Adaptive neural network surrogate model for solving the nonlinear elastic inverse problem via Bayesian inference

In this paper, we consider a Bayesian method for nonlinear elastic inverse problems. As a working model, we are interested in the inverse problem of restoring elastic properties from measured tissue displacement. In order to reduce the computational cost, we will use the following multi-fidelity model approach. First, we construct a surrogate low-fidelity DNNs-based model in the prior distribution, then use a certain number of simulations of high fidelity model associated with an adaptive strategy online to update the low-fidelity model locally. Numerical examples show that the proposed method can solve nonlinear elastic inverse problems efficiently and accurately.