Systems Aliasing in Dynamic Network Reconstruction: Issues on Low Sampling Frequencies

Network reconstruction of dynamical continuous-time (CT) systems is motivated by applications in many fields. Due to experimental limitations, especially in biology, data could be sampled at low frequencies, leading to significant challenges in network inference. We introduce the concept of "system aliasing" and characterize the minimal sampling frequency that allows reconstruction of CT systems from low sampled data. A test criterion is also proposed to check whether system aliasing is presented. With no system aliasing, the paper provides an algorithm to reconstruct dynamic network from data in the presence of noise. In addition, when there is system aliasing we perform studies that add additional prior information of the system such as sparsity. This paper opens new directions in modelling of network systems where samples have significant costs. Such tools are essential to process the available data in applications subject to current experimental limitations.