Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.mrao.cam.ac.uk/downloads/cosmonet/algorithm.pdf Дата изменения: Mon Aug 7 18:43:28 2006 Дата индексирования: Sat Mar 1 02:37:43 2014 Кодировка: Поисковые слова: п п п п п п п п п

C O S M O N E T: How to build a map from cosmological parameters to the CMB power spectrum using a neural network.
C
OSMO

N

ET

's neural network maps are all based on Multi-Layer Perceptrons (MLPs) with 3 layers of neurons.

A 3-Layer Multi-Layer Perceptron Neural Network. For a set of cosmological input parameters, each neuron in the network takes a particular numerical value called an activation. The activations of the neurons in each layer of the network depend on those of the neurons in the preceding layer, according to a feed-forward calculation detailed below. The activations of the input neurons depend on the values of the cosmological input parameters and the ones at the output layer are the predicted values of the CMB power spectrum at the values of l commonly output by CAMB, and used as input by C O S M O M C.

Calculation Details:
First, the inputs, x, are simply assigned the values of the cosmological parameters for the model under consideration. In the case of the flat C DM model, the inputs are: h2 b , h2 c , , , ns and As . The activations of the nodes in the second, hidden layer, and output layer, are then calculated as:
(1) j (1) j (2) i (1) (1) j

hidden layer: hj = tanh(f output layer: yi = f

); f f

=
l

wj l xl +
(2)

, ,

(2) i

;

=
j

wij hj +

(2) i

where the index l runs over input nodes, j runs over hidden nodes and i runs over output nodes. The output vector y then has entries which are the CMB spectrum at the commonly used values of l. The parameters of the network are wj l , neurons in the hidden layer, and N values of
(2) wij (1) (1) j

, wij and

(2)

(2) i

. For a network with N
hid

an d N

out

values of

out (2) i.

values of l, there are Nin N

values of

in (1) wj l ,

cosmological parameters, N N
hid

hid out

values of

(1) j

,N

hid

N

Further Information:
The descriptions and parameters of C O S M O N E T networks for a variety of standard cosmological models are being released, starting with the flat C DM model. C O S M O N E T and an interface to C O S M O M C are publicly available at: www.mrao.cam.ac.uk/software/cosmonet.