Figure 5

Reconstruction success rates as a fraction of nt for NW, WS, BA and ER networks to compare two methods. The networks size N is 100. The elements of matrix B are randomly selected as 0 or 1, and the sparsity of the controlled matrix B is 4 (namely \({\parallel {\bar{B}}^{T}\parallel }_{0}=4\)). The input vector u is the \(M\times P\)-dimensional standard Gaussian noise. These experiments select measurement data from the time \(t=350\), nt is the ratio between the row and the column of the measurement matrix (in the QR-CS method, \(nt=(P-N)/M\), \(N+1\le P\le 2.2N\), and in the CS method (where state matrix X is replaced by stochastic Gaussian matrix), \(nt=P/N\), \(1\le P\le 1.2N\)), and \(M=100\). The success rate is defined as the ratio between the simulation number of successful reconstruction \(\alpha \) and the simulation number \(\beta \). In these experiments, 20 simulations are performed, and the error of each simulation is \(\varepsilon < {10}^{-6}\). (a–d) For these four model networks, the average node sparsity is \(\langle k\rangle =20\). (e–h) \(\langle k\rangle =50\). (i–l) \(\langle k\rangle =100\).