  We give an approximate solution to the difficult inverse problem of inferring
the topology of an unknown network from given time-dependent signals at the
nodes. For example, we measure signals from individual neurons in the brain,
and infer how they are inter-connected. We use Maximum Caliber as an inference
principle. The combinatorial challenge of high-dimensional data is handled
using two different approximations to the pairwise couplings. We show two
proofs of principle: in a nonlinear genetic toggle switch circuit, and in a toy
neural network.
