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Structure-Driven Methodology: An Emerging Cross-Domain Paradigm
| Title: | Structure-Driven Methodology: An Emerging Cross-Domain Paradigm |
|---|---|
| Authors: | Chen, Shengchang |
| Publication Year: | 2026 |
| Subject Terms: | History and Overview, Geophysics |
| Description: | 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.'' |
| Document Type: | Working Paper |
| DOI: | 10.48550/arXiv.2610.02698 |
| Access URL: | https://arxiv.org/abs/2610.02698 |
| Accession Number: | edsarx.2610.02698 |
| Database: | arXiv |
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