Algorithms and Applications - Japan

IBM Research is actively advancing the development of next-generation mathematical algorithms, based on the view that we are at the threshold of a transformative algorithmic era. Quantum computing and Artificial Intelligence are giving rise to new computational paradigms that fundamentally alter how algorithms are designed and deployed. Our research agenda concentrates on four foundational classes of computational mathematics: dynamical systems modeled through differential equations; optimization and combinatorial challenges; linear algebra and eigenvalue analysis; and probabilistic, statistical, and stochastic frameworks. Collectively, these areas form the foundation upon which the vast majority of real-world computational problems are built. At IBM Research Tokyo, we focus on the development of AI-based surrogate modeling techniques that enable significant gains in performance while dramatically improving the scalability of large and complex algorithmic workloads.

Combinatorial optimization has a long and rich history, yet its inherent computational intractability continues to limit its applicability to many real‑world industrial and scientific problems. We advance the state of the art by developing AI‑driven optimization methods capable of tackling problems that were previously infeasible, achieving unprecedented efficiency and scalability. We investigate foundational algorithmic principles, integrating supervised and reinforcement learning with discrete and continuous optimization techniques, and leveraging modern machine learning architectures including generative models. In parallel, we explore how emerging quantum computing technologies may further enhance optimization capabilities through hybrid classical–quantum approaches that exploit the complementary strengths of both paradigms. Together, these efforts aim to build next‑generation optimization frameworks capable of addressing challenges that remain beyond the reach of current methods.