5.5 Further Issues
375
Fig. 5.113 The sphere
positions in region B (a), C
(b), and D (c)
A, and L > 2d p in the region C. Generally, if the view factor X i j = f ( P 1 , P 2 , S n )
is affected directly by P k ( P k ∈ S n , k = 1, 2, …, n), it should satisfy that
(I) The projection of P k onto the line P i P j should be within the range from P i to
P j .
(II) The distance from P k to line P i P j is less than 2d p . For example, two typical
configurations of the pebbles for current view factor computation are shown in
Fig. 5.115, (Fig. 5.115a for n = 3 and Fig. 5.115b for n = 8).
5.5.3.3 Function Approximation and Neural Network Model
The Artificial Neural Networks (ANNs) have been widely applied to function approximation by deep learning. From the universal approximation theorem, it is proven
that a feed-forward network (e.g., see Fig. 5.116) with one or more hidden layers is
capable of approximating the general multivariate continuous functions.
375
Fig. 5.113 The sphere
positions in region B (a), C
(b), and D (c)
A, and L > 2d p in the region C. Generally, if the view factor X i j = f ( P 1 , P 2 , S n )
is affected directly by P k ( P k ∈ S n , k = 1, 2, …, n), it should satisfy that
(I) The projection of P k onto the line P i P j should be within the range from P i to
P j .
(II) The distance from P k to line P i P j is less than 2d p . For example, two typical
configurations of the pebbles for current view factor computation are shown in
Fig. 5.115, (Fig. 5.115a for n = 3 and Fig. 5.115b for n = 8).
5.5.3.3 Function Approximation and Neural Network Model
The Artificial Neural Networks (ANNs) have been widely applied to function approximation by deep learning. From the universal approximation theorem, it is proven
that a feed-forward network (e.g., see Fig. 5.116) with one or more hidden layers is
capable of approximating the general multivariate continuous functions.