Tomczak J M. Deep Generative Modeling. Springer International Publishing,2022
Murphy K P. Probabilistic Machine Learning: Advanced Topics. MIT Press,2023
Bishop C M,Bishop H. Deep Learning:Foundations and Concepts. Springer International Publishing,2024
Ackley D H,Hinton G E,Sejnowski T J. Cognitive Science,1985, 9(1):147
Nguyen H C,Zecchina R,Berg J. Advances in Physics,2017,66(3):197
Vincent P. Neural Computation,2011,23(7):1661
Song Y,Ermon S. Generative Modeling by Estimating Gradients of the Data Distribution. In: Wallach H et al (Ed.). Advances in Neural Information Processing Systems 32,2019
Kirkpatrick S,Gelatt C D,Vecchi M P. Science,1983,220(4598):671
Sohl-Dickstein J,Weiss E A,Maheswaranathan N et al. International Conference on Machine Learning,2015,37:2256
Vaswani A,Shazeer N,Parmar N et al. Advances in Neural Information Processing Systems,2017,30:6000
Wei J,Tay Y,Bommasani R et al. 2022,arXiv:2206.07682
Kaplan J et al. 2020,arXiv:2001.08361
Schaeffer R et al. 2023,arXiv:2304.15004
Papamakarios G et al. Journal of Machine Learning Research, 2021,22:1
Kingma D P,Dhariwal P. Advances in Neural Information Processing Systems,2018,32:10236
Li S H,Wang L. Phys. Rev. Lett.,2018,121:260601
Li S H,Dong C X,Zhang L F et al. Phys. Rev. X,2020,10: 021020
Chen R T Q,Rubanova Y,Bettencourt J et al. Advances in Neural Information Processing Systems,2018,32:6572
Zhang L F,Weinan E,Wang L. 2018,arXiv:1809.10188
Maoutsa D,Reich S,Opper M. Entropy,2020,22(8):802
Song Y,Sohl-Dickstein J,Kingma D P et al. 2020,arXiv: 2011.13456
Lipman Y,Chen R T Q,Ben-Hamu H et al. 2022,arXiv: 2210.02747
Liu X C,Gong C Y,Liu Q. 2022,arXiv:2209.03003
Albergo M S,Vanden-Eijnden E. 2022,arXiv:2209.15571
Zhao L,Wang L. Chin. Phys. Lett.,2023,40:120201
Gómez-Bombarelli R,Wei J N,Duvenaud D et al. ACS Central Science,2018,4(2):268
Cédric V. Topics in Optimal Transportation,vol. 58. American Mathematical Soc.,2016
训练数据的重要性. 2023,https://nonint.com/2023/06/10 /the-itin-ai-models-is-the-dataset/
Ingraham J B,Baranov M,Costello Z et al. Nature,2023,623: 1070
DALL.E.3,https://openai.com/index/dall-e-3
Madani A,Krause B,Greene E R et al. Nature Biotechnology, 2023,41:1099
Xie T,Fu X,Ganea O et al. 2021,arXiv:2110.06197
Jiao R,Huang W B,Lin P J et al. Advances in Neural Information Processing Systems,2024,36:11464
Zeni C,Pinsler R,Zügner D et al. 2023,arXiv:2312.03687
Flam-Shepherd D,Aspuru-Guzik A. 2023,arXiv:2305.05708
Antunes L M,Butler K T,Grau-Crespo R. 2023,arXiv: 2307.04340
Cao Z D,Luo X S,Lv J et al. 2024,arXiv:2403.15734
Merchant A,Batzner S,Schoenholz S S et al. Nature,2023,624: 80
Cheetham A K,Seshadri R. Chemistry of Materials,2024,36(8): 3490
Wu D,Wang L,Zhang P. Phys. Rev. Lett.,2019,122(8):080602
Xie H,Li Z H,Wang H et al. Phys. Rev. Lett.,2023,131(12): 126501
Xie H,Zhang L F,Wang L. SciPost Physics,2023,14:154
Feynman R P,Cohen M. Physical Review,1956,102:1189
He K M,Zhang X Y,Ren S Q et al. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition,2016. pp. 770—778