在這我們使用四種不同的方法來對勞倫茲混沌系統做混沌預測.分別
是(I)局部近似-Local predictor, (II)整體近似-人工神經網路,即利用
一個加速學習的多層感知機網路-OLL(層層線性化的學習演算法),(III)複
合式網路:以整體近似的網路架構為主,以Localpredictor中,鄰居數據來
做訓練範例的人工神經網路,以層層線性化演算法來作演算,(IV)自我調適
人工神經網路-OLL+鄰居數據+參數調整,另外以三種方式來做預測分別是
a.新值預測:不更新預測點(原本預測出的值)的值來預測下一點(誤差累
積),b.最佳值預測:更新預測點的值來預測下一點(改善誤差累積)及c.定
點預測:以不同的對應數據來預測每一點. 由結果中得知,方法(III)
得到相當好的準度,約可達1e-8;而對於方法(IV),卻無法看出其調整參數
後,是否準度提高優點為何;不過我們嚐試各種不同的網路架構,在比較之
下,由網路來根據所接受資訊或數據點之複雜性來作調整而得到最佳網路
架構,仍是可行的.由預測模式來看,不管是準度或是預測範圍都是以最佳
值預測的結果最好(b>a>c).

Chaotic predictions are carried out for a chaotic Lorenz
time seriersby four different methods:(I)A local predictor, (II)
A global ANN with an accelerated alorithm for multilayer
preceptron - an OLL(Optimization Layerby Layer) learning scheme,
(III)A hybrid neural network - A global ANN withthe nearest
neighbors as the training datas with an OLL learning scheme.
(IV)A self-tuned ANN with the nearest neighbors and an OLL
learning scheme.Then, we use three prediction techniques: a.New
value prediction - predict next step without updataing the data.
b.Superior prediction - prediction nextstep with updataing data.
c.Prediction from fixed point - we predict next step from a
fixed point with every different data pair. Results indicate
that prediction accuracy for the method(III) is extremelygood.
Its relative error below 1e-8, but we can't obtain any benefit
from IV.We have attempted many kinds of network structures for
predicting chaotic time series, and we know the different
results are obtained for network, the method whose structure
changed from simple to complicate ones. It seem to tell us that
we can find the optimal network structure for the studied
system, but we must use the other method for reduce the number
of weights. The prediction accuracy and the predict horizon of
three method are b>a>c.