Inverse problems for partial differential equations play an important role in a wide range of scientific disciplines and enable us to recover crucial information about underlying physical processes. In this paper, we present a machine-learning algorithm for solving inverse source problems of time fractional wave equations using support vector regression with polynomial kernels. This innovative approach leverages the power of machine-learning to estimate elusive source parameters, providing a highly accurate and efficient solution. By combining the principles of support vector regression and polynomial kernels, our method offers a promising alternative to traditional numerical techniques, achieving remarkable results while maintaining computational efficiency. Through comprehensive experiments and comparisons, we demonstrate the superior performance and potential of our approach in addressing inverse source problems of time fractional wave equations in linear and nonlinear cases.
Tari Marzabad, A. and Mohammadi, A. (2025). A supervised learning algorithm for the inverse source problem of fractional wave equations. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2025.64556.2927
MLA
Tari Marzabad, A. , and Mohammadi, A. . "A supervised learning algorithm for the inverse source problem of fractional wave equations", Computational Methods for Differential Equations, , , 2025, -. doi: 10.22034/cmde.2025.64556.2927
HARVARD
Tari Marzabad, A., Mohammadi, A. (2025). 'A supervised learning algorithm for the inverse source problem of fractional wave equations', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2025.64556.2927
CHICAGO
A. Tari Marzabad and A. Mohammadi, "A supervised learning algorithm for the inverse source problem of fractional wave equations," Computational Methods for Differential Equations, (2025): -, doi: 10.22034/cmde.2025.64556.2927
VANCOUVER
Tari Marzabad, A., Mohammadi, A. A supervised learning algorithm for the inverse source problem of fractional wave equations. Computational Methods for Differential Equations, 2025; (): -. doi: 10.22034/cmde.2025.64556.2927
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