Thermoacoustic stability analysis is an essential part of the engine development process. Typically, thermoacoustic stability is determined by hybrid approaches such as network models or Helmholtz solvers. These approaches require information on the flame dynamic response. The combined approach of advanced System identification (SI) and Large Eddy Simulation (LES) is an efficient strategy to compute the flame dynamic response to flow perturbation in terms of the Finite Impulse Response (FIR). The identified FIR is uncertain due in part to the aleatoric uncertainties caused by applying SI on systems with combustion noise and partly due to epistemic uncertainties caused by lack of knowledge of operating or boundary conditions. Carrying out traditional uncertainty quantification techniques, such as Monte Carlo, in the framework of LES/SI would be computationally prohibitive. As a result, the present paper proposes a methodology to build a surrogate model in the presence of both aleatoric and epistemic uncertainties. More specifically, we propose a univariate Gaussian Process (GP) surrogate model, where the final trained GP takes into account the uncertainty of SI and the uncertainty in the combustor back plate temperature, which is known to have considerable impact on the flame dynamics. The GP model is trained on the FIRs obtained from the LES/SI of turbulent pre-mixed swirled combustor at different combustor back plate temperatures. Due to the change in the combustor back plate temperature the flame topology changes, which in turn influences the FIR. The trained GP model is successful in interpolating the FIR with confidence intervals covering the “true” FIR from LES/SI.