张鑫洁;高婷婷;严钢;

• 1:同济大学物理科学与工程学院
• 2:同济大学上海自主智能无人系统科学中心
• 3:中国科学院脑科学与智能技术卓越创新中心

摘要(Abstract)：

神经元之间的联接结构和脑网络动力学是探究脑原理的两个重要视角，也是进行脑模拟不可或缺的两个重要元素。学界已通过实验和算法成功描绘了线虫以及果蝇中部脑区的神经元层次联接图谱，但构建其他动物的全脑神经联接图谱仍需时日。得益于近年来脑成像技术在分辨率、速度、深度和视场等方面取得的快速进步，学界积累了越来越多的神经活动数据。因此，通过数据驱动的方式，从神经活动数据逆向推理神经联接网络的结构和动力学模式正成为一个重要的研究方向。本文将从网络科学的角度，梳理基于节点活动数据的有向网络结构和动力学推理方法，并简述该方向上的研究进展，最后讨论仍面临的困难和挑战。

关键词(KeyWords)： 脑网络;神经动力学;数据驱动建模;因果推理

Abstract:

Keywords:

基金项目(Foundation):

作者(Authors): 张鑫洁;高婷婷;严钢;

参考文献(References)：

• [1]WHITE J G,SOUTHGATE E,THOMSON J N,et al.The structure of the nervous system of the nematode Caenorhabditis elegans:the mind of a worm[J].Philosophical Transactions of the Royal Society of London,1986,314(1):340.
• [2]COOK S J,JARRELL T A,BRITTIN C A,et al.Whole-animal connectomes of both Caenorhabditis elegans sexes[J].Nature,2019,571(7763):63-71.
• [3]SCHEFFER L K,XU C S,JANUSZEWSKI M,et al.A connectome and analysis of the adult Drosophila central brain[J].Elife,2020,9.
• [4]BRAIN INITIATIVE CELL CENSUS NETWORK (BICCN).A multimodal cell census and atlas of the mammalian primary motor cortex[J].Nature,2021,598(7879):86-102.
• [5]BENTLEY B,BRANICKY R,BARNES C L,et al.The multilayer connectome of Caenorhabditis elegans[J].PLo S computational biology,2016,12(12):e1005283.
• [6]TAKEMURA S-Y,BHARIOKE A,LU Z,et al.A visual motion detection circuit suggested by Drosophila connectomics[J].Nature,2013,500(7461):175-81.
• [7]LICHTMAN J W,DENK W.The big and the small:challenges of imaging the brain's circuits[J].Science,2011,334(6056):618-23.
• [8]BASSETT D S,SPORNS O.Network neuroscience[J].Nature neuroscience,2017,20(3):353-64.
• [9]YAN G,VéRTES P E,TOWLSON E K,et al.Network control principles predict neuron function in the Caenorhabditis elegans connectome[J].Nature,2017,550(7677):519-23.
• [10]MOTTA A,BERNING M,BOERGENS K M,et al.Dense connectomic reconstruction in layer 4 of the somatosensory cortex[J].Science,2019,366(6469):eaay3134.
• [11]GAO L,LIU S,GOU L,et al.Single-neuron projectome of mouse prefrontal cortex[J].Nature Neuroscience,2022,25(4):515-29.
• [12]SHAPSON-COE A,JANUSZEWSKI M,BERGER D R,et al.A connectomic study of a petascale fragment of human cerebral cortex[J].BioRxiv,2021.
• [13]GRANGER C W.Investigating causal relations by econometric models and cross-spectral methods[J].Econometrica:journal of the Econometric Society,1969:424-38.
• [14]MARINAZZO D,PELLICORO M,STRAMAGLIA S.Kernel-Granger causality and the analysis of dynamical networks[J].Physical review E,2008,77(5):056215.
• [15]WRIGHT S.The relative importance of heredity and environment in determining the piebald pattern of guinea-pigs[J].Proceedings of the National Academy of Sciences,1920,6(6):320-32.
• [16]MARREIROS A C,STEPHAN K E,FRISTON K J.Dynamic causal modeling[J].Scholarpedia,2010,5(7):9568.
• [17]SCANAGATTA M,DE CAMPOS C P,CORANI G,et al.Learning Bayesian networks with thousands of variables[J].Advances in neural information processing systems,2015,28.
• [18]PEARL J,MACKENZIE D.The book of why:the new science of cause and effect[M].Basic books,2018.
• [19]CUI L,MOORE J M.Causal network reconstruction from nonlinear time series:A comparative study[J].International Journal of Modern Physics C,2021,32(4):2150049.
• [20]SCHREIBER T.Measuring information transfer[J].Physical review letters,2000,85(2):461.
• [21]BARNETT L,BARRETT A B,SETH A K.Granger causality and transfer entropy are equivalent for Gaussian variables[J].Physical review letters,2009,103(23):238701.
• [22]SUN J,TAYLOR D,BOLLT E M.Causal network inference by optimal causation entropy[J].SIAM Journal on Applied Dynamical Systems,2015,14(1):73-106.
• [23]TAKENS F.Detecting strange attractors in turbulence[M]//Dynamical systems and turbulence,Warwick 1980.Springer.1981:366-81.
• [24]SUGIHARA G,MAY R,YE H,et al.Detecting causality in complex ecosystems[J].Science,2012,338(6106):496-500.
• [25]HARNACK D,LAMINSKI E,SCHüNEMANN M,et al.Topological causality in dynamical systems[J].Physical Review Letters,2017,119(9):098301.
• [26]LENG S,MA H,KURTHS J,et al.Partial cross mapping eliminates indirect causal influences[J].Nature Communications,2020,11(1):1-9.
• [27]YING X,LENG S Y,MA H F,et al.Continuity scaling:A rigorous framework for detecting and quantifying causality accurately[J].Research,2022,2022.
• [28]CASADIEGO J,NITZAN M,HALLERBERG S,et al.Model-free inference of direct network interactions from nonlinear collective dynamics[J].Nature Communications,2017,8(1):1-10.
• [29]RUNGE J,NOWACK P,KRETSCHMER M,et al.Detecting and quantifying causal associations in large nonlinear time series datasets[J].Science Advances,2019,5(11):eaau4996.
• [30]LJUNG L.Perspectives on system identifcation[J].Annual Reviews in Control,2010,34(1):1-12.
• [31]KUTZ J N,BRUNTON S L.Parsimony as the ultimate regularizer for physics-informed machine learning[J].Nonlinear Dynamics,2022,107(3):1801-17.
• [32]KOZA J R.Genetic programming as a means for programming computers by natural selection[J].Statistics and Computing,1994,4(2):87-112.
• [33]SCHMIDT M,LIPSON H.Distilling free-form natural laws from experimental data[J].science,2009,324(5923):81-85.
• [34]VIRGOLIN M,PISSIS S P.Symbolic Regression is NP-hard[EB/OL].(2022-07-11)[2022-11-29].https://arxiv.org/abs/2207.01018.
• [35]UDRESCU S M,TEGMARK M.AI Feynman:A physics-inspired method for symbolic regression[J].Science Advances,2020,6(16):eaay2631.
• [36]PETERSEN B K,LARMA M L,MUNDHENK T N,et al.Deep symbolic regression:Recovering mathematical expressions from data via risk-seeking policy gradients[EB/OL].(2021-04-05)[2022-11-29].https://arxiv.org/abs/1912.04871.
• [37]CRANMER M,SANCHEZ GONZALEZ A,BATTAGLIA P,et al.Discovering symbolic models from deep learning with inductive biases[J].Advances in Neural Information Processing Systems,2020,33:17429-17442.
• [38]BRUNTON S L,PROCTOR J L,KUTZ J N.Discovering governing equations from data by sparse identifcation of nonlinear dynamical systems[J].Proceedings of the national academy of sciences,2016,113(15):3932-3937.
• [39]RUDY S H,BRUNTON S L,PROCTOR J L,et al.Data-driven discovery of partial differential equations[J].Science Advances,2017,3(4):e1602614.
• [40]MANGAN N M,BRUNTON S L,PROCTOR J L,et al.Inferring biological networks by sparse identifcation of nonlinear dynamics[J].IEEE Transactions on Molecular,Biological and Multi-Scale Communications,2016,2(1):52-63.
• [41]ITEN R,METGER T,WILMING H,et al.Discovering physical concepts with neural networks[J].Physical Review Letters,2020,124(1):010508.
• [42]BRüCKNER D B,RONCERAY P,BROEDERSZ C P.Inferring the dynamics of underdamped stochastic systems[J].Physical Review Letters,2020,125(5):058103.
• [43]GAO T T,YAN G.Autonomous inference of complex network dynamics from incomplete and noisy data[J].Nature Computational Science,2022,2(3):160-168.