  In applied sciences, we often deal with deterministic simulation models that
are too slow for simulation-intensive tasks such as calibration or real-time
control. In this paper, an emulator for a generic dynamic model, given by a
system of ordinary non-linear differential equations, is developed. The
non-linear differential equations are linearized and Gaussian white noise is
added to account for the non-linearities. The resulting linear stochastic
system is conditioned on a set of solutions of the non-linear equations that
have been calculated prior to the emulation. A path-integral approach is used
to derive the Gaussian distribution of the emulated solution. The solution
reveals that most of the computational burden can be shifted to the
conditioning phase of the emulator and the complexity of the actual emulation
step only scales like $\mathcal O(Nn)$ in multiplications of matrices of the
dimension of the state space. Here, $N$ is the number of time-points at which
the solution is to be emulated and $n$ the number of solutions the emulator is
conditioned on.
  The applicability of the algorithm is demonstrated with the hydrological
model logSPM.
