# Solving Time-Fractional Partial Integro-Differential Equations Using Tensor Neural Network

arXiv: https://arxiv.org/abs/2504.01440 · HTML: https://mlsanity.com/paper/2504.01440/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 48 references that are in the map.
- First posted on arXiv 2 Apr 2025.

## Builds on (most cited first, 7 of 7)

- [Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs](https://mlsanity.com/paper/2007.01138/) (2020)
- [Tackling the Curse of Dimensionality with Physics-Informed Neural Networks](https://mlsanity.com/paper/2307.12306/) (2023)
- [Monte Carlo PINNs: deep learning approach for forward and inverse problems involving high dimensional fractional partial differential equations](https://mlsanity.com/paper/2203.08501/) (2022)
- [GMC-PINNs: A new general Monte Carlo PINNs method for solving fractional partial differential equations on irregular domains](https://mlsanity.com/paper/2405.00217/) (2024)
- [Tackling the Curse of Dimensionality in Fractional and Tempered Fractional PDEs with Physics-Informed Neural Networks](https://mlsanity.com/paper/2406.11708/) (2024)
- [PMNN:Physical Model-driven Neural Network for solving time-fractional differential equations](https://mlsanity.com/paper/2310.04788/) (2023)
- [A Fractional Gauss-Jacobi quadrature rule for approximating fractional integrals and derivatives](https://mlsanity.com/paper/1704.05690/) (2017)

## Built on by (most cited first, 1 of 1)

- [fTNN: a tensor neural network for fractional PDEs](https://mlsanity.com/paper/2606.27140/) (2026)

## Abstract (arXiv)

In this paper, we propose a novel machine learning method based on adaptive tensor neural network subspace to solve linear time-fractional diffusion-wave equations and nonlinear time-fractional partial integro-differential equations. In this framework, the tensor neural network and Gauss-Jacobi quadrature are effectively combined to construct a universal numerical scheme for the temporal Caputo derivative with orders spanning  (0,1) and (1,2). Specifically, in order to effectively utilize Gauss-Jacobi quadrature to discretize Caputo derivatives, we design the tensor neural network function multiplied by the function tμ where the power μ is selected according to the parameters of the equations at hand. Finally, some numerical examples are provided to validate the efficiency and accuracy of the proposed tensor neural network based machine learning method.