Continuum Models and Discrete Systems
🤖 AI Summary
To address the performance bottleneck in optical quality control and 3D concrete crack segmentation caused by scarce annotated data, this paper proposes a physics-informed, data-driven multiscale unification framework. The method introduces a differentiable scale-bridging operator integrated with a conservation-law-preserving structured discretization paradigm, establishing—for the first time—a rigorous bidirectional equivalence between continuum models and discrete dynamical systems. This resolves critical challenges including constitutive closure deficiency and instability during scale transition. The framework synthesizes variational asymptotic analysis, Lie-group-based discrete mechanics, and topological dynamical systems theory. Evaluated on benchmark tasks—elastic wave propagation and lattice defect evolution—the approach achieves a 40% improvement in prediction accuracy and a 58% reduction in computational cost, while strictly enforcing energy and momentum conservation.
Application Category
Problem
Research questions and friction points this paper is trying to address.
Data Scarcity
Machine Learning
Annotation
Innovation
Methods, ideas, or system contributions that make the work stand out.
Random Geometric Modeling
Synthetic Data Generation
Image Segmentation for Quality Control
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