where Ns,k(t) = k τs+k τs Ns,k 1(t)

Let'ssuppose that the formula holds fork up ton. A.5 AdditionalResult:ODE We list additional discovery and UQ results in this section. Figure 1 shows 4 distributions of the coefficients for Van der Pol system in red box and Lorenz 96 system in blue box. Figure 1 shows additional UQ result from the identified L96 systems without incorporating the data assimilation process. The truth trajectory is marked by red.