# narnet

Nonlinear autoregressive neural network

## Description

`narnet(`

takes these arguments:`feedbackDelays`

,`hiddenSizes`

,`feedbackMode`

,`trainFcn`

)

Row vector of increasing 0 or positive feedback delays,

`feedbackDelays`

Row vector of one or more hidden layer sizes,

`hiddenSizes`

Type of feedback,

`feedbackMode`

Training function,

`trainFcn`

and returns a NAR neural network.

You can train NAR (nonlinear autoregressive) neural networks to predict a time series from the past values of that series.

## Examples

### Train NAR Network and Predict on New Data

Train a nonlinear autoregressive (NAR) neural network and predict on new time series data. Predicting a sequence of values in a time series is also known as *multistep prediction*. Closed-loop networks can perform multistep predictions. When external feedback is missing, closed-loop networks can continue to predict by using internal feedback. In NAR prediction, the future values of a time series are predicted only from past values of that series.

Load the simple time series prediction data.

T = simplenar_dataset;

Create a NAR network. Define the feedback delays and size of the hidden layers.

net = narnet(1:2,10);

Prepare the time series data using `preparets`

. This function automatically shifts input and target time series by the number of steps needed to fill the initial input and layer delay states.

[Xs,Xi,Ai,Ts] = preparets(net,{},{},T);

A recommended practice is to fully create the network in an open loop, and then transform the network to a closed loop for multistep-ahead prediction. Then, the closed-loop network can predict as many future values as you want. If you simulate the neural network in closed-loop mode only, the network can perform as many predictions as the number of time steps in the input series.

Train the NAR network. The `train`

function trains the network in an open loop (series-parallel architecture), including the validation and testing steps.

net = train(net,Xs,Ts,Xi,Ai);

Display the trained network.

view(net)

Calculate the network output `Y`

, final input states `Xf`

, and final layer states `Af`

of the open-loop network from the network input `Xs`

, initial input states `Xi`

, and initial layer states `Ai`

.

[Y,Xf,Af] = net(Xs,Xi,Ai);

Calculate the network performance.

perf = perform(net,Ts,Y)

perf = 1.0100e-09

To predict the output for the next 20 time steps, first simulate the network in closed-loop mode. The final input states `Xf`

and layer states `Af`

of the open-loop network `net`

become the initial input states `Xic`

and layer states `Aic`

of the closed-loop network `netc`

.

[netc,Xic,Aic] = closeloop(net,Xf,Af);

Display the closed-loop network. The network has only one input. In closed-loop mode, this input connects to the output. A direct delayed output connection replaces the delayed target input.

view(netc)

To simulate the network 20 time steps ahead, input an empty cell array of length 20. The network requires only the initial conditions given in `Xic`

and `Aic`

.

Yc = netc(cell(0,20),Xic,Aic)

`Yc=`*1×20 cell array*
Columns 1 through 5
{[0.8346]} {[0.3329]} {[0.9084]} {[1.0000]} {[0.3190]}
Columns 6 through 10
{[0.7329]} {[0.9801]} {[0.6409]} {[0.5146]} {[0.9746]}
Columns 11 through 15
{[0.9077]} {[0.2807]} {[0.8651]} {[0.9897]} {[0.4093]}
Columns 16 through 20
{[0.6838]} {[0.9976]} {[0.7007]} {[0.4311]} {[0.9660]}

## Input Arguments

`feedbackDelays`

— Feedback delays

`[1:2]`

(default) | row vector

Zero or positive feedback delays, specified as an increasing row vector.

`hiddenSizes`

— Hidden sizes

`10`

(default) | row vector

Sizes of the hidden layers, specified as a row vector of one or more elements.

`feedbackMode`

— Feedback mode

`'open'`

(default) | `'closed'`

| `'none'`

Type of feedback, specified as either `'open'`

,
`'closed'`

, or `'none'`

.

`trainFcn`

— Training function name

`'trainlm'`

(default) | `'trainbr'`

| `'trainbfg'`

| `'trainrp'`

| `'trainscg'`

| ...

Training function name, specified as one of the following.

Training Function | Algorithm |
---|---|

`'trainlm'` | Levenberg-Marquardt |

`'trainbr'` | Bayesian Regularization |

`'trainbfg'` | BFGS Quasi-Newton |

`'trainrp'` | Resilient Backpropagation |

`'trainscg'` | Scaled Conjugate Gradient |

`'traincgb'` | Conjugate Gradient with Powell/Beale Restarts |

`'traincgf'` | Fletcher-Powell Conjugate Gradient |

`'traincgp'` | Polak-Ribiére Conjugate Gradient |

`'trainoss'` | One Step Secant |

`'traingdx'` | Variable Learning Rate Gradient Descent |

`'traingdm'` | Gradient Descent with Momentum |

`'traingd'` | Gradient Descent |

**Example: **For example, you can specify the variable learning rate gradient descent
algorithm as the training algorithm as follows:
`'traingdx'`

For more information on the training functions, see Train and Apply Multilayer Shallow Neural Networks and Choose a Multilayer Neural Network Training Function.

**Data Types: **`char`

## Version History

**Introduced in R2010b**

## See Also

`preparets`

| `removedelay`

| `timedelaynet`

| `narxnet`

| `closeloop`

| `network`

| `train`

| `openloop`

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