Solving Time-Fractional Partial Integro-Differential Equations Using Tensor Neural Network
Abstract
Abstract. In this paper, we propose a novel machine learning method based on the tensor neural network subspace to solve linear time-fractional subdiffusion/diffusion-wave equations and nonlinear time-fractional partial integro-differential equations. Within this framework, the trial function is formulated as the tensor neural network function multiplied by [Formula: see text] where the exponent [Formula: see text] is chosen according to the fractional-order operator. The Gauss–Jacobi quadrature is then employed to accurately evaluate the temporal Caputo derivative. Moreover, an alternating optimization strategy is adopted during the training process inspired by the concept of neural network subspace. Finally, several numerical examples are provided to validate the efficiency and accuracy of the proposed tensor neural network–based machine learning method.
Fields of Study & Subjects
Fractional Differential Equations Solutions
Tensor decomposition and applications
Numerical methods for differential equations
Publication details
- Journal / source
- SIAM Journal on Scientific Computing
- Publisher
- Society for Industrial & Applied Mathematics (SIAM)
- Volume
- 48
- Issue
- 1
- Pages
- C164–C189
- Publication date
- 13 February 2026
- Language
- EN