nlarxOptions

R2026b

Option set for nlarx

Syntax

opt = nlarxOptions

opt = nlarxOptions(Name=Value)

Description

opt = nlarxOptions creates the default option set for nlarx. Use dot notation to modify this option set for your specific application. Any options that you do not modify retain their default values.

opt = nlarxOptions(Name=Value) creates an option set with options specified by one or more name-value arguments.

Examples

Create Default Option Set for Nonlinear ARX Estimation

opt = nlarxOptions;

Create and Modify Default Nonlinear ARX Option Set

Create a default option set for nlarx, and use dot notation to modify specific options.

opt = nlarxOptions;

Turn on the estimation progress display.

opt.Display = 'on';

Minimize the norm of the simulation error.

opt.Focus = 'simulation';

Use a subspace Gauss-Newton least squares search with a maximum of 25 iterations.

opt.SearchMethod = 'gn';
opt.SearchOptions.MaxIterations = 25;

Specify Options for Nonlinear ARX Estimation

Create an option set for nlarx specifying the following options:

• Turn off iterative estimation for the default wavelet network estimation.

• Turn on the estimation progress-viewer display.

opt = nlarxOptions('IterativeWavenet','off','Display','on');

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: Focus="simulation"

Use name-value arguments to specify the object properties such as the minimization objective, numerical search method used for iterative parameter estimation, and so on.

Focus — Minimization objective

"prediction" (default) | "simulation"

Minimization objective, specified as the comma-separated pair consisting of "Focus" and one of the following:

• "prediction" — Minimize the norm of the prediction error, which is defined as the difference between the measured output and the one-step ahead predicted response of the model.

• "simulation" — Minimize the norm of the simulation error, which is defined as the difference between the measured output and simulated response of the model.

Display — Estimation progress display setting

'off' (default) | 'on'

Estimation progress display setting, specified as the comma-separated pair consisting of 'Display' and one of the following:

• 'off' — No progress or results information is displayed.

• 'on' — Information on model structure and estimation results are displayed in a progress-viewer window.

OutputWeight — Weighting of prediction error in multi-output estimations

'noise' (default) | positive semidefinite matrix

Weighting of prediction error in multi-output model estimations, specified as the comma-separated pair consisting of 'OutputWeight' and one of the following:

• 'noise' — Optimal weighting is automatically computed as the inverse of the estimated noise variance. This weighting minimizes det(E'*E), where E is the matrix of prediction errors. This option is not available when using 'lsqnonlin' as a 'SearchMethod'.

• A positive semidefinite matrix, W, of size equal to the number of outputs. This weighting minimizes trace(E'*E*W/N), where E is the matrix of prediction errors and N is the number of data samples.

Normalize — Option to normalize estimation data

true (default) | false

Option to normalize estimation data, specified as true or false. If Normalize is true, then the algorithm uses the method specified in NormalizationOptions to normalize the data.

NormalizationOptions — Option set for configuring normalization

option set

Option set for configuring normalization, specified as the options shown in the following table. The first option, NormalizationMethod, determines which method the algorithm uses. The default option is 'auto'. For idnlarx models, a setting of 'auto' is equivalent to a setting of 'center'. Except for 'medianiqr', each specific method in NormalizationMethod has an associated configuration option, such as CenterMethodType when you specify the 'center' method. For more information about these methods, see the MATLAB^® function normalize.

Method or Method Option	Value	Description	Default
NormalizationMethod	'auto'	Set method automatically.	'auto' (equivalent to 'center')
	'center'	Center data to have mean 0.
	'zscore'	z-score with mean 0 and standard deviation 1.
	'norm'	2-norm.
	'scale'	Scale by standard deviation.
	'range'	Rescale range of data to [min,max].
	'medianiqr'	Center and scale data to have median 0 and interquartile scale of 1.
CenterMethodType (applies to 'center')	'mean'	Center to have mean 0.	'mean'
	'median'	Center to have median 0.
ZScoreType (applies to 'zscore')	'std'	Center and scale to have mean 0 and standard deviation 1.	'std'
	'robust'	Center and scale to have median 0 and median absolute deviation 1.
ScaleMethodType (applies to 'scale')	'std'	Scale by standard deviation.	'std'
	'mad'	Scale by median absolute deviation.
	'iqr'	Scale by interquartile range.
	'first'	Scale by first element of data.
NormValue (applies to 'norm')	Positive integer	p-norm, where p is a positive integer.	2
Range (applies to 'range')	2-element row vector	Rescale range of data to an interval of the form [a b], where a < b.	[0 1]

SearchMethod — Numerical search method used for iterative parameter estimation

'auto' (default) | 'gn' | 'gna' | 'lm' | 'grad' | 'lsqnonlin' | 'patternsearch' | 'fmincon' | 'adam' | 'sgdm' | 'lbfgs'

Numerical search method used for iterative parameter estimation, specified as the one of the values in the following table.

SearchMethod	Description
'auto'	Automatic method selection A combination of the line search algorithms, 'gn', 'lm', 'gna', and 'grad', is tried in sequence at each iteration. The first descent direction leading to a reduction in estimation cost is used.
'gn'	Subspace Gauss-Newton least-squares search Singular values of the Jacobian matrix less than GnPinvConstant*eps*max(size(J))*norm(J) are discarded when computing the search direction. J is the Jacobian matrix. The Hessian matrix is approximated as JTJ. If this direction shows no improvement, the function tries the gradient direction.
'gna'	Adaptive subspace Gauss-Newton search Eigenvalues less than gamma*max(sv) of the Hessian are ignored, where sv contains the singular values of the Hessian. The Gauss-Newton direction is computed in the remaining subspace. gamma has the initial value InitialGnaTolerance (see Advanced in 'SearchOptions' for more information). This value is increased by the factor LMStep each time the search fails to find a lower value of the criterion in fewer than five bisections. This value is decreased by the factor 2*LMStep each time a search is successful without any bisections.
'lm'	Levenberg-Marquardt least squares search Each parameter value is -pinv(H+d*I)*grad from the previous value. H is the Hessian, I is the identity matrix, and grad is the gradient. d is a number that is increased until a lower value of the criterion is found. This algorithm requires Optimization Toolbox™ software.
'grad'	Steepest descent least-squares search
'lsqnonlin'	Trust-region-reflective algorithm of lsqnonlin (Optimization Toolbox) This algorithm requires Optimization Toolbox software.
'patternsearch'	Solver for nonlinearities without well-defined gradients You can use the patternsearch (Global Optimization Toolbox) solver to find the minimum of a nonlinear function that does not have a well-defined gradient. This solver requires Global Optimization Toolbox software.
'fmincon'	Constrained nonlinear solvers You can use the sequential quadratic programming (SQP) and trust-region-reflective algorithms of the fmincon (Optimization Toolbox) solver. If you have Optimization Toolbox software, you can also use the interior-point and active-set algorithms of the fmincon solver. Specify the algorithm in the SearchOptions.Algorithm option. The fmincon algorithms might result in improved estimation results in the following scenarios: Constrained minimization problems when bounds are imposed on the model parameters. Model structures where the loss function is a nonlinear or nonsmooth function of the parameters. Multiple-output model estimation. A determinant loss function is minimized by default for multiple-output model estimation. fmincon algorithms are able to minimize such loss functions directly. The other search methods such as 'lm' and 'gn' minimize the determinant loss function by alternately estimating the noise variance and reducing the loss value for a given noise variance value. Hence, the fmincon algorithms can offer better efficiency and accuracy for multiple-output model estimations.
'adam'	Adaptive moment estimation (Adam) Adam is a first-order adaptive gradient solver. It supports mini-batch operation when data is segmented into multiple frames or batches. For more information, see Adaptive Moment Estimation (Deep Learning Toolbox).
'sgdm'	Stochastic gradient descent with momentum (SGDM) SGDM is a first-order momentum-based gradient solver. It supports mini-batch operation when data is segmented into multiple frames or batches. For more information, see Stochastic Gradient Descent with Momentum (Deep Learning Toolbox).
'lbfgs'	Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) L-BFGS is a quasi-Newton solver that approximates the inverse Hessian using a limited history of curvature pairs. For more information, see Limited-Memory BFGS (Deep Learning Toolbox).

SearchOptions — Option set for search algorithm

search option set

Option set for the search algorithm, specified as the comma-separated pair consisting of 'SearchOptions' and a search option set with fields that depend on the value of SearchMethod:

SearchOptions Structure When SearchMethod Is Specified as 'gn', 'gna', 'lm', 'grad', or 'auto'

Field Name	Description	Default
Tolerance	Minimum percentage difference between the current value of the loss function and its expected improvement after the next iteration, specified as a positive scalar. When the percentage of expected improvement is less than Tolerance, the iterations stop. The estimate of the expected loss-function improvement at the next iteration is based on the Gauss-Newton vector computed for the current parameter value.	1e-5
MaxIterations	Maximum number of iterations during loss-function minimization, specified as a positive integer. The iterations stop when MaxIterations is reached or another stopping criterion is satisfied, such as Tolerance. Setting MaxIterations = 0 returns the result of the start-up procedure. Use sys.Report.Termination.Iterations to get the actual number of iterations during an estimation, where sys is an idtf model.	20
Advanced	Advanced search settings, specified as a structure with the following fields: Field Name Description Default GnPinvConstant Jacobian matrix singular value threshold, specified as a positive scalar. Singular values of the Jacobian matrix that are smaller than GnPinvConstant*max(size(J)*norm(J)*eps) are discarded when computing the search direction. Applicable when SearchMethod is 'gn'. 10000 InitialGnaTolerance Initial value of gamma, specified as a positive scalar. Applicable when SearchMethod is 'gna'. 0.0001 LMStartValue Starting value of search-direction length d in the Levenberg-Marquardt method, specified as a positive scalar. Applicable when SearchMethod is 'lm'. 0.001 LMStep Size of the Levenberg-Marquardt step, specified as a positive integer. The next value of the search-direction length d in the Levenberg-Marquardt method is LMStep times the previous one. Applicable when SearchMethod is 'lm'. 2 MaxBisections Maximum number of bisections used for line search along the search direction, specified as a positive integer. 25 MaxFunctionEvaluations Maximum number of calls to the model file, specified as a positive integer. Iterations stop if the number of calls to the model file exceeds this value. Inf MinParameterChange Smallest parameter update allowed per iteration, specified as a nonnegative scalar. 0 RelativeImprovement Relative improvement threshold, specified as a nonnegative scalar. Iterations stop if the relative improvement of the criterion function is less than this value. 0 StepReduction Step reduction factor, specified as a positive scalar that is greater than 1. The suggested parameter update is reduced by the factor StepReduction after each try. This reduction continues until MaxBisections tries are completed or a lower value of the criterion function is obtained. StepReduction is not applicable for SearchMethod 'lm' (Levenberg-Marquardt method). 2

SearchOptions Structure When SearchMethod Is Specified as 'lsqnonlin'

Field Name	Description	Default
FunctionTolerance	Termination tolerance on the loss function that the software minimizes to determine the estimated parameter values, specified as a positive scalar. The value of FunctionTolerance is the same as that of opt.SearchOptions.Advanced.TolFun.	1e-5
StepTolerance	Termination tolerance on the estimated parameter values, specified as a positive scalar. The value of StepTolerance is the same as that of opt.SearchOptions.Advanced.TolX.	1e-6
MaxIterations	Maximum number of iterations during loss-function minimization, specified as a positive integer. The iterations stop when MaxIterations is reached or another stopping criterion is satisfied, such as FunctionTolerance. The value of MaxIterations is the same as that of opt.SearchOptions.Advanced.MaxIter.	20

SearchOptions Structure When SearchMethod Is Specified as 'patternsearch'

Field Name	Description	Default
Algorithm	patternsearch optimization algorithm, specified as one of these values: 'classic' 'nups' 'nups-gps' 'nups-mads' For algorithm details, see How Pattern Search Polling Works (Global Optimization Toolbox) and Nonuniform Pattern Search (NUPS) Algorithm (Global Optimization Toolbox). For examples of algorithm effects, see Explore patternsearch Algorithms (Global Optimization Toolbox) and Explore patternsearch Algorithms in Optimize Live Editor Task (Global Optimization Toolbox).	'nups'
FunctionTolerance	Termination tolerance on the loss function that the software minimizes to determine the estimated parameter values, specified as a positive scalar.	1e-6
StepTolerance	Termination tolerance on the estimated parameter values, specified as a positive scalar.	1e-6
MaxIterations	Maximum number of iterations during loss function minimization, specified as a positive integer. The iterations stop when MaxIterations is reached or another stopping criterion is satisfied, such as FunctionTolerance.	'100*numberOfVariables', where numberOfVariables is the number of problem variables
UseParallel	Option to enable or disable parallel processing for improved performance, specified as one of these values: "off" — Run in serial on the MATLAB client. "auto" — Use a parallel pool if one is open or if MATLAB can automatically create one. If a parallel pool is not available, run in serial on the MATLAB client. "on" — Use a parallel pool if one is open or if MATLAB can automatically create one. If a parallel pool is not available, throw an error. If you do not have a parallel pool open and automatic pool creation is enabled, MATLAB opens a pool using the default cluster profile. To use a parallel pool to run computations in MATLAB, you must have Parallel Computing Toolbox™. Before R2026b: To run in parallel, set UseParallel to true.	"off"

SearchOptions Structure When SearchMethod Is Specified as 'fmincon'

Field Name	Description	Default
Algorithm	fmincon optimization algorithm, specified as one of the following: 'sqp' — Sequential quadratic programming algorithm. The algorithm satisfies bounds at all iterations, and it can recover from NaN or Inf results. It is not a large-scale algorithm. For more information, see Sparsity in Optimization Algorithms (Optimization Toolbox). 'trust-region-reflective' — Subspace trust-region method based on the interior-reflective Newton method. It is a large-scale algorithm. 'interior-point' — Large-scale algorithm that requires Optimization Toolbox software. The algorithm satisfies bounds at all iterations, and it can recover from NaN or Inf results. 'active-set' — Requires Optimization Toolbox software. The algorithm can take large steps, which adds speed. It is not a large-scale algorithm. For more information about the algorithms, see Constrained Nonlinear Optimization Algorithms (Optimization Toolbox) and Choosing the Algorithm (Optimization Toolbox).	'sqp'
FunctionTolerance	Termination tolerance on the loss function that the software minimizes to determine the estimated parameter values, specified as a positive scalar.	1e-6
StepTolerance	Termination tolerance on the estimated parameter values, specified as a positive scalar.	1e-6
MaxIterations	Maximum number of iterations during loss function minimization, specified as a positive integer. The iterations stop when MaxIterations is reached or another stopping criterion is satisfied, such as FunctionTolerance.	100

SearchOptions Structure When SearchMethod Is Specified as 'adam'

Field Name	Description	Default
LearnRate	Learning rate, or the step size, used for training, specified as a positive scalar. If the learning rate is too small, then training can take a long time. If the learning rate is too large, then training can be fast but it might reach a suboptimal result, diverge, or oscillate. The learning rate is denoted by α in the Adaptive Moment Estimation (Deep Learning Toolbox) section. If you specify LearnRateSchedule as "piecewise", then LearnRate is the learning rate before any scheduled drops.	0.001
GradientDecayFactor	Exponential decay rate of gradient moving average for the Adam solver, specified as a positive scalar less than 1. It controls the smoothing of the exponentially decaying average of past gradients. The gradient decay rate is denoted by β1 in the Adaptive Moment Estimation (Deep Learning Toolbox) section. If the value of GradientDecayFactor is closer to 1, then the smoothing increases. If the value of GradientDecayFactor is closer to 0, then recent gradients have more impact on the training.	0.9
SquaredGradientDecayFactor	Exponential decay rate of squared gradient moving average for the Adam solver, specified as a positive scalar less than 1. It controls the smoothing of the exponentially decaying average of past squared gradients. The squared gradient decay rate is denoted by β2 in the Adaptive Moment Estimation (Deep Learning Toolbox) section. Larger values of SquaredGradientDecayFactor adapt more slowly but provide a more stable variance estimate.	0.999
Epsilon	Small constant for numerical stability, specified as a positive scalar. To avoid division by zero when updating network parameters, the solver adds this constant to the denominator. Epsilon is denoted by ϵ in the Adaptive Moment Estimation (Deep Learning Toolbox) section.	1e-8
MaxEpochs	Maximum number of parameter updates or iterations to use for training, specified as a nonnegative integer. If you specify MaxEpochs as 0, the software disables iterations and only runs initialization or post-processing.	200
MaxFunctionEvaluations	Maximum number of objective function evaluations, specified as a positive integer.	intmax
LearnRateSchedule	Learning rate schedule type, specified as "none" or "piecewise". "none" — No learning rate schedule. This schedule keeps the learning rate constant and equal to LearnRate. "piecewise" — Piecewise learning rate schedule. This schedule multiplies the learning rate by LearnRateDropFactor every LearnRateDropPeriod number of iterations.	"none"
LearnRateDropFactor	Multiplicative factor for dropping the learning rate, specified as a positive scalar less than or equal to 1. You can specify this option only when you specify the LearnRateSchedule training option as "piecewise". The software multiplies the learning rate with the factor specified by LearnRateDropFactor every time a certain number of iterations passes. Specify the number of iterations using the LearnRateDropPeriod training option.	0.1
LearnRateDropPeriod	Number of iterations in between learning rate drops, specified as a positive integer. You can specify this option only when you specify the LearnRateSchedule training option as "piecewise". The software multiplies the learning rate with the drop factor every time the number of iterations specified by LearnRateDropPeriod passes. Specify the drop factor using the LearnRateDropFactor training option.	10
MinCostValue	Target objective value, specified as a nonnegative scalar. If the objective value at the current iteration is less than or equal to MinCostValue, the training stops.	0
ModelSelection	Iteration used to return the model parameters, specified as "best" or "last". If you specify ModelSelection as "best", the software returns the parameters corresponding to the iteration with the lowest objective value. If you specify ModelSelection as "last", the software returns the parameters corresponding to the final iteration.	"best"
Advanced	Structure used to specify advanced search options consisting of these fields:
	WeightDecay — Strength of L2 regularization applied to learnable parameters, specified as a nonnegative scalar. If WeightDecay>0 and UseDecoupledWeightDecay=1, weight decay is applied in a decoupled manner before update computations. If WeightDecay>0 and UseDecoupledWeightDecay=0, classical L2 regularization is applied by augmenting gradients before update computations. To disable this option, specify WeightDecay as 0.	0
	UseDecoupledWeightDecay — Flag to control whether weight decay is applied directly to parameters or is folded into the gradient as L2 penalty, specified as a logical scalar. If UseDecoupledWeightDecay=1, decoupled weight decay is applied directly. If UseDecoupledWeightDecay=0, L2 penalty term is added to the gradient. Decoupling prevents regularization strength from being implicitly modulated by momentum dynamics.	1
	ClipGradNorm — Maximum allowed L2 norm of the flattened gradient vector, specified as a nonnegative scalar. If the gradient norm exceeds this value, the gradient is rescaled. This rescaling helps prevent unstable updates when gradients spike, such as in recurrent models or stiff dynamical systems. To disable this option, specify ClipGradNorm as 0.	0
	NormEpsilon — Small constant used to avoid division by zero and underflow when computing safe norms and normalized quantities, especially when ClipGradNorm is enabled, specified as a positive scalar.	1e-12

SearchOptions Structure When SearchMethod Is Specified as 'sgdm'

Field Name	Description	Default
LearnRate	Learning rate, or the step size, used for training, specified as a positive scalar. If the learning rate is too small, then training can take a long time. If the learning rate is too large, then training can be fast but it might reach a suboptimal result, diverge, or oscillate. The learning rate is denoted by α in the Stochastic Gradient Descent with Momentum (Deep Learning Toolbox) section. If you specify LearnRateSchedule as "piecewise", then LearnRate is the learning rate before any scheduled drops.	0.01
Momentum	Momentum coefficient, specified as a positive scalar less than or equal to 1. This coefficient controls the contribution of the previous gradient step to the current iteration. The momentum coefficient is denoted by γ in the Stochastic Gradient Descent with Momentum (Deep Learning Toolbox) section. If the value of Momentum is closer to 1, then the smoothing increases. If the value of Momentum is closer to 0, then the solver behaves closer to the stochastic gradient descent algorithm.	0.95
MaxEpochs	Maximum number of parameter updates or iterations to use for training, specified as a nonnegative integer. If you specify MaxEpochs as 0, the software disables iterations and only runs initialization or post-processing.	200
MaxFunctionEvaluations	Maximum number of objective function evaluations, specified as a positive integer.	intmax
LearnRateSchedule	Learning rate schedule type, specified as "none" or "piecewise". "none" — No learning rate schedule. This schedule keeps the learning rate constant and equal to LearnRate. "piecewise" — Piecewise learning rate schedule. This schedule multiplies the learning rate by LearnRateDropFactor every LearnRateDropPeriod number of iterations.	"none"
LearnRateDropFactor	Multiplicative factor for dropping the learning rate, specified as a positive scalar less than or equal to 1. You can specify this option only when you specify the LearnRateSchedule training option as "piecewise". The software multiplies the learning rate with the factor specified by LearnRateDropFactor every time a certain number of iterations passes. Specify the number of iterations using the LearnRateDropPeriod training option.	0.1
LearnRateDropPeriod	Number of iterations in between learning rate drops, specified as a positive integer. You can specify this option only when you specify the LearnRateSchedule training option as "piecewise". The software multiplies the learning rate with the drop factor every time the number of iterations specified by LearnRateDropPeriod passes. Specify the drop factor using the LearnRateDropFactor training option.	10
MinCostValue	Target objective value, specified as a nonnegative scalar. If the objective value at the current iteration is less than or equal to MinCostValue, the training stops.	0
ModelSelection	Iteration used to return the model parameters, specified as "best" or "last". If you specify ModelSelection as "best", the software returns the parameters corresponding to the iteration with the lowest objective value. If you specify ModelSelection as "last", the software returns the parameters corresponding to the final iteration.	"best"
Advanced	Structure used to specify advanced search options consisting of these fields:
	WeightDecay — Strength of L2 regularization applied to learnable parameters, specified as a nonnegative scalar. If WeightDecay>0 and UseDecoupledWeightDecay=1, weight decay is applied in a decoupled manner before update computations. If WeightDecay>0 and UseDecoupledWeightDecay=0, classical L2 regularization is applied by augmenting gradients before update computations. To disable this option, specify WeightDecay as 0.	0
	UseDecoupledWeightDecay — Flag to control whether weight decay is applied directly to parameters or is folded into the gradient as L2 penalty, specified as a logical scalar. If UseDecoupledWeightDecay=1, decoupled weight decay is applied directly. If UseDecoupledWeightDecay=0, L2 penalty term is added to the gradient. Decoupling prevents regularization strength from being implicitly modulated by momentum dynamics.	1
	ClipGradNorm — Maximum allowed L2 norm of the flattened gradient vector, specified as a nonnegative scalar. If the gradient norm exceeds this value, the gradient is rescaled. This rescaling helps prevent unstable updates when gradients spike, such as in recurrent models or stiff dynamical systems. To disable this option, specify ClipGradNorm as 0.	0
	NormEpsilon — Small constant used to avoid division by zero and underflow when computing safe norms and normalized quantities, especially when ClipGradNorm is enabled, specified as a positive scalar.	1e-12

SearchOptions Structure When SearchMethod Is Specified as 'lbfgs'

Field Name	Description	Default
MaxIterations	Maximum number of quasi-Newton iterations to use for training, specified as a nonnegative integer. Each iteration forms a search direction using the stored curvature pairs and then performs a line search. If you specify MaxIterations as 0, the software disables iterations and only runs initialization or post-processing.	200
MaxFunctionEvaluations	Maximum number of objective function evaluations, including evaluations performed by line search, specified as a positive integer.	intmax
HistorySize	Number of curvature pairs or state updates to store, specified as a positive integer. The L-BFGS algorithm uses a history of gradient calculations to approximate the Hessian matrix recursively. Larger values of HistorySize can improve the Hessian approximation but will increase memory usage and cost per iteration. For more information, see the Limited-Memory BFGS (Deep Learning Toolbox) section.	10
GradientTolerance	Stopping tolerance on the relative gradient, specified as a positive scalar. The software stops training when the relative gradient is less than or equal to GradientTolerance.	1e-6
StepTolerance	Stopping tolerance on the step size, specified as a positive scalar. StepTolerance specifies the minimum allowable change in the parameters between successive iterations. The software stops training when the step that the algorithm takes is less than or equal to StepTolerance.	1e-12
FunctionTolerance	Stopping tolerance on the improvement in the objective value, specified as a positive scalar. FunctionTolerance specifies the minimum required decrease in the objective function value between iterations. The software stops training when the objective value improvement is less than or equal to FunctionTolerance.	1e-12
LineSearchMethod	Method to find a suitable step size, specified as one of these values: "strong-wolfe" — Search for a step size that satisfies the strong Wolfe conditions (sufficient decrease and strong curvature). This method maintains a positive definite approximation of the inverse Hessian matrix. "weak-wolfe" — Search for a step size that satisfies the weak Wolfe conditions (sufficient decrease and curvature). This method maintains a positive definite approximation of the inverse Hessian matrix. It can accept longer steps. "armijo" — Search for a learning rate that satisfies sufficient decrease conditions only. This method does not maintain a positive definite approximation of the inverse Hessian matrix. It is often more tolerant of noisy gradients but can accept shorter steps.	"strong-wolfe"
MaxNumLineSearchIterations	Maximum number of line search trials per iteration to determine the step size, specified as a positive integer.	40
InitialStepSize	Step size for the starting line search trial, specified as a positive scalar.	1.0
Advanced	Structure used to specify advanced search options consisting of these fields:
	MinStepSize — Smallest step size permitted by line search, specified as a positive scalar. If the step size for a trial goes below this value, the line search fails and the solver can stop or fall back depending on the implementation.	1e-16
	MaxStepSize — Largest step size permitted by line search, specified as a positive scalar. This upper bound for the trial step size prevents excessively large moves that can cause numerical overflow or objective evaluation failures.	1e+16
	GradientClipNorm — Maximum allowed L2 norm of the gradient vector used by the quasi-Newton update and line search, specified as a nonnegative scalar. If the gradient norm exceeds this value, the gradient is rescaled. This rescaling helps improve robustness on problems with occasional gradient spikes or poor scaling. To disable this option, specify GradientClipNorm as 0.	0
	WolfeC1 — Armijo condition (sufficient decrease) constant for Wolfe line search, specified as a positive scalar less than 1. Smaller values of WolfeC1 make sufficient decrease easier to satisfy.	1e-4
	WolfeC2 — Curvature condition constant for Wolfe line search, specified as positive scalar less than 1. Larger values of WolfeC2 make the curvature condition easier to satisfy whereas smaller values enforce a stronger curvature requirement.	0.9
	ZoomMaxIterations — Maximum number of iterations allowed in the "zoom" procedure of Wolfe line search, specified as a positive integer.	40
	BacktrackingFactor — Step size shrink factor during backtracking used to reduce trial step sizes when conditions are not satisfied, specified as a positive scalar less than 1. Values closer to 0 shrink the step size more aggressively while values closer to 1 shrink the step size more conservatively.	0.5
	CurvatureThreshold — Number to control whether a new curvature pair is accepted into the limited-memory history, specified as a positive scalar. Specifying CurvatureThreshold prevents storing nearly singular or noisy curvature information that can destabilize the inverse-Hessian approximation.	1e-10
	PowellDamping — Number to control the amount of Powell damping applied when the curvature condition is weak, specified as a nonnegative number less than 1. Damping enforces positive curvature and a positive-definite inverse-Hessian approximation. To disable this option, specify PowellDamping as 0.	0
	UseInitialScaling — Flag to control whether the initial inverse-Hessian is scaled each iteration using curvature information, specified as a logical scalar. This scaling often improves practical performance.	1

To specify field values in SearchOptions, create a default nlarxOptions set and modify the fields using dot notation. Any fields that you do not modify retain their default values.

opt = nlarxOptions;
opt.SearchOptions.MaxIter = 15;
opt.SearchOptions.Advanced.RelImprovement = 0.5;

SparsifyRegressors — Option to remove sparse regressors

0 or false (default) | 1 or true

Option to remove sparse regressors from the nonlinear ARX model, specified as logical 0 (false) or logical 1 (true).

Set this option to true to use a sparsification algorithm in the nlarx function to identify sparse regressors. The function removes these regressors from the nonlinear mapping function of the output idnlarx model, leaving only the optimal subset of regressors. To see which regressors are removed, enter sys.RegressorUsage at the command line, where sys is the idnlarx model.

To configure the sparsification algorithm, use the option SparsificationOptions.

The sparsification algorithm, also known as structured pruning, is similar to the lasso (least absolute shrinkage and selection operator) technique.

SparsificationOptions — Option set for configuring sparsification

option set

Option set for configuring sparsification, specified as one or more of the options shown in this table.

Option	Description	Default
SparsityMeasure	Form of the sparsification penalty added to the prediction error minimization objective, specified as one of these values: "l1" — L1 norm of the parameters that multiply the regressors "l0" — L0 pseudonorm of the parameters that multiply the regressors "log-sum" — Sum of the log of the absolute values of the parameters that multiply the regressors If several parameters multiply a certain regressor in different parts of the nonlinear mapping function, interpret the sparsification penalty in the group sense.	"log-sum"
GroupNorm	Norm used to measure the contribution of each parameter group to the sparsification penalty, specified as 2 or Inf. The default of 2 implies that the 2-norm of each parameter group is used in the sparsity measure.	2
Lambda	Sparsification penalty, λ, specified as a positive scalar. The sparsification penalty is the cost, c, of a regressor being identified as sparse in the minimization objective, defined as c = f + λ × p, where: f is the fitting objective (prediction error norm). p is the parameter property (l1 or l0 norm of the parameter groups multiplying the regressors, normalized by the minimum parameter group norm).	1
MaxIterations	Maximum number of Alternating Direction Method of Multipliers (ADMM) iterations to run to sparsify the regressor selection, specified as a positive integer.	20

When configuring the sparsification algorithm, keep these points in mind:

• Getting the best results can require trying various solver and sparsification options. The options with the most significant effect on the results are the:

  • Choice of sparsification measure (SparsificationOptions.SparsityMeasure = 'log-sum', 'l1', or 'l0')

  • Search method (SearchMethod = 'lm', 'lsqnonlin', and so on)

  • Value of the SparsificationOptions.Lambda option, which describes the strength of the sparsification penalty in the minimization objective

• Sparsification with the Focus property set to 'prediction' can be significantly faster than specification with Focus = 'simulation', but the results might not lead to good simulation models. To balance these approaches, consider performing sparsification with Focus = 'prediction' first. Then, perform a follow-up estimation using the selected regressors and Focus = 'simulation'.

Dependencies

To enable these options, set SparsifyRegressors to true.

IterativeWavenet — Iterative idWaveletNetwork estimation setting

'auto' (default) | 'on' | 'off'

Iterative idWaveletNetwork estimation setting, specified as the comma-separated pair consisting of 'IterativeWavenet' and one of the following:

• 'auto' — First estimation is noniterative and subsequent estimations are iterative.

• 'on' — Perform iterative estimation only.

• 'off' — Perform noniterative estimation only.

This option applies only when using an idWaveletNetwork nonlinearity estimator.

InputInterSample — Input-channel intersample behavior

'auto' | 'zoh' | 'foh' | 'bl'

Input-channel intersample behavior for transformations between discrete time and continuous time, specified as 'auto', 'zoh','foh', or 'bl'.

The definitions of the three behavior values are as follows:

• 'zoh' — Zero-order hold maintains a piecewise-constant input signal between samples.

• 'foh' — First-order hold maintains a piecewise-linear input signal between samples.

• 'bl' — Band-limited behavior specifies that the continuous-time input signal has zero power above the Nyquist frequency.

iddata objects have a similar property, data.InterSample, that contains the same behavior value options. When the InputInterSample value is 'auto' and the estimation data is in an iddata object data, the software uses the data.InterSample value. When the estimation data is instead contained in a timetable or a matrix pair, with the 'auto' option, the software uses 'zoh'.

The software applies the same option value to all channels and all experiments.

Regularization — Options for regularized estimation of model parameters

structure

Options for regularized estimation of model parameters, specified as the comma-separated pair consisting of 'Regularization' and a structure with fields:

Field Name	Description	Default
Lambda	Bias versus variance tradeoff constant, specified as a nonnegative scalar.	0 — Indicates no regularization.
R	Weighting matrix, specified as a vector of nonnegative scalars or a square positive semidefinite matrix. The length must be equal to the number of free parameters in the model, np. Use the nparams command to determine the number of model parameters.	1 — Indicates a value of eye(np).
Nominal	The nominal value towards which the free parameters are pulled during estimation, specified as one of the following: 'zero' — Pull parameters towards zero. 'model' — Pull parameters towards preexisting values in the initial model. Use this option only when you have a well-initialized idnlarx model with finite parameter values.	'zero'

To specify field values in Regularization, create a default nlarxOptions set and modify the fields using dot notation. Any fields that you do not modify retain their default values.

opt = nlarxOptions;
opt.Regularization.Lambda = 1.2;
opt.Regularization.R = 0.5*eye(np);

Regularization is a technique for specifying model flexibility constraints, which reduce uncertainty in the estimated parameter values. For more information, see Regularized Estimates of Model Parameters.

WindowSize — Size of data frames

intmax (default) | positive integer

Number of samples in each frame or batch when segmenting data for model training, specified as a positive integer.

Overlap — Size of overlap

"auto" (default) | integer

Number of samples in the overlap between successive frames when segmenting data for model training, specified as an integer. A negative integer indicates that certain data samples are skipped when creating the data frames.

The default value, "auto", implies that the size of the overlap is equal to the maximum delay across all model regressors. To get the delay information for the model structure, use getDelayInfo.

CrossValidate — Option to reserve data for cross-validation for training cascade-correlation neural networks

true (default) | false

Option to reserve data for cross-validation, specified as a logical scalar. If you specify this value as true, the software reserves a percentage of the training data for cross-validation. If you specify this value as false, the stopping criterion used is given by the normalized measure of Akaike's Information Criterion, defined as:

$$nAIC=log\left(trace\left(\frac{1}{N}{E}^{T}E\right)\right)+\frac{2\ast n_p}{N},$$

where N is the number of data samples, E is the error matrix with the prediction error value at time t=i as the i^th row, and n_p is the number of free parameters in the model. For more information, see Loss Function and Model Quality Metrics.

Specify CrossValidate when the output function of the nlarx model is a cascade-correlation neural network.

CrossValidationOptions — Option set for configuring cross-validation

option set

Option set for configuring cross-validation, with one option 'HoldoutFraction', specified as a scalar between zero and one. 'HoldoutFraction' is the fraction of training data used for cross-validation and its default value is 0.3.

To specify CrossValidationOptions, first create an nlarxOptions set. You can see that the CrossValidate property is true, by default. Then, modify 'HoldoutFraction' using dot notation.

opt = nlarxOptions;
opt.CrossValidationOptions.HoldoutFraction = 0.25;

To reserve a sample of data for cross-validation, the software uses the holdout method. For more information on cross-validation techniques, see What is Cross-Validation?

Specify CrossValidationOptions when the output function of the nlarx model is a cascade-correlation neural network.

Advanced — Additional advanced options

structure

Additional advanced options, specified as the comma-separated pair consisting of 'Advanced' and a structure with fields:

Field Name	Description	Default
ErrorThreshold	Threshold for when to adjust the weight of large errors from quadratic to linear, specified as a nonnegative scalar. Errors larger than ErrorThreshold times the estimated standard deviation have a linear weight in the loss function. The standard deviation is estimated robustly as the median of the absolute deviations from the median of the prediction errors, divided by 0.7. If your estimation data contains outliers, try setting ErrorThreshold to 1.6.	0 — Leads to a purely quadratic loss function.
MaxSize	Maximum number of elements in a segment when input-output data is split into segments, specified as a positive integer.	250000

To specify field values in Advanced, create a default nlarxOptions set and modify the fields using dot notation. Any fields that you do not modify retain their default values.

opt = nlarxOptions;
opt.Advanced.ErrorThreshold = 1.2;

Output Arguments

opt — Option set for nlarx command

nlarxOptions option set

Option set for nlarx command, returned as an nlarxOptions option set.

Extended Capabilities

Automatic Parallel Support

Accelerate code by automatically running computation in parallel using Parallel Computing Toolbox™.

The nlarxOptions object has automatic parallel support if its SearchMethod property is set to "patternsearch".

To run computations in parallel, set the SearchMethod property to "patternsearch" and the SearchOptions.UseParallel property to "on" or "auto".

Version History

Introduced in R2015a

R2026b: Enhanced control over parallel execution with SearchOptions.UseParallel property

When the SearchMethod property is "patternsearch", the SearchOptions.UseParallel property now accepts "off", "auto", or "on" values instead of true or false. This change gives you more control over when to use a parallel pool for parallel execution.

Specifying the SearchOptions.UseParallel property as true or false is not recommended.

R2026b: New Adam, SGDM, and L-BFGS solvers available for estimation

You can now use the adaptive moment estimation (Adam), stochastic gradient descent with momentum (SGDM), or limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) solvers to estimate models by setting the SearchMethod property to 'adam', 'sgdm', or 'lbfgs', respectively. You can change the default search option set using the SearchOptions property.

R2025a: New options added for cross-validation

You can now reserve a sample of data for cross-validation during training of a nonlinear ARX model by configuring the CrossValidate and CrossValidationOptions properties of the nlarxOptions option set. You can only set these properties when the output function of the nonlinear ARX model is a cascade-correlation neural network.

R2025a: New options added for data segmentation

You can specify the number of samples in each frame and in the overlap between successive frames using the new options WindowSize and Overlap, respectively.

R2025a: New pattern search solver available for estimation

You can now set the SearchMethod property to 'patternsearch' to estimate a system that has a nonlinearity without a well-defined gradient. You can change the default option set for this search algorithm using the SearchOptions property. This method requires Global Optimization Toolbox software.

R2022b: InputInterSample option allows intersample behavior specification for continuous models estimated from timetables or matrices.

iddata objects contain an InterSample property that describes the behavior of the signal between sample points. The InputInterSample option implements a version of that property in nlarxOptions so that intersample behavior can be specified also when estimation data is stored in timetables or matrices.

R2018a: Renaming of Estimation and Analysis Options

The names of some estimation and analysis options were changed in R2018a. Prior names still work.