Statement of Retraction: Training an innovative physics-learned deep neural network by the Adam optimization method to simulate the responses of the hybrid multilayer system

Abstract

We, the Editors and Publisher of Waves in Random and Complex Media, have retracted the following article: Shengfeng Gan, Yishu Liu, Xinyu Ran & Xu Fang (2021) Training an innovative physics-learned deep neural network by the Adam optimization method to simulate the responses of the hybrid multilayer system, Waves in Random and Complex Media, DOI: https://doi.org/10.1080/17455030.2021.1936282 The article has significant overlap with the following articles: Liu, W., Deng, L., Cai, Z. et al. Impact of in-plane follower force on the frequency response of the hybrid angle-ply laminated system via dynamic simulation and generalized differential quadrature framework. Engineering with Computers (2021). https://doi.org/10.1007/s00366-020-01215-4. Chi, Z., Jiang, Z., Kamruzzaman, M.M. et al. Adaptive momentum-based optimization to train deep neural network for simulating the static stability of the composite structure. Engineering with Computers (2021). https://doi.org/10.1007/s00366-021-01335-5. Further to this, some authors have raised a dispute about the authorship list, however all listed authors agree to this retraction. We have been informed in our decision-making by our policy on publishing ethics and integrity and the COPE guidelines on retractions. The retracted article will remain online to maintain the scholarly record, but it will be digitally watermarked on each page as ‘Retracted’.