In Situ Adaptive Tabulation
Encyclopedia
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 network
s that is receiving increased attention for desirable characteristics, namely:
ISAT was first proposed by Stephen B. Pope for computational reduction of turbulent combustion
simulation
. It has been extended to a general framework that accepts general input and output data.
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
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 network
Artificial neural network
An artificial neural network , usually called neural network , is a mathematical model or computational model that is inspired by the structure and/or functional aspects of biological neural networks. A neural network consists of an interconnected group of artificial neurons, and it processes...
s that is receiving increased attention for desirable characteristics, namely:
- scales quadraticQuadraticIn mathematics, the term quadratic describes something that pertains to squares, to the operation of squaring, to terms of the second degree, or equations or formulas that involve such terms...
ally with increased dimension - approximates functions with discontinuities
- maintains explicit bounds on approximation errorApproximation errorThe approximation error in some data is the discrepancy between an exact value and some approximation to it. An approximation error can occur because#the measurement of the data is not precise due to the instruments...
- controls local derivativeDerivativeIn calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...
s of the approximating function - delivers new data training without re-optimizationOptimizationOptimization or optimality may refer to:* Mathematical optimization, the theory and computation of extrema or stationary points of functionsEconomics and business* Optimality, in economics; see utility and economic efficiency...
ISAT was first proposed by Stephen B. Pope for computational reduction of turbulent combustion
Combustion
Combustion or burning is the sequence of exothermic chemical reactions between a fuel and an oxidant accompanied by the production of heat and conversion of chemical species. The release of heat can result in the production of light in the form of either glowing or a flame...
simulation
Simulation
Simulation is the imitation of some real thing available, state of affairs, or process. The act of simulating something generally entails representing certain key characteristics or behaviours of a selected physical or abstract system....
. It has been extended to a general framework that accepts general input and output data.
See also
- Predictive analyticsPredictive analyticsPredictive analytics encompasses a variety of statistical techniques from modeling, machine learning, data mining and game theory that analyze current and historical facts to make predictions about future events....
- Radial basis function networkRadial basis function networkA radial basis function network is an artificial neural network that uses radial basis functions as activation functions. It is a linear combination of radial basis functions...
- Recurrent neural networks
- Support vector machineSupport vector machineA support vector machine is a concept in statistics and computer science for a set of related supervised learning methods that analyze data and recognize patterns, used for classification and regression analysis...
- Tensor product networkTensor product networkA tensor product network, in neural networks, is a network that exploits the properties of tensors to model associative concepts such as variable assignment...