Multi-level Methods for the Advancement of Data Science

Mathematical and computational sciences form the backbone of modern data science, yet their theoretical underpinnings remain underdeveloped compared to the field’s rapid practical progress. While significant advancements have occurred in areas such as machine learning, artificial intelligence and computer-aided design, the mathematical frameworks that could unify and deepen these approaches are still emerging. Multi-level, multi-scale, and multi-layer mathematical methods have long been cornerstones in applied mathematics, providing robust analytical and algorithmic structures. However, their integration into data science, especially for developing interpretable and theoretically grounded models, requires further exploration. Recent studies in spline functions, multi-resolution analysis, and wavelet-based techniques reveal promising directions, but gaps remain in establishing coherent mathematical foundations that connect traditional computational methods with modern data-centric paradigms like deep learning.This Research Topic aims to promote the theoretical and computational development of multi-level methods to strengthen the foundations of data science. Its goal is to foster the exchange of ideas among mathematicians, computer scientists and data scientists, and encourage the creation of generalized frameworks that bridge theory and practice. Contributions are expected to address core mathematical questions relating to convergence, stability and expressivity of hierarchical models, while also demonstrating how these principles can advance deep learning architectures, data representation methods, and efficient computational schemes. By uniting diverse strands of applied mathematics and data-driven modeling, this Research Topic seeks to chart a path toward a more integrated and rigorous understanding of data science methodologies.To gather further insights into the structural and theoretical boundaries of data science through multi-level methods, we welcome articles addressing, but not limited to, the following themes: - Multi-level, multi-scale, and multi-layer mathematical modeling and analysis - Theoretical foundations of deep learning and hierarchical architectures - Applications of spline functions, wavelets, and multi-resolution analysis in data processing - Unified frameworks connecting computational mathematics and machine learning - Advances in algorithmic design for scalable data-driven computation - Applications of multi-level mathematics in engineering, physics, and computer-aided design - Hybrid approaches integrating theoretical models with empirical data science methods Topic editors: Charles K. Chui, Qingtang Jiang, Ding-Xuan Zhou Source: https://www.frontiersin.org/research-topics/85220/multi-level-methods-for-the-advancement-of-data-science