In situ adaptive tabulation: Difference between revisions

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In situ adaptive tabulation (ISAT) is an algorithm for the approximation of nonlinear 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.

References

^ 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.

External links

[1] 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.

[2] 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.

[3] 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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+{{Short description|Algorithm for  approximating  nonlinear relationships}}
-'''In Situ Adaptive Tabulation''' (ISAT) is an algorithm for the approximation of nonlinear 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.
+'''''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
-ISAT is an alternative to artificial neural networks that is recieving increased attention for desireable characteristics, namely:
+* 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 | issue=1 | pages=44–63| doi=10.1080/713665229 | bibcode=1997CTM.....1...41P }}</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 | issue=4–5 | pages=706–714| doi=10.1016/j.compchemeng.2007.02.010 }}</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 | issue=2 | pages=361–386| doi=10.1016/j.jcp.2008.09.015 | bibcode=2009JCoPh.228..361L }}</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.
-* quadratic scaling with increasing dimensionality
-* approximates functions with discontinuities
-* maintains explicit bounds on approximation error and approximation derivatives
-* delivers new data training without re-optimization
+==See also==
-ISAT was first proposed by Stephen Pope for computational reduction of turbulent combustion simulation<ref>{{cite journal | last=Pope | first=S. | title=Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation | journal=Combustion Theory and Modelling | year=1997 | url=http://eccentric.mae.cornell.edu/~tcg/pubs/Pope_CTM_97.pdf | volume=1 | pages=44-63}}</ref>.  It has been extended to a general framework that accepts general input and output data.
-== See also ==
-*[[Artificial neural network]]
 *[[Predictive analytics]]
 *[[Radial basis function network]]
@@ Line 19: / Line 19: @@
 ==References==
-{{reflist}}
+{{Reflist}}
 ==External links==
-*[http://eccentric.mae.cornell.edu/~tcg/isat.html In Situ Adaptive Tabulation (ISAT) in Turbulent Combustion]
+*[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]
-*[http://www.fluent.com/software/fluent/focus/reacting.htm ISAT in Fluent]
+*[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]]