In situ adaptive tabulation
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.
See also[edit]
- Predictive analytics
- Radial basis function network
- Recurrent neural networks
- Support vector machine
- Tensor product network
References[edit]
- ^ 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[edit]
- In Situ Adaptive Tabulation (ISAT) in Turbulent Combustion
- Tutorial Overview of ISAT
- ISAT-CK7: an implementation in Fortran 90 developed by Turbulence and Combustion Group at Cornell
- ISAT-CK7-Cantera: an adaptation of Cornell code to use with Cantera library
- CRFlowLib: alternative implementation in C language