Speaker
Description
Inverse uncertainty quantification (UQ) tasks, such as Bayesian parameter estimation, are computationally demanding when the forward model is a physics-based numerical solver. In particular, for PDE-governed systems, full-order discretizations (e.g., finite element or finite volume models) make conventional Markov chain Monte Carlo (MCMC) sampling prohibitively expensive due to the large number of forward evaluations required. Surrogate models can reduce this cost, but their effectiveness is often limited by the offline generation of high-fidelity training data. A natural remedy is to construct the surrogate online, i.e., concurrently with posterior sampling, so that training points concentrate in posterior-relevant regions.
We propose an adaptive delayed-acceptance MCMC method in which a Gaussian process (GP) regression surrogate provides a cheap first-stage approximation of the likelihood. The surrogate is refined sequentially during sampling, and its predictive uncertainty is used to decide when a high-fidelity model evaluation is required. The delayed-acceptance construction preserves the high-fidelity posterior as the invariant target distribution, while substantially reducing the number of expensive solver calls.
Numerical experiments on two benchmark inverse problems: (i) a mass-spring-damper system and (ii) an incompressible Navier-Stokes problem with variable geometry-demonstrate that the proposed strategy achieves accurate posterior estimates with markedly improved computational efficiency compared with standard single-stage MCMC and non-adaptive surrogate schemes.