Document Type : Research Article

**Authors**

Department of Mathematics, Shahed University, Tehran, Iran.

10.22067/ijnao.2024.86883.1392

**Abstract**

The inverse problems in various fields of applied sciences and industrial design are concerned with the estimation of parameters that cannot be directly measured. In this work, we present a novel numerical approach for addressing the fractional inverse source problem by a machine learning algorithm and considering the ideas behind the spectral methods. The introduced algorithm utilizes a space-time Galerkin type of least-squares support vector regression to approximate the unknown source in a finitedimensional space, providing a stable and efficient solution. With the proposed machine learning method, we overcome the limitations of classical numerical methods and offer a promising alternative for tackling inverse source problems while avoiding overfitting by carefully selecting regularization parameters. To validate the effectiveness of our approach and illustrate an exponential convergence, we present some test problems along with the corresponding numerical results. The proposed method’s superior accuracy compared to the existing methods is also illustrated.

**Keywords**

- Machine learning
- Support vector machines
- Inverse Source problem
- Time fractional wave equation
- Space-time Galerkin

**Main Subjects**

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