Abstract
The rapidly advancing fields of machine learning and mathematical modeling, greatly enhanced by the recent growth in artificial intelligence, are the focus of this special issue. This issue compiles extensively revised and improved versions of the top papers from the workshop on Mathematical Modeling and Problem Solving at PDPTA'23, the 29th International Conference on Parallel and Distributed Processing Techniques and Applications. Covering fundamental research in matrix operations and heuristic searches to real-world applications in computer vision and drug discovery, the issue underscores the crucial role of supercomputing and parallel and distributed computing infrastructure in research. Featuring nine key studies, this issue pushes forward computational technologies in mathematical modeling, refines techniques for analyzing images and time-series data, and introduces new methods in pharmaceutical and materials science, making significant contributions to these areas.
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1 Main
The field of machine learning and mathematical modeling is rapidly evolving, significantly impacting diverse research areas. The recent surge in artificial intelligence technologies has further accelerated this trend, highlighting the growing importance of “mathematical modeling and problem solving” in scientific endeavors [1]. Modeling natural phenomena and engineering systems not only deepens our understanding of fundamental principles but also drives the development of innovative technologies for effective control. These advancements have considerable implications for both industry and academia.
This special issue showcases the latest advancements in mathematical modeling and problem solving across various disciplines. The scope of topics is wide, encompassing everything from foundational research in new matrix operation methods, heuristic search, and constrained optimization techniques to practical research in computer vision, drug discovery, materials science, financial engineering, and mechanical processes.
A key aspect of contemporary mathematical modeling research is its integration with supercomputing, which involves extensive parallel and distributed computing. The sheer volume and augmented data often require rapid computational strategies. The infrastructure, including hardware and software, supporting parallel and distributed computing is thus vital for applied research. This issue includes a selection of research presented at the “Mathematical Modeling and Problem Solving” workshop during the 29th International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA’23). After a thorough selection process, nine significant studies were chosen as articles on this issue.
Four papers focus on computational technologies foundational to mathematical modeling. Chiyonobu and colleagues enhance the two-sided Jacobi method for singular value decomposition for complex matrices, previously effective only for real matrices [2]. They incorporate QR decomposition for complex matrix scenarios, offering two distinct implementations for both complex and real matrices. Zhong et al. introduce a novel hyper-heuristic algorithm, the evolutionary multi-mode slime mold optimization (EMSMO), inspired by slime mold behaviors [3]. This algorithm demonstrates superior performance in benchmarks and engineering problems, outperforming traditional evolutionary and hyper-heuristic algorithms. Zhang et al. unveil the meta-generative data augmentation optimization (MGDAO), a method that advances data augmentation in foundational machine learning for image and natural language processing [4]. This technique surpasses standard auto-augmentation methods in few-shot image and text classification benchmarks. Matsuzaki and colleagues propose a mixed-integer programming (MIP)-based method for scheduling machining operations in automated manufacturing, considering worker conditions [5]. They validate this method through computer experiments modeled on real-world machining tasks.
Two papers address applications involving image and time-series data, traditional targets of mathematical modeling. Ishikawa et al. enhance concrete crack detection by using strongly blurred images in training data, improving recognizer accuracy [6]. Takata et al. develop a method for recommending stock combinations by analyzing price change waveforms, showing potential for diversifying portfolios and minimizing risks [7].
Last but not least, three papers focus on pharmaceutical and materials science applications. Ueki and Ohue assess AlphaFold2 and binder hallucination techniques for improving antibody binding affinity, indicating a more efficient method than traditional experimental approaches [8]. Morikawa et al. introduce a machine learning method using graph kernels for predicting metal–organic frameworks (MOFs) combinations, demonstrating accurate MOF structure prediction without physical synthesis [9]. Furui and Ohue present an enhanced version of the lead optimization mapper (Lomap) algorithm for drug discovery [10]. This improved algorithm offers a faster approach to create free energy perturbation (FEP) graphs for numerous compounds, while maintaining the quality of the output.
In summary, this special issue represents a significant contribution to the fields of mathematical modeling and application, providing innovative methods to the community. As editors, we extend our gratitude to all researchers who contributed to this collection, paving the way for the next era of mathematical modeling and problem solving.
References
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This study was partially supported by JSPS KAKENHI (23H04887) (M.O.).
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Ohue, M., Sasayama, K. & Takata, M. Mathematical modeling and problem solving: from fundamentals to applications. J Supercomput 80, 14116–14119 (2024). https://doi.org/10.1007/s11227-024-06007-x
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DOI: https://doi.org/10.1007/s11227-024-06007-x