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RISModified Least Squares Method and a Review of Its Applications in Machine Learning and Fractional Differential/Integral Equations
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: Abstract. The least squares method provides the best-fit curve by minimizing the total squared error. In this work, we propose a modified least squares method based on fractional orthogonal polynomials that belong to the ...
A New Perspective for Scientific Modelling: Sparse Reconstruction-Based Approach for Learning Time-Space Fractional Differential Equations
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: This paper studies a sparse reconstruction-based approach to learn time–space fractional differential equations (FDEs), i.e., to identify parameter values and particularly the order of the fractional derivatives. The ...
High-Order Approximation to Caputo Derivative on Graded Mesh and Time-Fractional Diffusion Equation for Nonsmooth Solutions
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: In this paper, a high-order approximation to Caputo-type time-fractional diffusion equations (TFDEs) involving an initial-time singularity of the solution is proposed. At first, we employ a numerical algorithm based on the ...