Figure 1

Structures of functional networks. (a) Functional network consisting of two black-box nodes, represented by the functions $u(x_1)$ and $v(x_2)$, and a mechanistic model, exemplified by the function $y(x_1,x_2)=u(x_1)+v(x_2)$. u and v are the input-output functions of the respective nodes. The outputs u and v are input variables of the downstream nodes as well, indicating that a functional network represents a concatenation of functions. (b) Functional network consisting of three black-box nodes, represented by the functions $u(x_1,x_2)$, $v(x_3,x_4)$ and $w(u,v)$, depending on two input variables each.