Su, Zijie, Ren, Mengke, Liu, Yunpu, Pan, Sheng, Li, Zheng et Shen, Changyu.
2025.
« Finite volume neural network (FVNN) with reduced derivative order for incompressible flows ».
In Proceedings of the CSME-CFDSC-CSR 2025 International Congress (Montreal, QC, Canada, May 25-28, 2025)
Coll. « Progress in Canadian Mechanical Engineering », vol. 8.
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Résumé
Physics-Informed Neural Networks (PINN) have emerged as a powerful tool for solving partial differential equations (PDEs) and have been extensively applied in various fields such as energy, environment, and engineering. Typically, PINNs utilize Automatic Differentiation (AD) to compute the residuals of governing equations, which may lead to precision loss. Although recent studies have attempted to integrate traditional numerical methods with PINNs, these approaches are mostly data-driven and remain dependent on traditional numerical solvers for generating training data. In contrast, this paper proposes a purely physics-driven Finite Volume Neural Network (FVNN) method, completely independent of conventional numerical solvers, specifically designed to solve steady-state incompressible flow problems. Inspired by the Finite Volume Method, the FVNN approach divides the solution domain into multiple grids and employs Gauss's theorem to evaluate the residuals of the Navier-Stokes equations at Gaussian integral points located on grid boundaries, rather than at collocation points within the grids as in traditional PINNs. The loss function is constructed using the Gaussian integral approach, effectively reducing the order of derivatives required for velocity calculations. To validate the effectiveness of the proposed method, we predict velocity and pressure fields for two representative examples in fluid topology optimization. Results are compared against both commercial software and traditional PINNs. Numerical cases demonstrate that the FVNN significantly improves the accuracy of velocity and pressure field predictions while accelerating the network's training speed compared to traditional PINNs.
| Type de document: | Compte rendu de conférence |
|---|---|
| Éditeurs: | Éditeurs ORCID Hof, Lucas A. NON SPÉCIFIÉ Di Labbio, Giuseppe NON SPÉCIFIÉ Tahan, Antoine NON SPÉCIFIÉ Sanjosé, Marlène NON SPÉCIFIÉ Lalonde, Sébastien NON SPÉCIFIÉ Demarquette, Nicole R. NON SPÉCIFIÉ |
| Date de dépôt: | 18 déc. 2025 15:33 |
| Dernière modification: | 18 déc. 2025 15:33 |
| URI: | https://espace2.etsmtl.ca/id/eprint/32509 |
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