HiDeNN-PGD: reduced-order hierarchical deep learning neural networks
This work addresses the need for fast and accurate simulations in large-scale engineering problems, representing an incremental improvement by integrating existing HiDeNN and PGD techniques.
The paper tackles the challenge of achieving high accuracy with reduced computational cost in engineering simulations by proposing HiDeNN-PGD, a reduced-order model combining hierarchical deep learning neural networks and proper generalized decomposition, which uses orders of magnitude fewer degrees of freedom than finite element methods while maintaining accuracy.
This paper presents a proper generalized decomposition (PGD) based reduced-order model of hierarchical deep-learning neural networks (HiDeNN). The proposed HiDeNN-PGD method keeps both advantages of HiDeNN and PGD methods. The automatic mesh adaptivity makes the HiDeNN-PGD more accurate than the finite element method (FEM) and conventional PGD, using a fraction of the FEM degrees of freedom. The accuracy and convergence of the method have been studied theoretically and numerically, with a comparison to different methods, including FEM, PGD, HiDeNN and Deep Neural Networks. In addition, we theoretically showed that the PGD converges to FEM at increasing modes, and the PGD error is a direct sum of the FEM error and the mode reduction error. The proposed HiDeNN-PGD performs high accuracy with orders of magnitude fewer degrees of freedom, which shows a high potential to achieve fast computations with a high level of accuracy for large-size engineering problems.