Conference ID: 970-573-54154
PIN Code: 658801
In Bayesian inverse problems, surrogate models are often constructed to speed up the computational procedure, as the parameter-to-data map can be very expensive to evaluate. However, due to the curse of dimensionality and the nonlinear concentration of the posterior, traditional surrogate approaches are still not feasible for large scale problems. In this talk, we present an adaptive multi-fidelity surrogate modeling framework based on deep neural networks (DNN). More precisely, we first construct offline a DNN-based surrogate according to the prior distribution, and then, this prior-based surrogate will be adaptively refined online using only a few high-fidelity simulations. In particular, in the refine procedure, we construct a new shallow neural network that view the previous constructed surrogate as an input variable – yielding a composite multi-fidelity neural network approach. This makes the online computational procedure rather efficient. Numerical examples are presented to confirm that the proposed approach can obtain accurate posterior information with a limited number of forward simulations.