Neural Network Time Series Prediction - changing the inital state -

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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

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Greg Heath
Greg Heath 2015-12-28
编辑:Greg Heath 2015-12-28
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
  1 个评论
Image Analyst
Image Analyst 2015-12-29
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

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