]] *[[Support vector machine]] *[[Tensor product network]] ==References== {{Reflist}} ==External links== *[http://tcg.mae.cornell.edu/isat.html In Situ Adaptive Tabulation (ISAT) in Turbulent Combustion] *[http://www.hedengren.net/research/isat.htm Tutorial Overview of ISAT] *[https://tcg.mae.cornell.edu/ISATCK7/ ISAT-CK7: an implementation in Fortran 90 developed by Turbulence and Combustion Group at Cornell] *[https://github.com/nogenmyr/ISAT-CK7-Cantera ISAT-CK7-Cantera: an adaptation of Cornell code to use with Cantera library] *[https://github.com/americocunhajr/CRFlowLib CRFlowLib: alternative implementation in C language] [[Category:Computer networking]]'