N/A

We solved the multiple excited-state energies of Schrödinger equation by the neural network model on multi-GPU system. We considered two potentials, including simple harmonic oscillators and random potentials. A three-layer Inception block has been proposed as the training model for solving this problems, but the training time was excessively long on a single GPU. To address this problem, we employed TensorFlow's distributed training approach as MirroredStrategy, and leveraged multiple GPUs for computation. This enabled us to significantly reduce the required training time, with the use of four GPUs resulting in a 70% reduction in training time. Besides, we incorporated a Squeeze-and-Excitation Network (SE-Net) after the Inception block as an additional attention mechanism to enhance the precision of the model.

References
[1] https://www.tensorflow.org/guide/distributed_training.
[2] https://www.twcc.ai/.
[3] https://reurl.cc/M84ram.
[4] https://www.tensorflow.org/api_docs/python/tf/distribute/MirroredStrategy.
[5] S. Albawi, T. A. Mohammed, and S. Al-Zawi. Understanding of a convolutional neural network. In 2017 international conference on engineering and technology (ICET), pages 1–6. IEEE, 2017.
[6] D. Dongand, H. Wu, W. He, D. Yu, and H. Wang. Multi-task learning for multiple language translation. In Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference on Natural Language Processing (Volume 1: Long Papers), pages 1723–1732, 2015.
[7] A. Garcia-Garcia, S. Orts-Escolano, S. Oprea, V. Villena-Martinez, and J. Garcia-Rodriguez. A review on deep learning techniques applied to semantic segmentation. arXiv preprint arXiv:1704.06857, 2017.
[8] S. Grigorescu, B. Trasnea, T. Cocias, and G. Macesanu. A survey of
deep learning techniques for autonomous driving. Journal of Field Robotics, 37(3):362–386, 2020.
[9] J. Gu, Z. Wang, J. Kuen, L. Ma, A. Shahroudy, B. Shuai, T. Liu, X. Wang, G. Wang, J. Cai, et al. Recent advances in convolutional neural networks. Pattern recognition, 77:354–377, 2018.
[10] Y. Han, G. Huang, S. Song, L. Yang, H.Wang, and Y.Wang. Dynamic neural networks: A survey. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(11):7436–7456, 2021.
[11] R. M. Haralick, K. Shanmugam, and I. H. Dinstein. Textural features for image classification. IEEE Transactions on systems, man, and cybernetics, (6):610–621, 1973.
[12] J. Hu, L. Shen, and G. Sun. Squeeze-and-excitation networks. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7132–7141, 2018.
[13] S. Jeaugey. Nccl 2.0. In GPU Technology Conference (GTC), volume 2, 2017.
[14] Y. Kim, H. Choi, J. Lee, J. S. Kim, H. Jei, and H. Roh. Efficient largescale deep learning framework for heterogeneous multi-gpu cluster. In 2019 IEEE 4th International Workshops on Foundations and Applications of Self* Systems (FAS* W), pages 176–181. IEEE, 2019.
[15] S. Lawrence, C. L. Giles, A. C. Tsoi, and A. D. Back. Face recognition: A convolutional neural-network approach. IEEE transactions on neural networks, 8(1):98–113, 1997.
[16] Y. LeCun, Y. Bengio, and G. Hinton. Deep learning. nature, 521(7553):436–444, 2015.
[17] A. Li, X. Peng, Y. Yin, X. Liu, Q. Zhao, K. K¨orner, and W. Osten. Fringe projection based quantitative 3d microscopy. Optik, 124(21):5052–5056, 2013.
[18] T. I. Liu. Solving excited-state energies of Schrödinger equation via Inception deep convolutional neural network. 2022.
[19] D. Lu and Q. Weng. A survey of image classification methods and techniques for improving classification performance. International journal of Remote sensing, 28(5):823–870, 2007.
[20] K. Mills, M. Spanner, and I. Tamblyn. Deep learning and the Schrödinger equation. Physical Review A, 96(4):042113, 2017.
[21] V. Nair and G. E. Hinton. Rectified linear units improve restricted boltzmann machines. In Proceedings of the 27th international conference on machine learning (ICML-10), pages 807–814, 2010.
[22] M. Negnevitsky. Artificial intelligence: a guide to intelligent systems. Pearson education, 2005.
[23] Z. Niu, G. Zhong, and H. Yu. A review on the attention mechanism of deep learning. Neurocomputing, 452:48–62, 2021.
[24] O. M. Parkhi, A. Vedaldi, and A. Zisserman. Deep face recognition. 2015.
[25] S. J. Russell. Artificial intelligence a modern approach. Pearson Education, Inc., 2010.
[26] J. D. Schaffer, D. Whitley, and L. J. Eshelman. Combinations of genetic algorithms and neural networks: A survey of the state of the art. In [Proceedings] COGANN-92: International Workshop on Combinations of Genetic Algorithms and Neural Networks, pages 1–37. IEEE, 1992.
[27] C. Szegedy, S. Ioffe, V. Vanhoucke, and A. Alemi. Inception-v4, Inception- ResNet and the impact of residual connections on learning. In Proceedings of the AAAI conference on artificial intelligence, volume 31, 2017.
[28] C. Szegedy, V. Vanhoucke, S. Ioffe, J. Shlens, and Z. Wojna. Rethinking the Inception architecture for computer vision. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 2818–2826, 2016.
[29] S. Venugopalan, H. Xu, J. Donahue, M. Rohrbach, R. Mooney, and K. Saenko. Translating videos to natural language using deep recurrent neural networks. arXiv preprint arXiv:1412.4729, 2014.
[30] P. Wang, P. Chen, Y. Yuan, D. Liu, Z. Huang, X. Hou, and G. Cottrell. Understanding convolution for semantic segmentation. In 2018 IEEE winter conference on applications of computer vision (WACV), pages 1451–1460. IEEE, 2018.
[31] E. Yurtsever, J. Lambert, A. Carballo, and K. Takeda. A survey of autonomous driving: Common practices and emerging technologies. IEEE access, 8:58443–58469, 2020.
[32] W. Zhao, R. Chellappa, P. J. Phillips, and A. Rosenfeld. Face recognition: A literature survey. ACM computing surveys (CSUR), 35(4):399–458, 2003.
[33] Z. Q. Zhao, P. Zheng, S. T. Xu, and X. Wu. Object detection with deep learning: A review. IEEE transactions on neural networks and learning systems, 30(11):3212–3232, 2019.