Monday, September 11 2017
10:00am - 11:00am
Computational Mathematics Colloquium
Computational Mathematics Colloquium: Bayesian inversion with implicit particle filters and reduced order modeling with application to a hydrological model

Bayesian inverse modeling techniques are computationally expensive because many forward simulations are needed when sampling the posterior distribution of the parameters. In this paper, we combine the implicit particle filtering method and generalized polynomial chaos expansion (gPCE) to significantly reduce the computational cost of performing Bayesian inverse modeling. The cost of constructing the gPCE-based surrogate model is further decreased by using sparse Bayesian learning to reduce the number of gPCE coefficients that have to be determined. We demonstrate the approach for a synthetic ponded infiltration experiment simulated with TOUGH2. The surrogate model is highly accurate with mean relative error that is <0.035% in predicting saturation and <0.25% in predicting the likelihood function. The posterior distribution of the parameters obtained using our proposed technique is nearly indistinguishable from the results obtained from either an implicit particle filtering method or a Markov chain Monte Carlo method utilizing the full model.
Speaker:Yaning Liu
Affiliation:Department of Mathematical and Statistical Science, University of Colorado Denver
Location:SCB 4113

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