—An adaptive time-stepping scheme in accordance with the local convergence of computation often involves computationally expensive procedures. As a result, many computer simulators have avoided utilizing such an adaptive scheme, while its advantages are well recognized; the scheme not only efficiently allocates computational resources, but also makes the results of the computation more reliable. In this paper, we propose a fast adaptive time-stepping scheme, ATLAS (Adaptive Time-step Learning and Adjusting Scheme), which approximates such an expensive yet beneficial scheme by using support vector machines (SVMs). We demonstrate that ATLAS performs quite favorably when compared with computations without it. ATLAS can incorporate existing solvers and other fast but unreliable adaptive schemes to meet the different criteria required in various applications.
—Adaptive time step control, machine learning, ordinary differential equations, severe accident analysis.
K. Kawaguchi, J. Ishikawa, and Y. Maruyama are with the Severe Accident Analysis Research Group, the Nuclear Risk Analysis Research Unit, Japan Atomic Energy Agency, 2-4 Shiragata-Shirane, Tokai-Mura, Ibaraki, Japan (e-mail: firstname.lastname@example.org).
Cite:Kenji Kawaguchi, Jun Ishikawa, and Yu Maruyama, "An Adaptive Time-Stepping Scheme with Local Convergence Verification Using Support Vector Machines," International Journal of Engineering and Technology vol. 6, no. 2, pp. 104-108, 2014.