An Adaptive Time-Stepping Scheme with Local Convergence Verification Using Support Vector Machines

Abstract

Abstract-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.Index Terms-Adaptive time step control, machine learning, ordinary differential equations, severe accident analysis.

An Unsupervised Approach for Extraction of Blood Vessels from Fundus Images

“…where ω, the weighting parameter, lies between 0 and 1. D(T) is the data term and R(T) is the regularization term and can be given as [42] D…”

“…If maximum iterations are not reached, then first, D(T) and R(T) are computed using Eqs. (2) and 3, then the cost function F is differentiated with respect to ω and equating it to 0 to obtained maximum; ω * is obtained which can be given as [42] Again, F is minimized using gradient descent technique for T keeping ω * for ω to be fixed and the process continued until the minimum solution is reached. The equation can be expressed as follows [43]:…”