Papers › Solving a class of multi-scale elliptic PDEs by means of Fourier-based mixed physics...
Solving a class of multi-scale elliptic PDEs by means of Fourier-based mixed physics informed neural networks
Xi'an Li, Jinran Wu, You-Gan Wang, Xin Tai, Jianhua Xu
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Deep neural networks have garnered widespread attention due to their simplicity and flexibility in the fields of engineering and scientific calculation. In this study, we probe into solving a class of elliptic partial differential equations(PDEs) with multiple scales by utilizing Fourier-based mixed physics informed neural networks(dubbed FMPINN), its solver is configured as a multi-scale deep neural network. In contrast to the classical PINN method, a dual (flux) variable about the rough coefficient of PDEs is introduced to avoid the ill-condition of neural tangent kernel matrix caused by the oscillating coefficient of multi-scale PDEs. Therefore, apart from the physical conservation laws, the discrepancy between the auxiliary variables and the gradients of multi-scale coefficients is incorporated into the cost function, then obtaining a satisfactory solution of PDEs by minimizing the defined loss through some optimization methods. Additionally, a trigonometric activation function is introduced for FMPINN, which is suited for representing the derivatives of complex target functions. Handling the input data by Fourier feature mapping will effectively improve the capacity of deep neural networks to solve high-frequency problems. Finally, to validate the efficiency and robustness of the proposed FMPINN algorithm, we present several numerical examples of multi-scale problems in various dimensional Euclidean spaces. These examples cover both low-frequency and high-frequency oscillation cases, demonstrating the effectiveness of our approach. All code and data accompanying this manuscript will be made publicly available at \href{https://github.com/Blue-Giant/FMPINN}{https://github.com/Blue-Giant/FMPINN}.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections