Patent ID: 7191161

Claim:
A method for constructing a composite response surface based on neural networks and selected functions, the method comprising providing a computer that is programmed: (1) to provide a set of h initial parameters that determine variation of provided data for a target variable, where each parameter corresponds to a coordinate in an h-dimensional parameter space G; (2) to decompose the h parameters into a first set of s simple parameters f i , numbered i=1, . . . , s, that may be used to describe the provided data with polynomials of total degree no greater than a selected number M s , and a second set of c complex parameters g j , numbered j=1, . . . , c, that may be used to describe the provided data using neural networks, and with s+c=h, where s, c and M s are selected positive integers; (3) to provide a simplex, having s+1 vertices, numbered k=1, . . . , s+1, and centered at a selected point in the space G; (4) to apply a neural network for each of the s+1 vertices, and to train each of the s+1 neural networks, using selected simulation data obtained by varying the parameters g j to generate a first sequence of network functions R k (g 1 , . . . , g c ); (5) to provide a second sequence of shape functions P k (f 1 , . . . , f s ) that satisfy the conditions P k (f 1 , . . . , f s )=1 at the vertex numbered k and P k (f 1 , . . . , f s )=0 at any vertex other than vertex number k, and ΣP k (f 1 , . . . , f s )=1 for all values of f 1 , . . . , f s ; and (6) to form a composite function CRS(f i , g j ) defined by CRS ⁢ { f i ⁢ g j } = ∑ k = 1 s + 1 ⁢ ⁢ P k ⁡ ( f 1 , … ⁢ , f s ) · R k ⁡ ( g 1 , … ⁢ , g c ) .