pETNNs: Partial Evolutionary Tensor Neural Networks for Solving Time-dependent Partial Differential Equations
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915654684114944 |
|---|---|
| author | Kao, Tunan Zhang, He Zhang, Lei Zhao, Jin |
| author_facet | Kao, Tunan Zhang, He Zhang, Lei Zhao, Jin |
| contents | We present the partial evolutionary tensor neural networks (pETNNs), a novel framework for solving time-dependent partial differential equations with high accuracy and capable of handling high-dimensional problems. Our architecture incorporates tensor neural networks and evolutionary parametric approximation. A posterior error bounded is proposed to support the extrapolation capabilities. In the numerical implementations, we adopt a partial update strategy to achieve a significant reduction in computational cost while maintaining precision and robustness. Notably, as a low-rank approximation method of complex dynamical systems, pETNNs enhance the accuracy of evolutionary deep neural networks and empower computational abilities to address high-dimensional problems. Numerical experiments demonstrate the superior performance of the pETNNs in solving time-dependent complex equations, including the incompressible Navier-Stokes equations, high-dimensional heat equations, high-dimensional transport equations, and dispersive equations of higher-order derivatives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06084 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | pETNNs: Partial Evolutionary Tensor Neural Networks for Solving Time-dependent Partial Differential Equations Kao, Tunan Zhang, He Zhang, Lei Zhao, Jin Numerical Analysis Computational Physics 35Q30, 65M22, 68T07, 68W20 We present the partial evolutionary tensor neural networks (pETNNs), a novel framework for solving time-dependent partial differential equations with high accuracy and capable of handling high-dimensional problems. Our architecture incorporates tensor neural networks and evolutionary parametric approximation. A posterior error bounded is proposed to support the extrapolation capabilities. In the numerical implementations, we adopt a partial update strategy to achieve a significant reduction in computational cost while maintaining precision and robustness. Notably, as a low-rank approximation method of complex dynamical systems, pETNNs enhance the accuracy of evolutionary deep neural networks and empower computational abilities to address high-dimensional problems. Numerical experiments demonstrate the superior performance of the pETNNs in solving time-dependent complex equations, including the incompressible Navier-Stokes equations, high-dimensional heat equations, high-dimensional transport equations, and dispersive equations of higher-order derivatives. |
| title | pETNNs: Partial Evolutionary Tensor Neural Networks for Solving Time-dependent Partial Differential Equations |
| topic | Numerical Analysis Computational Physics 35Q30, 65M22, 68T07, 68W20 |
| url | https://arxiv.org/abs/2403.06084 |