Maximally predictive ensemble dynamics from data
Maximally predictive ensemble dynamics from data
复制标题
从数据中最大程度地预测系综动态
DOI：
10.1101/2021.05.26.445816
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
G. Stephens
中科院分区：
文献类型：
--
作者：
Antonio C. Costa;Tosif Ahamed;David J. Jordan;G. Stephens
我们利用微观可变性和宏观秩序之间的相互作用，直接从数据中连接跨尺度的物理描述，而无需基础方程。我们通过在时间上连接测量值来重建状态空间，建立所得序列的最大熵分区，并选择序列长度以最大化预测信息。交易的线性，合奏演变的非线性轨迹，我们分析重建动态通过传输运营商。演化由过渡时间τ参数化：在小τ处捕获源熵率，并在较大τ处通过算符谱揭示与集体相干态的时标分离。适用于确定性和随机系统，我们说明了我们的方法，通过朗之万动力学的粒子在双阱势和洛伦兹系统。应用于线虫C. elegans，我们直接从姿势动力学中推导出“跑步和旋转”导航策略。我们演示了如何从合奏进化模拟序列捕捉精细尺度姿态动态和大规模有效扩散蠕虫的质心轨迹，并引入一个自上而下的，基于操作员的聚类揭示了微妙的细分的“运行”的行为。复杂的结构通常由有限的一组相对简单的构建块组成;例如从字母或蛋白质到氨基酸的小说。在音乐创作中，例如，声音和沉默联合收割机形成更长的时间尺度结构;主题形成段落，而段落又形成运动。我们所面临的挑战是如何确定集体变量，区分结构在这样不同的时间尺度。我们介绍了一个原则性的框架，直接从观察学习有效的描述。就像一首乐曲从一个乐章过渡到下一个乐章一样，我们推断出的集体动力学由宏观状态之间的过渡组成，就像有效势能景观中亚稳态之间的跳跃一样。这些转换的统计数据由传输操作符来捕获。这些运营商发挥了核心作用，指导建设最大的预测短期状态从不完整的测量和识别集体模式通过本征值分解。我们展示了我们的分析在随机和确定性系统中，并与应用程序的整个有机体的运动动力学，解开新的见解，在长时间尺度的行为状态直接从姿势动态的测量。原则上，我们也可以将时间尺度与更长或更短的时间尺度联系起来。微观上，姿势动力学是由肌肉中肌动蛋白和肌球蛋白的精细相互作用以及大脑和神经系统中的电脉冲引起的。宏观上，行为动力学可以扩展到更长的时间尺度，情绪或性格，包括衰老过程中的变化，或由于生态或进化适应而产生的世代变化。我们的方法的一般性提供了机会，洞察各种复杂系统内的长期动态。
We leverage the interplay between microscopic variability and macroscopic order to connect physical descriptions across scales directly from data, without underlying equations. We reconstruct a state space by concatenating measurements in time, building a maximum entropy partition of the resulting sequences, and choosing the sequence length to maximize predictive information. Trading non-linear trajectories for linear, ensemble evolution, we analyze reconstructed dynamics through transfer operators. The evolution is parameterized by a transition time τ : capturing the source entropy rate at small τ and revealing timescale separation with collective, coherent states through the operator spectrum at larger τ. Applicable to both deterministic and stochastic systems, we illustrate our approach through the Langevin dynamics of a particle in a double-well potential and the Lorenz system. Applied to the behavior of the nematode worm C. elegans, we derive a “run-and-pirouette” navigation strategy directly from posture dynamics. We demonstrate how sequences simulated from the ensemble evolution capture both fine scale posture dynamics and large scale effective diffusion in the worm’s centroid trajectories and introduce a top-down, operator-based clustering which reveals subtle subdivisions of the “run” behavior. POPULAR SUMMARY Complex structure is often composed from a limited set of relatively simple building blocks; such as novels from letters or proteins from amino acids. In musical composition, e.g., sounds and silences combine to form longer time scale structures; motifs form passages which in turn form movements. The challenge we address is how to identify collective variables which distinguish structures across such disparate time scales. We introduce a principled framework for learning effective descriptions directly from observations. Just as a musical piece transitions from one movement to the next, the collective dynamics we infer consists of transitions between macroscopic states, like jumps between metastable states in an effective potential landscape. The statistics of these transitions are captured compactly by transfer operators. These operators play a central role, guiding the construction of maximally-predictive short-time states from incomplete measurements and identifying collective modes via eigenvalue decomposition. We demonstrate our analysis in both stochastic and deterministic systems, and with an application to the movement dynamics of an entire organism, unravelling new insight in long time scale behavioral states directly from measurements of posture dynamics. We can, in principle, also make connections to both longer or shorter timescales. Microscopically, postural dynamics result from the fine scale interactions of actin and myosin in the muscles, and from electrical impulses in the brain and nervous system. Macroscopically, behavioral dynamics may be extended to longer time scales, to moods or dispositions, including changes during aging, or over generations due to ecological or evolutionary adaptation. The generality of our approach provides opportunity for insights on long term dynamics within a wide variety of complex systems.
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影响因子：
7.5
作者：
Sourjik, Victor;Wingreen, Ned S.
通讯作者：
Wingreen, Ned S.
DOI：
10.1103/physreve.96.022417
发表时间：
2017-08
期刊：
Physical review. E
影响因子：
--
作者：
Alves LGA;Winter PB;Ferreira LN;Brielmann RM;Morimoto RI;Amaral LAN
通讯作者：
Amaral LAN
影响因子：
48
作者：
Bargmann, Cornelia I.;Marder, Eve
通讯作者：
Marder, Eve
影响因子：
4.4
作者：
Prinz, Jan-Hendrik;Wu, Hao;Noe, Frank
通讯作者：
Noe, Frank