反演成像技术在地球物理探测、生物医学成像、工业无损探伤等领域具有广泛应用。目前反演算法面临的挑战包括：难以兼顾精度与效率，对基于知识与经验的先验信息利用不充分等。近年来，机器学习技术迅速发展，有望改变传统的数据处理方式。探索基于机器学习的反演成像算法，对降低反演病态性，提高成像的精度和效率，拓展对测量数据的理解与认知，均具有十分重要的意义。本文重点研究融合物理规律与机器学习的反演算法，从学习模型更新方向、学习模型空间映射、学习反演逆函数三方面，分别提出了监督下降反演算法、深度学习约束的联合反演算法、融合物理的深度学习逆散射成像算法，文章主要内容与创新点总结如下:为提升反演的精度和效率，提出了监督下降反演算法。该算法通过线下训练的下降方向与线上计算的数据残差更新模型，具有较高的成像精度、速度与泛化能力。通过微波逆散射成像完成了算法的理论验证，并研究了基于监督下降法的瞬变电磁反演、大地电磁反演、地震波层析成像，相较于传统算法，成像精度显著提升，成像速度提高7倍以上，为深部矿产资源的准确、快速反演与解释提供了技术手段。为提高多学科地球物理数据反演与解释精度，提出了深度学习约束的地球物理联合反演算法，建立了联合反演目标函数，设计了电阻率—速度映射神经网络，完成了大地电磁—地震波初至时数据联合反演，相较于单独反演与传统联合反演，成像精度更高，且数据残差更低。 为探索高速、高精度、高泛化能力的正反演算法，提出了融合物理规律与深度学习的积分方程求解算法，设计了面积分方程与体积分方程神经网络求解器，前者平均数值误差低于6%，后者平均数值误差低于1%；提出了基于物理建模的深度学习逆散射成像算法，设计了微波逆散射成像神经网络，实现了非均匀介质目标的快速重建。仿真与实测数据反演表明，该网络能实现超分辨成像，成像速度比传统算法提升近百倍，且具备很高的泛化能力。
Inversion has wide applications in geophysical exploration, biomedical imaging, industrial non-destructive testing, etc. The challenges of existing inversion algorithms include difficulties in balancing accuracy and efficiency, and insufficient utilization of prior information from knowledge and experience. The recent development of machine learning has the potential of changing the ways of data processing. Studies on machine-learning-based inversion algorithms are important for reducing the ill-posedness of inverse problems, improving the accuracy and efficiency of imaging, and extending the understanding and cognition of measured data.This dissertation studies inversion algorithms that fuse physical laws and machine learning. In order to learn the model update directions, learn the map of model spaces, and learn the inverse function of reconstruction, this work proposes an inversion algorithm based on the supervised descent method, a joint inversion algorithm based on deep learning constraint, and a physics embedded deep learning algorithm for the inverse scattering problem, respectively. The main content and novelty are summarized as follows:To improve the accuracy and efficiency of data inversion, an inversion algorithm based on the supervised descent method is proposed. It updates the model through the offline trained descent direction and the online computed data residual, which possesses high accuracy, efficiency, and generalization ability. The algorithm is validated by solving the microwave inverse scattering problem. Then, the applications of the supervised descent method to transient electromagnetic inversion, magnetotelluric (MT) inversion, and seismic travel-time tomography are studied. Examples show that the method can reconstruct more accurate models and be 7 times faster than conventional methods, providing an effective approach for accurate and fast inversion and interpretation in deep mineral exploration. To improve the accuracy of multi-geophysical data inversion and interpretation, a joint inversion algorithm for geophysical data with deep learning constraint is proposed. The cost function of deep-learning based joint inversion is established. After training a neural network for resistivity-velocity transformation, the joint inversion of MT and seismic travel-time data is achieved. Compared with separate inversion and conventional joint inversion, this scheme can reconstruct models with higher accuracy meanwhile keeping lower data misfit.To develop fast forward modeling and inversion algorithm with good accuracy and generalization ability, a physics embedded deep learning algorithm for solving integral equations is proposed. Neural network solvers for both surface integral equation and volume integral equation are designed, and the mean computation error can be lower than 6% and 1%, respectively. A physics embedded deep learning algorithm for solving the inverse scattering problem is proposed, and the corresponding neural network is designed for microwave imaging to reconstruct inhomogeneous targets. The inversion of both synthetic and experimental data shows that the neural network can achieve super-resolution imaging and be 100 times faster than the conventional method. In addition, the designed network shows high generalization ability.
