Continuum Models and Discrete Systems

2025-01-30

Springer Proceedings in Mathematics & Statistics

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.

Technology Category

• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Computer Vision: Low Level & Physics-based Vision

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Problem

• Data Scarcity
• Machine Learning
• Annotation

Innovation

• Random Geometric Modeling
• Synthetic Data Generation
• Image Segmentation for Quality Control