A Physics Based Surrogate Model in Bayesian Uncertainty Quantification involving Elliptic PDEs
arxiv(2023)
摘要
The paper addresses Bayesian inferences in inverse problems with uncertainty
quantification involving a computationally expensive forward map associated
with solving a partial differential equations. To mitigate the computational
cost, the paper proposes a new surrogate model informed by the physics of the
problem, specifically when the forward map involves solving a linear elliptic
partial differential equation. The study establishes the consistency of the
posterior distribution for this surrogate model and demonstrates its
effectiveness through numerical examples with synthetic data. The results
indicate a substantial improvement in computational speed, reducing the
processing time from several months with the exact forward map to a few
minutes, while maintaining negligible loss of accuracy in the posterior
distribution.
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