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Available Mapping Functions for Nonlinear ARX Models

A nonlinear ARX model consists of model regressors and an output function. The output function includes one or more mapping objects, one object for each output of the model. Each mapping object maps a set of input signals into a single output signal, and typically includes a nonlinear function, a linear function, and an offset. For more information about nonlinear ARX model structure, see What are Nonlinear ARX Models?.

The System Identification Toolbox™ software provides several mapping objects for nonlinear ARX models. When you estimate nonlinear ARX models in the app or at the command line, the software creates and configures the mapping objects that you specify. You can also create and configure mapping objects independently at the command line and then specify these customized objects when you perform estimation.

Some mapping functions represent the nonlinear function as a summed series of nonlinear units, such as wavelet networks or sigmoid functions. Others use models that draw on machine learning algorithms. One mapping object contains no nonlinear function at all, just a linear function and an offset. The following table lists the available mapping objects. For a detailed description of an object, see the corresponding reference page.

NonlinearityMapping ObjectDescriptionComments
Wavelet networkidWaveletNetworkSum of dilated and translated wavelets in a wavelet network.Default
One layer sigmoid networkidSigmoidNetworkSum of dilated and translated sigmoid unit functions. 
Tree partitionidTreePartitionPiecewise linear function over partitions of the regressor space defined by a binary tree.Useful for modeling data collected over a range of operating conditions.
LinearidLinearContains only a linear component and an offset. This estimator produces a model that is similar to the linear ARX model, but offers the additional flexibility of specifying custom regressors.Use to create linear model structures with nonlinearities embedded in the regressors.

Custom network

idCustomNetworkSimilar to sigmoid network but with a user-defined unit function.User Defined. For advanced use.
Multilayered neural networkidNeuralNetworkNeural network that can be a regression neural network (RegressionNeuralNetwork (Statistics and Machine Learning Toolbox)), a deep neural network (dlnetwork (Deep Learning Toolbox)), or a shallow neural network (network (Deep Learning Toolbox)).Requires Statistics and Machine Learning Toolbox™ or Deep Learning Toolbox™.
Gaussian process (GP) regression modelidGaussianProcessKernel-based zero-mean Gaussian random process regression model.Useful when measurement data is limited. Requires Statistics and Machine Learning Toolbox.
Tree ensemble regression modelidTreeEnsembleDecision tree ensemble regression model, which is an ensemble of binary decision trees.Typically good predictive performance because using a tree combination reduces overfitting. Can invoke parallel processing. Requires Statistics and Machine Learning Toolbox.
Support vector machine (SVM) regression modelidSupportVectorMachineKernel-based SVM regression model with constraints.Robust to outliers. Requires Statistics and Machine Learning Toolbox.

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