| Frequency principle: Fourier analysis sheds light on deep neural networks ZQJ Xu*, Y Zhang, T Luo, Y Xiao, Z Ma Communications in Computational Physics (2020), 2019 | 500 | 2019 |
| Training behavior of deep neural network in frequency domain ZQJ Xu*, Y Zhang, Y Xiao Neural Information Processing: 26th International Conference, ICONIP 2019 …, 2019 | 297 | 2019 |
| Multi-scale deep neural network (MscaleDNN) for solving Poisson-Boltzmann equation in complex domains Z Liu, W Cai, ZQJ Xu* Communications in Computational Physics, 2020 | 167* | 2020 |
| Understanding training and generalization in deep learning by fourier analysis ZJ Xu arXiv preprint arXiv:1808.04295, 2018 | 83 | 2018 |
| Theory of the frequency principle for general deep neural networks T Luo, Z Ma, ZQJ Xu, Y Zhang CSIAM Transactions on Applied Mathematics (Alphabetic order), 2019 | 79 | 2019 |
| Phase diagram for two-layer relu neural networks at infinite-width limit T Luo#, ZQJ Xu#, Z Ma, Y Zhang* The Journal of Machine Learning Research 22 (1), 3327-3373, 2021 | 62 | 2021 |
| A type of generalization error induced by initialization in deep neural networks Y Zhang, ZQJ Xu*, T Luo, Z Ma Mathematical and Scientific Machine Learning, 144-164, 2020 | 51 | 2020 |
| Overview frequency principle/spectral bias in deep learning ZQJ Xu*, Y Zhang, T Luo arXiv preprint arXiv:2201.07395, 2022 | 48 | 2022 |
| A multi-scale DNN algorithm for nonlinear elliptic equations with multiple scales XA Li, ZQJ Xu*, L Zhang Communications in Computational Physics (Alphabetic order), 2020 | 48 | 2020 |
| Causal and structural connectivity of pulse-coupled nonlinear networks D Zhou, Y Xiao, Y Zhang, Z Xu, D Cai Physical review letters 111 (5), 054102, 2013 | 48 | 2013 |
| A multi-scale sampling method for accurate and robust deep neural network to predict combustion chemical kinetics T Zhang*, Y Yi, Y Xu, ZX Chen, Y Zhang, W E, ZQJ Xu* arXiv preprint arXiv:2201.03549 (Combustion and Flame), 2022 | 47 | 2022 |
| Granger causality network reconstruction of conductance-based integrate-and-fire neuronal systems D Zhou, Y Xiao, Y Zhang, Z Xu, D Cai PloS one 9 (2), e87636, 2014 | 44 | 2014 |
| On the exact computation of linear frequency principle dynamics and its generalization T Luo, Z Ma, ZQJ Xu, Y Zhang arXiv preprint arXiv:2010.08153 (SIAM Journal on Mathematics of Data Science …, 2020 | 41* | 2020 |
| Deep frequency principle towards understanding why deeper learning is faster ZQJ Xu, H Zhou 2021 Proceedings of the AAAI Conference on Artificial Intelligence, 2020 | 35 | 2020 |
| MOD-Net: A machine learning approach via model-operator-data network for solving PDEs L Zhang, T Luo, Y Zhang, ZQJ Xu*, Z Ma* arXiv preprint arXiv:2107.03673 (Communications in Computational Physics), 2021 | 34 | 2021 |
| Embedding Principle of Loss Landscape of Deep Neural Networks Y Zhang*, Z Zhang, T Luo, ZQJ Xu* NeurIPS (spotlight) 2021, 2021 | 33 | 2021 |
| Embedding Principle: a hierarchical structure of loss landscape of deep neural networks Y Zhang*, Y Li, Z Zhang, T Luo, ZQJ Xu* arXiv preprint arXiv:2111.15527 (Journal of Machine Learning), 2021 | 27 | 2021 |
| Towards understanding the condensation of neural networks at initial training H Zhou, Q Zhou, T Luo, Y Zhang*, ZQ Xu* Advances in Neural Information Processing Systems 35, 2184-2196, 2022 | 23 | 2022 |
| A linear frequency principle model to understand the absence of overfitting in neural networks Y Zhang, T Luo, Z Ma, ZQJ Xu* Chinese Physics Letters 38 (3), 038701, 2021 | 22 | 2021 |
| Subspace decomposition based DNN algorithm for elliptic type multi-scale PDEs XA Li, ZQJ Xu, L Zhang* Journal of Computational Physics (Alphabetic order) 488, 112242, 2023 | 20 | 2023 |
Yaoyu ZhangShanghai Jiao Tong UniversityVerified email at sjtu.edu.cn