Efficient Bayesian Parameter Inversion Facilitated by Multi-Fidelity Modeling
Keywords:
Bayesian parameter inversion, implicit particle filters, proper orthogonal decomposition mapping method, multifidelity modeling, surrogate modelingAbstract
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. We consider solving the equation with a coarsely-discretized finite difference scheme, of which the solutions are used as the low-fidelity solutions, and a Fourier spectral collocation method, which can provide high-fidelity solutions. The results demonstrate that the computational cost of characterizing the posterior distribution of viscosity is greatly reduced by utilizing the low-fidelity simulations, while the loss of accuracy is unnoticeable.
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