背景知识：
唯象重整化群和拉普拉斯重整化群
不可分解高阶相互作用
单纯形路径积分
单纯形重整化群
Cheng, A., Xu, Y., Sun, P., & Tian, Y. (2024). Simplex path integral and simplex renormalization group for high-order interactions. arXiv preprint arXiv:2305.01895. Accepted by Reports on Progress in Physics
Lucas M, Cencetti G, Battiston F. Multiorder Laplacian for synchronization in higher-order networks[J]. Physical Review Research, 2020, 2(3): 033410.
Villegas P, Gili T, Caldarelli G, et al. Laplacian renormalization group for heterogeneous networks[J]. Nature Physics, 2023, 19(3): 445-450.
Bradde S, Bialek W. Pca meets rg[J]. Journal of statistical physics, 2017, 167: 462-475.
AI for PDE和算子学习概述
Koopman理论入门
Xiong, W., Huang, X., Zhang, Z., Deng, R., Sun, P., & Tian, Y. (2024). Koopman neural operator as a mesh-free solver of non-linear partial differential equations. Journal of Computational Physics, 113194.
Xiong, W., Ma, M., Huang, X., Zhang, Z., Sun, P., & Tian, Y. (2023). Koopmanlab: machine learning for solving complex physics equations. APL Machine Learning, 1(3).
Kovachki, N., Li, Z., Liu, B., Azizzadenesheli, K., Bhattacharya, K., Stuart, A., & Anandkumar, A. (2023). Neural operator: Learning maps between function spaces with applications to pdes. Journal of Machine Learning Research, 24(89), 1-97.
Li, Z., Kovachki, N., Azizzadenesheli, K., Liu, B., Bhattacharya, K., Stuart, A., & Anandkumar, A. (2020). Fourier neural operator for parametric partial differential equations. arXiv preprint arXiv:2010.08895.
Lu, L., Jin, P., Pang, G., Zhang, Z., & Karniadakis, G. E. (2021). Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators. Nature machine intelligence, 3(3), 218-229.
Brunton, S. L., Budišić, M., Kaiser, E., & Kutz, J. N. (2021). Modern Koopman theory for dynamical systems. arXiv preprint arXiv:2102.12086.
斑图链接：https://pattern.swarma.org/study_group/45?from=wechat
大模型、多模态、多智能体层出不穷，各种各样的神经网络变体在AI大舞台各显身手。复杂系统领域对于涌现、层级、鲁棒性、非线性、演化等问题的探索也在持续推进。而优秀的AI系统、创新性的神经网络，往往在一定程度上具备优秀复杂系统的特征。因此，发展中的复杂系统理论方法如何指导未来AI的设计，正在成为备受关注的问题。
集智俱乐部联合加利福尼亚大学圣迭戈分校助理教授尤亦庄、北京师范大学副教授刘宇、北京师范大学系统科学学院在读博士张章、牟牧云和在读硕士杨明哲、清华大学在读博士田洋共同发起「AI By Complexity」读书会，探究如何度量复杂系统的“好坏”？如何理解复杂系统的机制？这些理解是否可以启发我们设计更好的AI模型？在本质上帮助我们设计更好的AI系统。读书会于6月10日开始，每周一晚上20:00-22:00举办。欢迎从事相关领域研究、对AI+Complexity感兴趣的朋友们报名读书会交流！
