Version 1
: Received: 29 June 2022 / Approved: 30 June 2022 / Online: 30 June 2022 (04:25:56 CEST)
Version 2
: Received: 31 March 2023 / Approved: 3 April 2023 / Online: 3 April 2023 (03:29:13 CEST)
Chadha, C., He, J., Abueidda, D. et al. Improving the accuracy of the deep energy method. Acta Mech (2023). https://doi.org/10.1007/s00707-023-03691-3
Chadha, C., He, J., Abueidda, D. et al. Improving the accuracy of the deep energy method. Acta Mech (2023). https://doi.org/10.1007/s00707-023-03691-3
Chadha, C., He, J., Abueidda, D. et al. Improving the accuracy of the deep energy method. Acta Mech (2023). https://doi.org/10.1007/s00707-023-03691-3
Chadha, C., He, J., Abueidda, D. et al. Improving the accuracy of the deep energy method. Acta Mech (2023). https://doi.org/10.1007/s00707-023-03691-3
Abstract
The deep energy method (DEM), a type of physics-informed neural network, is evolving as an alternative to finite element analysis. This method employs the principle of minimum potential energy to predict deformations under static loading conditions. However, the model’s accuracy is contingent upon choosing the appropriate architecture for the model, which can be challenging due to the high interactions between hyperparameters, large search space, difficulty in identifying objective functions, and non-convex relationships with the objective functions. To improve DEM’s accuracy, we first introduce random Fourier feature (RFF) mapping. RFF mapping helps with the training of the model by reducing bias towards high frequencies. The effects of six hyperparameters are then studied under compression, tension, and bending loads in planar linear elasticity. Based on this study, a systematic automated hyperparameter optimization approach is proposed. Due to the high interaction between hyperparameters and the non-convex nature of the optimization problem, Bayesian optimization algorithms are used. The models trained using optimized hyperparameters and having Fourier feature mapping can accurately predict deflections compared to finite element analysis. Additionally, the deflections obtained for tension and compression load cases are more sensitive to variations in hyperparameters than bending.
Computer Science and Mathematics, Computational Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Received:
3 April 2023
Commenter:
Diab Abueidda
Commenter's Conflict of Interests:
Author
Comment:
We added the effect of Fourier feature mapping on the optimization process of hyperparameters. Additionally, we removed redundant or well-established knowledge in the field of physics-informed neural networks (PINNs). The discussion of the results is revised to reflect the latest updates in the field.
Commenter: Diab Abueidda
Commenter's Conflict of Interests: Author