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A supervised learning algorithm for the inverse source problem of fractional wave equations | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 18 شهریور 1404 اصل مقاله (1.58 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.64556.2927 | ||
| نویسندگان | ||
| Abolfazl Tari Marzabad* 1؛ Abumoslem Mohammadi2 | ||
| 1Department of Mathematics, Shahed University, Tehran, Iran. | ||
| 2Department of Mathematics, Imam Ali University, Tehran, Iran. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Inverse problem؛ Support vector regression؛ Time-fractional PDEs؛ Model optimization | ||
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آمار تعداد مشاهده مقاله: 139 تعداد دریافت فایل اصل مقاله: 143 |
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