TY - JOUR
T1 - An Adaptive Surrogate Modeling Based on Deep Neural Networks for Large-Scale Bayesian Inverse Problems
AU - Yan , Liang
AU - Zhou , Tao
JO - Communications in Computational Physics
VL - 5
SP - 2180
EP - 2205
PY - 2020
DA - 2020/11
SN - 28
DO - http://doi.org/10.4208/cicp.OA-2020-0186
UR - https://global-sci.org/intro/article_detail/cicp/18409.html
KW - Bayesian inverse problems, deep neural networks, multi-fidelity surrogate modeling,
Markov chain Monte Carlo.
AB - <p style="text-align: justify;">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 (such us the
polynomial-based surrogates) are still not feasible for large scale problems. To this
end, we present in this work an adaptive multi-fidelity surrogate modeling framework based on deep neural networks (DNNs), motivated by the facts that the DNNs
can potentially handle functions with limited regularity and are powerful tools for
high dimensional approximations. More precisely, we first construct offline a DNN-based surrogate according to the prior distribution, and then, this prior-based DNN-surrogate will be adaptively &amp; locally refined online using only a few high-fidelity
simulations. In particular, in the refine procedure, we construct a new shallow neural
network that views 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.</p>