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SCIENTIA SINICA Informationis, Volume 51 , Issue 4 : 678(2021) https://doi.org/10.1360/SSI-2020-0158

Refined intelligence theory: artificial intelligence regarding complex dynamic objects

Zhiming ZHENG 1,2,3,4,5,6, Jinhu LU¨ 1,2,6,7, Wei WEI 3,4,5,6, Shaoting TANG 3,4,5,6,*
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  • ReceivedJun 2, 2020
  • AcceptedJun 18, 2020
  • PublishedMar 16, 2021

Abstract


Funded by

国际合作重大项目(2010DFR00700)

国家自然科学基金重大项目(11290140)

国防科工局[2010]1754号(AMS项目)


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  • Figure 1

    (Color online) The influence of data prior knowledge/mathematical and physical laws on function fitting approximation. The blue-dotted data is the original data, which is produced by $y=2{\rm~sin}(\frac{\pi}{4}-\frac{x}{2})cos(\frac{3x}{2}-\frac{\pi}{4})+N(0,0.05)={\rm~sin}x+{\rm~cos}2x+N(0,0.05)$, where $N$(0, 0.05) is Gaussian noise. The red curve is the result of approximation by Fourier series fitting, i.e., $y={\rm~sin}x+{\rm~cos}2x$. The green curve retains the 7th order polynomial for the approximation effect of power series fitting, i.e., $\tilde{y}=1+x-2x^2-\frac{x^3}{6}+\frac{2x^4}{3}+\frac{x^5}{120}-\frac{4x^6}{45}-\frac{x^7}{5040}$

  • Figure 2

    (Color online) The hierarchical structure of three-dimensional urban traffic network. In the figure, the $\alpha$ layer represents the urban surface public transport network, and the $\beta$ layer represents the underground rail transit network. The green node (such as node $j$) represents the ordinary station, and the red node (such as node $i$) represents the transfer hub between the ground bus and the underground rail transit

  • Figure 3

    (Color online) The iterative behavior of the system is compared with that of neural network fitting. The black curve in the figure is the iterative dynamic curve of the function $y=ax(1-x)$. The parameter $a$ is equal to 1.5, 3.4, 3.7 and 3.9, respectively. The red curve is the iterative dynamic curve of three-layer fully connected neural network (100 neurons, three layers with 10, 80 and 10 neurons respectively). The neural network is used to approximate the function of $y=ax(1-x)$ under the corresponding parameter values. The green curve is an iterative dynamic curve of 10 layer fully connected neural network (100 neurons, each layer has 2, 4, 8, 12, 36, 14, 10, 8, 4, 2 neurons). The neural network is used to approximate the function of $y=ax(1-x)$ under the corresponding parameter values

  • Table 1   Neural network approximation residuals for $y~=~ax~(1-x)~$
    Neural network layers/values of $a$ 1.5 3.4 3.7 3.9
    3 layers 0.00668 0.00026 0.00285 0.00032
    10 layers 0.00682 0.00165 0.00038 0.00017
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