发表机构
School of Earth Sciences, Zhejiang University（浙江大学地球科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出结构驱动方法论作为跨领域新范式，通过实例阐述其逻辑，并系统提出SDI（含MSDI和PSDI），强调其作为客观驱动范式的补充，带来效率与认知的双重提升。
AI 中文摘要
本文提出并阐述了结构驱动方法论作为一种新兴的跨领域范式。与主导逆问题求解逾两个世纪的客观驱动范式相反，结构驱动方法论主张识别并利用问题的内在结构来直接构建求解方法，而非通过迭代搜索逼近解。文章以Liouville变体Goldbach猜想、三维Kakeya猜想、Noether定理以及作者近四十年的地球物理反演实践为例，阐述了数论、纯数学、物理学和地震成像中结构驱动思维的共同逻辑。作者还系统性地提出了结构驱动反演（SDI）范式，包括数学结构驱动反演（MSDI）和物理结构驱动反演（PSDI）。结构驱动方法论并不否定客观驱动方法论，而是对其补充：客观驱动是一种通用搜索策略，而结构驱动是一种定制直接策略。文章总结认为，这一转变的意义不仅在于效率提升，更在于认知深化——面对复杂问题时，首要问题不再是“如何更快地解决问题”，而是“问题的结构是什么”。
英文摘要
This article proposes and articulates structure-driven methodology as an emerging cross-domain paradigm. In contrast to the objective-driven paradigm that has dominated inverse-problem solving for over two centuries, structure-driven methodology advocates identifying and exploiting the intrinsic structure of a problem to construct the solution method directly, rather than approaching the solution through iterative search. Drawing on examples from the Liouville-variant Goldbach conjecture, the three-dimensional Kakeya conjecture, Noether's theorem, and the author's nearly four decades of geophysical inversion practice, the article illustrates the common logic of structure-driven thinking in number theory, pure mathematics, physics, and seismic imaging. The author also systematically proposes the Structure-Driven Inversion (SDI) paradigm, comprising Mathematical Structure-Driven Inversion (MSDI) and Physical Structure-Driven Inversion (PSDI). Structure-driven methodology does not negate objective-driven methodology but complements it: objective-driven is a general search strategy, whereas structure-driven is a custom direct strategy. The article concludes that the significance of this shift lies not only in efficiency gains but also in cognitive deepening---when facing complex problems, the first question is no longer ``how to solve the problem faster'' but ``what is the structure of the problem.''
