戴文娇,颜子翔,高健,杨胡江,王新刚,肖井华

• 1:北京邮电大学理学院
• 2:陕西师范大学物理学与信息技术学院

摘要(Abstract)：

在当前推行数智化教育的时代背景下，如何实现人工智能与大学物理实验教学的有机融合是一个值得关注的问题。为探索这一融合的实践方式，本研究将一种机器学习方法——储备池计算与非线性电路实验进行结合，探索其在实际教学场景中的潜在应用。研究表明，RC方法在对三个电阻值下的两路电压信号进行学习后，便能准确给出这一非线性电路系统在电阻值连续变化时通向混沌的倍周期分岔道路。利用这一功能，学生在课堂中不仅能够更快、更深入、更全面地了解复杂非线性电路系统的本质，还能充分领略到机器学习的强大能力。这一尝试为数智化教育的实践提供了一种可行途径。

关键词(KeyWords)： 非线性物理实验;储备池计算;参数感知;倍周期分岔图

Abstract:

Keywords:

基金项目(Foundation): 2024高等学校计算物理课程教学研究项目(JZW-24-JW-06);; 2024年度全国高等学校大学物理改革研究项目(2024PR007);; 北京邮电大学重点教改项目(2023D11)

作者(Author): 戴文娇,颜子翔,高健,杨胡江,王新刚,肖井华

参考文献(References)：

• [1] SONG R,LIANG C,CAO H,et al.Collaborative semantic occupancy prediction with hybrid feature fusion in connected automated vehicles[J].arXiv preprint arXiv:2402.07635,2024.
• [2] CHEN G,PARADA C,SAINATH T N.Query-by-example keyword spotting using long short-term memory networks[C].2015 IEEE international conference on acoustics,speech and signal processing (ICASSP).IEEE,2015:5236-5240.
• [3] LECUN Y,BOTTOU L,BENGIO Y,et al.Gradient-based learning applied to document recognition[J].Proceedings of the IEEE,1998,86(11):2278-2324.
• [4] CHO K,VAN MERRI?NBOER B,GULCEHRE C,et al.Learning phrase representations using RNN encoder-decoder for statistical machine translation[J].arXiv preprint arXiv:1406.1078,2014.
• [5] LIPTON Z C,BERKOWITZ J,ELKAN C.A critical review of recurrent neural networks for sequence learning[J].arXiv preprint arXiv:1506.00019,2015.
• [6] JAEGER H.The “echo state” approach to analysing and training recurrent neural networks-with an erratum note[J].Bonn,Germany:German National Research Center for Information Technology GMD Technical Report,2001,148(34):13.
• [7] MAASS W,NATSCHL?GER T,MARKRAM H.Real-time computing without stable states:A new framework for neural computation based on perturbations[J].Neural computation,2002,14(11):2531-2560.
• [8] CAI H,AO Z,TIAN C,et al.Brain organoid reservoir computing for artificial intelligence[J].Nature Electronics,2023,6(12):1032-1039.
• [9] KRISHNAGOPAL S,GIRVAN M,OTT E,et al.Separation of chaotic signals by reservoir computing[J].Chaos:An Interdisciplinary Journal of Nonlinear Science,2020,30(2).
• [10] JAEGER H,HAAS H.Harnessing nonlinearity:Predicting chaotic systems and saving energy in wireless communication[J].Science,2004,304(5667):78-80.
• [11] PATHAK J,LU Z,HUNT B R,et al.Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data[J].Chaos:An Interdisciplinary Journal of Nonlinear Science,2017,27(12).
• [12] KONG L W,FAN H W,GREBOGI C,et al.Machine learning prediction of critical transition and system collapse[J].Physical Review Research,2021,3(1):013090.
• [13] KIM J Z,LU Z,NOZARI E,et al.Teaching recurrent neural networks to infer global temporal structure from local examples[J].Nature Machine Intelligence,2021,3(4):316-323.
• [14] ZHANG H,FAN H,DU Y,et al.Anticipating measure synchronization in coupled Hamiltonian systems with machine learning[J].Chaos:An Interdisciplinary Journal of Nonlinear Science,2022,32(8).
• [15] ZHANG H,FAN H,WANG L,et al.Learning Hamiltonian dynamics with reservoir computing[J].Physical Review E,2021,104(2):024205.
• [16] ROY M,MANDAL S,HENS C,et al.Model-free prediction of multistability using echo state network[J].Chaos:An Interdisciplinary Journal of Nonlinear Science,2022,32(10).
• [17] KONG L W,WENG Y,GLAZ B,et al.Reservoir computing as digital twins for nonlinear dynamical systems[J].Chaos:An Interdisciplinary Journal of Nonlinear Science,2023,33(3).
• [18] DOMINGO L,GRANDE M,BORONDO F,et al.Anticipating food price crises by reservoir computing[J].Chaos,Solitons & Fractals,2023,174:113854.
• [19] LU Z,PATHAK J,HUNT B,et al.Reservoir observers:Model-free inference of unmeasured variables in chaotic systems[J].Chaos:An Interdisciplinary Journal of Nonlinear Science,2017,27(4).
• [20] PATHAK J,HUNT B,GIRVAN M,et al.Model-free prediction of large spatiotemporally chaotic systems from data:A reservoir computing approach[J].Physical review letters,2018,120(2):024102.
• [21] WENG T,YANG H,GU C,et al.Synchronization of chaotic systems and their machine-learning models[J].Physical Review E,2019,99(4):042203.
• [22] GUO Y,ZHANG H,WANG L,et al.Transfer learning of chaotic systems[J].Chaos:An Interdisciplinary Journal of Nonlinear Science,2021,31(1).
• [23] LUO H,DU Y,FAN H,et al.Reconstructing bifurcation diagrams of chaotic circuits with reservoir computing[J].Physical Review E,2024,109(2):024210.
• [24] CHUA L O,KOCAREV L,ECKERT K,et al.Experiment chaos synchronization in chua's circuit[J].Internationl Journal of Bifurcation and Chaos,1992,2(3):705-708.
• [25] KENNEDY M P.Three steps to chaos.I[J].IEEE Transactions on Circuits & Systems I Fundamental Theory & Applications,1993,40(10):640-656.