{"id":52603,"date":"2024-09-10T11:31:03","date_gmt":"2024-09-10T03:31:03","guid":{"rendered":"https:\/\/swarma.org\/?p=52603"},"modified":"2024-09-10T11:31:03","modified_gmt":"2024-09-10T03:31:03","slug":"%e6%95%b0%e6%8d%ae%e9%a9%b1%e5%8a%a8%e7%9a%84%e5%a4%8d%e6%9d%82%e7%b3%bb%e7%bb%9f%e8%87%aa%e5%8a%a8%e5%bb%ba%e6%a8%a1%e4%b8%8e%e8%b0%83%e6%8e%a7%ef%bd%9c%e5%a4%8d%e6%9d%82%e7%b3%bb%e7%bb%9f%e8%87%aa","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=52603","title":{"rendered":"\u6570\u636e\u9a71\u52a8\u7684\u590d\u6742\u7cfb\u7edf\u81ea\u52a8\u5efa\u6a21\u4e0e\u8c03\u63a7\uff5c\u590d\u6742\u7cfb\u7edf\u81ea\u52a8\u5efa\u6a21\u8bfb\u4e66\u4f1a\u7b2c\u4e8c\u5b63\u7b2c\u4e8c\u671f"},"content":{"rendered":"
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Part 2 \u57fa\u4e8e\u673a\u5668\u5b66\u4e60\u7684\u590d\u6742\u7cfb\u7edf\u8c03\u63a7<\/span><\/strong><\/span><\/h3>\n
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Part 2 \u57fa\u4e8e\u673a\u5668\u5b66\u4e60\u7684\u590d\u6742\u7cfb\u7edf\u8c03\u63a7<\/span><\/strong><\/span><\/h3>\n
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Part 1 \u6570\u636e\u9a71\u52a8\u7684\u590d\u6742\u7cfb\u7edf\u81ea\u52a8\u5efa\u6a21<\/span><\/strong><\/span><\/h3>\n
\u50a8\u5907\u6c60\u8ba1\u7b97\uff08Reservoir computing\uff09<\/span><\/section>\n
\u795e\u7ecf\u5e38\u5fae\u5206\u65b9\u7a0b\uff08Neural ODE\uff09<\/span><\/section>\n
\u795e\u7ecf\u7b97\u5b50\uff08Neural operator\uff09<\/span><\/section>\n


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Part 2 \u57fa\u4e8e\u673a\u5668\u5b66\u4e60\u7684\u590d\u6742\u7cfb\u7edf\u8c03\u63a7<\/span><\/strong><\/span><\/h3>\n
\u968f\u673a\u52a8\u529b\u7cfb\u7edf\uff08Random dynamical systems\uff09<\/span><\/section>\n
\u6027\u80fd\u4fdd\u8bc1\uff08Performance guarantee\uff09<\/span><\/section>\n
\u540c\u6b65\uff08Synchronization\uff09<\/span><\/section>\n


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\u674e\u946b<\/strong>\uff0c\u56fd\u9632\u79d1\u6280\u5927\u5b66\u7406\u5b66\u9662\u7cfb\u7edf\u79d1\u5b66\u4e13\u4e1a\u535a\u58eb\u7814\u7a76\u751f\uff0c\u4e3b\u8981\u7814\u7a76\u65b9\u5411\u4e3a\u673a\u5668\u5b66\u4e60\u4e0e\u590d\u6742\u7cfb\u7edf\uff0c\u590d\u6742\u7f51\u7edc\u4e0e\u5927\u6570\u636e\uff0c\u4e3b\u8981\u5305\u62ec\u590d\u6742\u52a8\u529b\u7cfb\u7edf\u7684\u81ea\u52a8\u5efa\u6a21\u3001\u9884\u6d4b\u3001\u53d8\u70b9\u68c0\u6d4b\u3001\u4ee5\u53ca\u4e34\u754c\u9884\u6d4b\u7b49\u3002\u4ee5\u7b2c\u4e00\u4f5c\u8005\u5728Nature Communications, ICML, Research, Chaos\u7b49\u56fd\u9645\u671f\u520a\u3001\u4f1a\u8bae\u4e0a\u53d1\u8868\u591a\u7bc7\u6587\u7ae0\u3002<\/span><\/section>\n

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\u5f20\u9759\u4e1c<\/strong>\uff0c\u590d\u65e6\u5927\u5b66\u6570\u5b66\u79d1\u5b66\u5b66\u9662\u535a\u58eb\u751f\uff0c\u5e08\u4ece\u6797\u4f1f\u6559\u6388\uff0c\u73b0\u8bbf\u95ee\u963f\u4f2f\u4e01\u5927\u5b66\uff0c\u5bfc\u5e08\u4e3aCelso Grebogi\u6559\u6388\u30022020\u5e74\u5728\u590d\u65e6\u5927\u5b66\u83b7\u5f97\u6570\u5b66\u5b66\u58eb\u5b66\u4f4d\u3002\u7814\u7a76\u5174\u8da3\u4e3a\u590d\u6742\u7cfb\u7edf\u7684\u91cd\u6784\u548c\u8c03\u63a7\uff0c\u5305\u62ec\u968f\u673a\u7cfb\u7edf\u7684\u63a7\u5236\u7406\u8bba\uff0c\u57fa\u4e8e\u673a\u5668\u5b66\u4e60\u7684\u63a7\u5236\u65b9\u6cd5\uff0c\u6570\u7406\u77e5\u8bc6\u5d4c\u5165\u5f0f\u673a\u5668\u5b66\u4e60\u3002\u4ee5\u7b2c\u4e00\u4f5c\u8005\u5728NeurIPS\uff0cICLR\uff0cICML\u7b49\u56fd\u9645\u4f1a\u8bae\u548cPRR,PRE\u7b49\u56fd\u9645\u671f\u520a\u4e0a\u53d1\u8868\u591a\u7bc7\u6587\u7ae0\u3002<\/span><\/section>\n
\u4e2a\u4eba\u4e3b\u9875\uff1ahttps:\/\/www.researchgate.net\/profile\/Jingdong-Zhang-10<\/span><\/section>\n


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Part 1 \u6570\u636e\u9a71\u52a8\u7684\u590d\u6742\u7cfb\u7edf\u81ea\u52a8\u5efa\u6a21<\/span><\/strong><\/span><\/h3>\n

Tang Y, Kurths J, Lin W, et al. Introduction to focus issue: When machine  learning meets complex systems: Networks, chaos, and nonlinear dynamics [J]. Chaos:  An Interdisciplinary Journal of Nonlinear Science, 2020, 30 (6).<\/span><\/p>\n

Li X<\/strong>**<\/strong>, Zhu Q, Zhao C, et al.  Higher-order Granger reservoir computing: simultaneously achieving  scalable complex structures inference and accurate dynamics  prediction[J]. Nature Communications, 2024, 15(1): 2506.<\/span><\/p>\n

Chen R T, Rubanova Y, Bettencourt J, et al. Neural ordinary differential equations [J]. Advances in neural information processing systems, 2018, 31.<\/span><\/p>\n

Li X<\/strong>**<\/strong>, Zhang J, Zhu Q, et al. From Fourier to Neural ODEs: Flow Matching for Modeling Complex Systems. ICML:2405.11542, 2024.<\/span><\/p>\n

Lu L,Jin P, Pang G, et al. Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators [J]. Nature machine intelligence, 2021, 3 (3): 218\u2013229.<\/span><\/p>\n

Li Z, Kovachki N, Azizzadenesheli K, et al. Fourier neural operator for para metric partial differential equations [J]. arXiv preprint arXiv:2010.08895, 2020.<\/span><\/p>\n

Zhang R, Meng Q, Ma Z M. Deciphering and integrating invariants for neural operator learning with various physical mechanisms[J]. National Science Review, 2024, 11(4): nwad336.<\/span><\/p>\n

Cao Q, Goswami S, Karniadakis G E. Laplace neural operator for solving differential equations[J]. Nature Machine Intelligence, 2024: 1-10.<\/span><\/p>\n

Kontolati K, Goswami S, Em Karniadakis G, et al. Learning nonlinear operators in latent spaces for real-time predictions of complex dynamics in physical systems[J]. Nature Communications, 2024, 15(1): 5101.<\/span><\/p>\n


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Part 2 \u57fa\u4e8e\u673a\u5668\u5b66\u4e60\u7684\u590d\u6742\u7cfb\u7edf\u8c03\u63a7<\/strong><\/span><\/h3>\n
Chang, Y. C., Roohi, N., & Gao, S. (2019). Neural lyapunov control. Advances in neural information processing systems<\/em>, 32<\/em>.<\/span><\/section>\n
Dawson, C., Gao, S., & Fan, C. (2023). Safe control with learned certificates: A survey of neural lyapunov, barrier, and contraction methods for robotics and control. IEEE Transactions on Robotics<\/em>, 39<\/em>(3), 1749-1767.<\/span><\/section>\n
B\u00f6ttcher, L., Antulov-Fantulin, N., & Asikis, T. (2022). AI Pontryagin or how artificial neural networks learn to control dynamical systems. Nature communications<\/em>, 13<\/em>(1), 333.<\/span><\/section>\n
Clark, A. (2019, July). Control barrier functions for complete and incomplete information stochastic systems. In 2019 American Control Conference (ACC)<\/em> (pp. 2928-2935). IEEE.<\/span><\/section>\n
Zhang, J.<\/strong>**<\/strong>, Zhu, Q., & Lin, W. (2022). Neural stochastic control. Advances in neural information processing systems<\/em>, 35<\/em>, 9098-9110.<\/span><\/section>\n
Zhang, J.<\/strong>**<\/strong>, Zhu, Q., Yang, W., & Lin, W. (2023). SYNC: Safety-aware neural control for stabilizing stochastic delay-differential equations. In The eleventh international conference on learning representations<\/em>.<\/span><\/section>\n
Zhang, J.<\/strong>**<\/strong>, Yang, L., Zhu, Q., & Lin, W. FESSNC: Fast Exponentially Stable and Safe Neural Controller. In Forty-first International Conference on Machine Learning<\/em>.(ICML 2024)<\/em><\/span><\/section>\n
Lechner, M., \u017dikeli\u0107, \u0110., Chatterjee, K., & Henzinger, T. A. (2022, June). Stability verification in stochastic control systems via neural network supermartingales. In Proceedings of the AAAI Conference on Artificial Intelligence<\/em> (Vol. 36, No. 7, pp. 7326-7336).<\/span><\/section>\n
Wang, L. Z., Su, R. Q., Huang, Z. G., Wang, X., Wang, W. X., Grebogi, C., & Lai, Y. C. (2016). A geometrical approach to control and controllability of nonlinear dynamical networks. Nature communications<\/em>, 7<\/em>(1), 11323.<\/span><\/section>\n

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