Neural Network Time Series Prediction - changing the inital state -

Hello, I'm working currently with prediction-problems for dynamical systems, e.g. single pendulum with friction. At the moment I'm testing neural networks for time series predictions, although my knowledge is very basic. My understanding of neural networks in light of dynamical systems is that they are working like a flexible state-space-model. Training the neural network with some testdata should result in an accurate state-space-model, which can be used for predictions, am I right?

Lets say, I split my testdata into two sections. The first one will be used for training purpose and the second one for validation (in reference to my attached file). The prediction gives good results on the validation data, going forward, we are using the same net, but vary the inital state, here the inital angle of the pendulum. Is it even possible to vary the inital state? Does the net just predict on a one-off basis of the training data?

I'm referring to ANN Examples ,especially example 9 (Prediction of chaotic time series with NAR neural network).

Regards

Answer 1

[Greg Heath]

NEURAL NETWORK SUBSET TERMINOLOGY(comp.ai.neural-nets):

 data        = training + validation + test
 design      = training + validation
 nondesign   = test
 nontraining = validation + test

TRAINING:

 1. Given input matrix, target matrix and training parameters, 
estimate the weights and biases.

 2. Performance estimate is biased because the same data is used for 
training and performance estimation.

VALIDATION:

Used with multiple designs to

 1. Choose nonweight parameters (e.g., learning rate, momentum 
constant, stopping epoch...) 

 2. Rank multiple designs

 3. Performance estimates slightly biased because the same data is 
used to choose parameters

TEST:

Used to obtain UNBIASED performance estimates of designs ranked by 
validation data.

BASIC ASSUMPTIONS:

 REGRESSION AND CLASSIFICATION:

 All data assumed to be randomly chosen from the same parent 
probability distribution.

 TIME SERIES

 All data segments assumed to have the same summary statistics, 
i.e., mean, variance 
and correlations

If you vary the initial pendulum angle, the angle has to be part of the input matrix AND training has to include the range of angles considered.

Hope this helps.

Thank you for formally accepting my answer

Greg

[Image Analyst]

Michael's "Answer" moved here to be a comment:

Hello Greg,

Sorry, I didn't notice that my File wasn't attached. I fixed that and also the link is now working.

If you vary the initial pendulum angle, the angle has to be part of the input matrix AND training has to include the range of angles considered.

Could you take a look over my matlab-script and give me some advice what has to be changed in order to predict the pendulum-motion with the new inital state?

Thanks and Regards