Machine learning, and specifically deep-learning (DL) techniques applied to geophysical inverse problems, is an attractive subject, which has promising potential and, at the same time, presents some challenges in practical implementation. Some obstacles relate to scarce knowledge of the searched geologic structures, a problem that can limit the interpretability and generalizability of the trained DL networks when applied to independent scenarios in real applications. Commonly used (physics-driven) least-squares optimization methods are very efficient local optimization techniques but require good starting models close to the correct solution to avoid local minima. We have developed a hybrid workflow that combines both approaches in a coupled physics-driven/DL inversion scheme. We exploit the benefits and characteristics of both inversion techniques to converge to solutions that typically outperform individual inversion results and bring the solution closer to the global minimum of a nonconvex inverse problem. The completely data-driven and self-feeding procedure relies on a coupling mechanism between the two inversion schemes taking the form of penalty functions applied to the model term. Predictions from the DL network are used to constrain the least-squares inversion, whereas the feedback loop from inversion to the DL scheme consists of the network retraining with partial results obtained from inversion. The self-feeding process tends to converge to a common agreeable solution, which is the result of two independent schemes with different mathematical formalisms and different objective functions on the data and model misfit. We determine that the hybrid procedure is converging to robust and high-resolution resistivity models when applied to the inversion of the synthetic and field transient electromagnetic data. Finally, we speculate that the procedure may be adopted to recast the way we solve inverse problems in several different disciplines.

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物理驱动的深度学习反演及其在瞬变电磁学中的应用

机器学习，特别是应用于地球物理逆问题的深度学习（DL）技术，是一个有吸引力的主题，它具有广阔的发展前景，同时在实际实施中也带来了一些挑战。一些障碍与对搜索到的地质结构缺乏了解有关，当在实际应用中将其应用于独立方案时，该问题可能会限制受过训练的DL网络的可解释性和可概括性。常用的（物理驱动）最小二乘法优化方法是非常有效的局部优化技术，但需要接近正确解决方案的良好启动模型来避免局部最小值。我们已经开发了一种混合工作流程，将两种方法结合在一起，采用了物理驱动/ DL反演方案。我们利用两种反演技术的优势和特点，收敛到通常优于单个反演结果的解决方案，并使解决方案更接近于非凸反问题的全局最小值。完全由数据驱动和自我馈送的过程依赖于两种反演方案之间的耦合机制，采取适用于模型项的惩罚函数的形式。来自DL网络的预测被用来约束最小二乘反演，而从反演到DL方案的反馈回路包括网络再训练以及从反演获得的部分结果。自给过程趋向于收敛到一个通用的解决方案，这是两个独立的方案的结果，这两个方案在数据和模型失配方面具有不同的数学形式和不同的目标函数。当将其应用于合成和现场瞬变电磁数据的反演时，我们确定混合程序正在收敛到鲁棒且高分辨率的电阻率模型。最后，我们推测可以采用该程序来重塑我们解决几种不同学科中的逆问题的方式。