Hokkaido University

Institute for Chemical Reaction Design and Discovery

Research Outline

My research field is mathematical engineering, a mathematics to solve scientific and engineering problems. My main interest is in combinatorial optimization, which is to study algorithms to identify the best option among multiple discrete choices. I have also worked on numerical analysis for solving differential equations as well as applications of combinatoial optimization in machine learning and computer algebra systems. At ICReDD, I am working on mathematical approaches to kinetic simulations of large-scale chemical reaction pathway networks that is obtained by the AFIR method.

Representative Research Achievements

• Differentiating the yield of chemical reactions using parameters in first-order kinetic equations to identify elementary steps that control the reactivity from complicated reaction path networks, Y. Harabuchi, T. Yokoyama, W. Matsuoka, T. Oki, S. Iwata, and S. Maeda, J. Phys. Chem., 2024, 128(14):2883–2890. DOI: 10.1021/acs.jpca.4c00204

• Algebraic algorithms for fractional linear matroid parity via non-commutative rank. T. Oki and T. Soma. In Proc. of the 34th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA ’23), 2023, pp. 4188–4204. DOI: 10.1137/1.9781611977554.ch161

• Discrete-convex-analysis-based framework for warm-starting algorithms with predictions. S. Sakaue and T. Oki. In Advances in Neural Information Processing Systems 35 (NeurIPS ’22), 2022, pp. 20988–21000（no DOI）

• Improved structural methods for nonlinear differential-algebraic equations via combinatorial relaxation. T. Oki, IMA J. Numer. Anal., 2023, 43(1):357–386. DOI: 10.1093/imanum/drab094

• Index Reduction for Differential-Algebraic Equations with Mixed Matrices, S. Iwata, T. Oki, M. Takamatsu, J. ACM, 2019, 66(5), 1-34. DOI: 10.1145/3341499