Accurate and efficient Bayesian parameter inversion based on low-fidelity model solutions

We propose an efficient Bayesian parameter inversion technique that utilizes the implicit particle filter to characterize the posterior distribution, and a multi-scale surrogate modeling method called the proper orthogonal decomposition mapping method to provide high-fidelity solutions to the forward model by conducting only low-fidelity simulations. The proposed method is applied to the nonlinear Burgers equation, widely used to model electromagnetic waves, with stochastic viscosity and periodic solutions.