Bifidelity Gradient-Based Approach for Nonlinear Well-Logging Inverse Problems

Solving a nonlinear 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 the local minima. Multifidelity optimization combines the low-fidelity model and the high-fidelity model to achieve both high accuracy and high efficiency. In this article, we present a bifidelity approach to solve nonlinear inverse problems. In the bifidelity 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 multistart 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 tested with two toy problems and then applied to an electromagnetic well-logging inverse problem, which is difficult to solve using traditional gradient-based methods. The bifidelity method provides promising inversion results and can be easily applied to traditional gradient-based methods.