Efficient Bi-Fidelity Gradient-Based Method For Non-Linear Inverse Problems

Solving a non-linear and high-dimensional inverse problem is challenging in computational science and engineering. Sampling-based methods require a large number of model evaluations; gradient-based methods require fewer model evaluations but only find local minima. Multifidelity optimization combines the low-fidelity model and the high-fidelity model to achieve both high accuracy and efficiency. In this paper, we present a bi-fidelity approach to solving non-linear inverse problems. In the bi-fidelity inversion method, the low-fidelity model is used to acquire a good initial guess, and the high-fidelity model is used to locate the global minimum. Combined with a multi-start optimization scheme, the proposed approach significantly increases the possibility of finding the global minimum for nonlinear inverse problems with many local minima. The method is applied to the inversion of electromagnetic well logging data, which is difficult to solve using traditional gradient-based methods. The bi-fidelity method provides promising inversion results and can be easily applied to traditional gradient-based methods.