非线性科学
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- [1] arXiv:2510.15069 [中文pdf, pdf, html, 其他]
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标题： 机器学习非线性波：用于计算机辅助发现方程、对称性、守恒定律和可积性的数据驱动方法标题： Machine Learning of Nonlinear Waves: Data-Driven Methods for Computer-Assisted Discovery of Equations, Symmetries, Conservation Laws, and Integrability主题： 模式形成与孤子 (nlin.PS) ; 动力系统 (math.DS) ; 精确可解与可积系统 (nlin.SI)
本文的目的是提供一个视角——尽管这无疑是一个相当主观的视角——关于机器学习/数据驱动方法与非线性波研究交叉领域的最新发展。 我们回顾了科学机器学习快速发展的领域中的一些近期支柱，包括深度学习、数据驱动方程发现和算子学习等。 然后，我们将这些方法应用于从学习格子动力学模型和有效动力学的降阶建模到发现守恒定律以及识别常微分方程和偏微分方程模型的可积性的各种应用。 我们的意图是明确这些机器学习方法是对非线性波领域现有强大工具的补充，并应整合到该工具箱中，以增强和推动数据时代数学发现和计算能力。
The purpose of this article is to provide a perspective - admittedly, a rather subjective one - of recent developments at the interface of machine learning/data-driven methods and nonlinear wave studies. We review some recent pillars of the rapidly evolving landscape of scientific machine learning, including deep learning, data-driven equation discovery, and operator learning, among others. We then showcase these methods in applications ranging from learning lattice dynamical models and reduced order modeling of effective dynamics to discovery of conservation laws and potential identification of integrability of ODE and PDE models. Our intention is to make clear that these machine learning methods are complementary to the preexisting powerful tools of the nonlinear waves community, and should be integrated into this toolkit to augment and enable mathematical discoveries and computational capabilities in the age of data.
- [2] arXiv:2510.15656 [中文pdf, pdf, 其他]
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标题： 活性物质同步与协同作用标题： Active matter synchronization and synergetics主题： 适应性与自组织系统 (nlin.AO) ; 统计力学 (cond-mat.stat-mech)
我们研究了一种活性物质的随机基于代理的模型中的集体行为。 在能量充分供应的情况下，代理生成两种商品$x$,$y$，它们遵循广义的Lotka-Volterra动力学。 对于孤立的代理，生产要么达到固定点，要么发散。 然而，通过$x$的平均场耦合代理的生产，如果代理在$x$的生产中合作，可能会导致同步振荡。 $y$的生产通过抑制波动和缓解代理之间的竞争来支持同步动力学的出现，从而稳定$x$的生产。 我们发现，在同步状态下，不同的代理群体共存，每个群体遵循自己的极限环。 组内的Kuramoto序参数较大，而组间的较小。 集体状态对来自暂时在合作与竞争之间切换的代理的冲击具有稳定性。 模型动力学说明了协同作用的原则，即在临界能量供应和合作相互作用下秩序的自发出现。
We study the collective behavior in a stochastic agent-based model of active matter. Provided a critical take-up of energy, agents produce two types of goods $x$, $y$ that follow a generalized Lotka-Volterra dynamics. For isolated agents, production would either reach a fixed point or diverge. Coupling agents' production via a mean field of $x$, however, can lead to synchronized oscillations if agents cooperate in the production of $x$. The production of $y$ supports the emergence of the synchronized dynamics by suppressing fluctuations and mitigating competition between agents, this way stabilizing the production of $x$. We find that in the synchronized state different groups of agents coexist, each following their own limit cycle. The Kuramoto order parameter is large within groups, and small across groups. The collective state is stable against shocks from agents temporarily switching between cooperation and competition. The model dynamics illustrates the principles of synergetics, i.e., the spontaneous emergence of order given a critical energy supply and cooperative interactions.
- [3] arXiv:2510.15658 [中文pdf, pdf, html, 其他]
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标题： 非线性耦合的网络上Stuart-Landau振子的同步标题： Synchronization of nonlinearly coupled Stuart-Landau oscillators on networks主题： 模式形成与孤子 (nlin.PS) ; 统计力学 (cond-mat.stat-mech) ; 动力系统 (math.DS)
耦合的Stuart-Landau振子的动力学在同步现象的研究中起着核心作用。先前的研究集中在不同配置下的线性耦合振子，例如全连接或一般的复杂网络，允许存在相互或非相互的连接。同步的出现可以通过证明Stuart-Landau模型极限环解的线性稳定性来推导；线性耦合假设使得问题能够进行完整的解析处理，主要是因为线性化系统变成了自治的。在本工作中，我们分析了通过非线性函数在无向和有向网络中耦合的Stuart-Landau振子；现在同步依赖于非自治线性系统的研究，因此需要新的工具来解决这个问题。我们提供了对某些非线性耦合选择的系统完整解析描述，例如在共振情况下。否则，我们开发了一个基于雅可比-安格展开和Floquet理论的半解析框架，这使我们能够推导出完全同步出现的精确条件。所得结果扩展了耦合振子的经典理论，并为未来对振子网络中非线性相互作用的研究铺平了道路。
The dynamics of coupled Stuart-Landau oscillators play a central role in the study of synchronization phenomena. Previous works have focused on linearly coupled oscillators in different configurations, such as all-to-all or generic complex networks, allowing for both reciprocal or non-reciprocal links. The emergence of synchronization can be deduced by proving the linear stability of the limit cycle solution for the Stuart-Landau model; the linear coupling assumption allows for a complete analytical treatment of the problem, mostly because the linearized system turns out to be autonomous. In this work, we analyze Stuart-Landau oscillators coupled through nonlinear functions on both undirected and directed networks; synchronization now depends on the study of a non-autonomous linear system and thus novel tools are required to tackle the problem. We provide a complete analytical description of the system for some choices of the nonlinear coupling, e.g., in the resonant case. Otherwise, we develop a semi-analytical framework based on Jacobi-Anger expansion and Floquet theory, which allows us to derive precise conditions for the emergence of complete synchronization. The obtained results extend the classical theory of coupled oscillators and pave the way for future studies of nonlinear interactions in networks of oscillators and beyond.
新提交 (展示 3 之 3 条目 )
- [4] arXiv:2510.15053 (交叉列表自 physics.soc-ph) [中文pdf, pdf, html, 其他]
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标题： 新闻、谣言和意见的物理学标题： The Physics of News, Rumors, and OpinionsGuido Caldarelli, Oriol Artime, Giulia Fischetti, Stefano Guarino, Andrzej Nowak, Fabio Saracco, Petter Holme, Manlio de Domenico评论： 67页，9图主题： 物理与社会 (physics.soc-ph) ; 适应性与自组织系统 (nlin.AO)
随着互联网及其无处不在的平台的出现，物理网络和社会网络之间的界限已经缩小。 这催生了一个复杂的适应性信息生态系统，其中个体和机器争夺关注，导致了集体现象的出现。 在这个生态系统中，信息的流动往往并不简单，涉及复杂的用户策略，从操纵性内容的制造或战略性放大，到大规模协调行为引发的虚假信息级联、回音室强化和观点极化。 我们认为，统计物理为分析社会技术系统中这些复杂动态的展开提供了合适且必要的框架。 这篇综述系统地涵盖了该框架的基础和应用方面。 这篇综述的结构首先建立分析这些复杂系统的理论基础，考察复杂网络的结构模型和社交动力学的物理模型（例如流行病模型和自旋模型）。 然后，我们通过描述当前这些动态发生的现代媒体生态系统来巩固这些概念，包括对平台的比较分析以及信息紊乱的挑战。 核心部分继续将这一框架应用于两个核心现象：首先，通过分析信息传播的集体动力学，专门关注模型、主要实证见解以及虚假信息的独特特征；其次，回顾当前的观点动力学模型，涵盖离散、连续和共演化方法。 总之，我们回顾了基于大规模数据分析的实证发现和理论进展，突出了基于物理学的努力在研究这些具有重大社会影响的现象中所获得的宝贵见解。
The boundaries between physical and social networks have narrowed with the advent of the Internet and its pervasive platforms. This has given rise to a complex adaptive information ecosystem where individuals and machines compete for attention, leading to emergent collective phenomena. The flow of information in this ecosystem is often non-trivial and involves complex user strategies from the forging or strategic amplification of manipulative content to large-scale coordinated behavior that trigger misinformation cascades, echo-chamber reinforcement, and opinion polarization. We argue that statistical physics provides a suitable and necessary framework for analyzing the unfolding of these complex dynamics on socio-technological systems. This review systematically covers the foundational and applied aspects of this framework. The review is structured to first establish the theoretical foundation for analyzing these complex systems, examining both structural models of complex networks and physical models of social dynamics (e.g., epidemic and spin models). We then ground these concepts by describing the modern media ecosystem where these dynamics currently unfold, including a comparative analysis of platforms and the challenge of information disorders. The central sections proceed to apply this framework to two central phenomena: first, by analyzing the collective dynamics of information spreading, with a dedicated focus on the models, the main empirical insights, and the unique traits characterizing misinformation; and second, by reviewing current models of opinion dynamics, spanning discrete, continuous, and coevolutionary approaches. In summary, we review both empirical findings based on massive data analytics and theoretical advances, highlighting the valuable insights obtained from physics-based efforts to investigate these phenomena of high societal impact.
- [5] arXiv:2510.15715 (交叉列表自 quant-ph) [中文pdf, pdf, html, 其他]
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标题： 非线性动力学的Carleman线性嵌入方法的全局化标题： Globalizing the Carleman linear embedding method for nonlinear dynamics主题： 量子物理 (quant-ph) ; 混沌动力学 (nlin.CD) ; 计算物理 (physics.comp-ph)
卡尔曼嵌入方法是一种广泛用于将非线性微分方程系统线性化的技术，但在存在多个固定点的区域中无法收敛。我们提出了并测试了三种不同的全局分段卡尔曼嵌入技术，这些技术基于将空间划分为多个区域，其中嵌入区域的中心和大小被选择以控制收敛性。第一种方法在轨迹到达当前线性化图的边界时，在固定大小的局部线性化区域之间切换。在转换过程中，嵌入在新创建的图中重建，以转换点为中心。第二种方法也动态调整图的大小，在存在多个固定点的区域中提高准确性。第三种方法使用静态网格对状态空间进行划分，并预先计算固定大小的线性化图，使其更适合需要高速的应用。所有技术都在多个可积和混沌的非线性动力系统上进行了数值测试，证明了它们在标准卡尔曼嵌入方法完全无法处理的问题中的适用性。如各种类型的奇异吸引子等混沌动力系统的模拟展示了自适应方法的力量，如果施加足够低的容差的话。尽管如此，具有固定中心和大小的线性化图的非自适应版本在模拟动力系统时可能更快，同时提供相似的准确性，可能更适合作为未来量子计算机算法的基础。
The Carleman embedding method is a widely used technique for linearizing a system of nonlinear differential equations, but fails to converge in regions where there are multiple fixed points. We propose and test three different versions of a global piecewise Carleman embedding technique, based on partitioning space into multiple regions where the center and size of the embedding region are chosen to control convergence. The first method switches between local linearization regions of fixed size once the trajectory reaches the boundary of the current linearization chart. During the transition, the embedding is reconstructed within the newly created chart, centered at the transition point. The second method also adapts the chart size dynamically, enhancing accuracy in regions where multiple fixed points are located. The third method partitions the state space using a static grid with precomputed linearization charts of fixed size, making it more suitable for applications that require high speed. All techniques are numerically tested on multiple integrable and chaotic nonlinear dynamical systems demonstrating their applicability for problems that are completely intractable for the standard Carleman embedding method. Simulations of chaotic dynamical systems such as various types of strange attractors demonstrate the power of the adaptive methods, if a sufficiently low tolerance is imposed. Still, the non-adaptive version of the method, with fixed centers and sizes of the linearization charts, can be faster in simulating dynamical systems while providing similar accuracy and may be more appropriate as the basis of algorithms for future quantum computers.
交叉提交 (展示 2 之 2 条目 )
- [6] arXiv:2404.08907 (替换) [中文pdf, pdf, html, 其他]
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标题： 近壁湍流中内运动和外运动的因果分析标题： Causal analysis of inner and outer motions in near-wall turbulence主题： 流体动力学 (physics.flu-dyn) ; 混沌动力学 (nlin.CD) ; 数据分析、统计与概率 (physics.data-an)
在本工作中，我们研究近壁面内层和外层湍流运动的因果关系。内层运动被定义为自维持的近壁面循环，而外层运动则是在对数层中存在并表现出近壁面区域特征的运动。进行了三种典型方法的因果推断，即转移熵、信息流和SURD（因果关系的协同-唯一-冗余分解）。这些因果推断方法首先应用于几个典型问题，以说明它们的能力和差异，包括一个线性问题、一个非线性问题和一个近壁湍流的低维模型。结果表明，所有三种方法都能产生一致的因果发现。此外，我们使用三种方法和改进的内层-外层分解方法研究了通道流动中内层和外层湍流运动之间的因果关系。结果表明，内层和外层运动都是自维持的，并且彼此独立，支持了所有尺度上湍流运动的自维持机制。我们还发现外层运动及其近壁面特征存在自上而下和自下而上的影响，挑战了传统的单一自上而下观点。更有趣的是，压力被识别为在内外层因果关系中起主动作用，可能作为连接内层和外层湍流运动的桥梁。
In this work, we study the causality of near-wall inner and outer turbulent motions. The inner motions are defined as the self-sustained near-wall cycle, and the outer motions as those living in the logarithmic layer exhibiting footprints on the near-wall region. Causal inference with three typical methods is performed, i.e. transfer entropy, information flow, and SURD (synergistic--unique--redundant decomposition of causality). The causal inference methods are first applied to several canonical problems to illustrate their abilities and differences, including a linear problem, a non-linear problem, and a low-dimensional model of near-wall turbulence. It is demonstrated that all three methods can produce consistent causal findings. Furthermore, we study the causalities between the inner and outer turbulent motions in a channel flow using the three methods with an improved inner-outer decomposition method. It is revealed that both the inner and outer motions are self-sustained and independent of each other, supporting the self-sustaining mechanism of turbulent motions at all scales. We also find that there are top-down and bottom-up influences in the outer motions and their near-wall footprints, challenging the traditional sole top-down view. More interestingly, pressure is identified to play an active role in the inner-outer causalities and may act as a bridge in linking the inner and outer turbulent motions.
- [7] arXiv:2506.13576 (替换) [中文pdf, pdf, html, 其他]
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标题： 关联记忆模式的振幅方程在空间分布系统中标题： Amplitude equations of associative memory patterns in spatially distributed systems评论： 4页，2图。替换：论点的澄清主题： 神经与认知 (q-bio.NC) ; 无序系统与神经网络 (cond-mat.dis-nn) ; 模式形成与孤子 (nlin.PS)
关联记忆的振幅演化方程被推导出来：非局部相互作用的分布式系统中存储的异质状态。 由此得到的耦合振幅方程描述了记忆回忆的时空动力学。 它们捕捉到了模式完成和选择，并表明短程连接可以在传播模式前沿的形式下维持时空记忆模式动力学。 推导出的振幅方程与描述经典模式形成不稳定性方程形式相同，表明非平衡系统中记忆回忆和模式形成的动力学具有普遍性。
Evolution equations are derived for the amplitudes of associative memories: heterogeneous states stored in the connectivity of distributed systems with non-local interactions. The resulting coupled amplitude equations describe the spatio-temporal dynamics of memory recall. They capture pattern completion and selection, and show that short-range connections can sustain spatio-temporal memory pattern dynamics in the form of propagating patterning fronts. The derived amplitude equations are of the same form as those describing classical pattern-forming instabilities, indicating a universality of the dynamics of memory recall and pattern formation in non-equilibrium systems.
- [8] arXiv:2507.10862 (替换) [中文pdf, pdf, html, 其他]
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标题： 霍金时间晶体标题： Hawking time crystals评论： 23页，10图，包括附录和补充材料。新增了关于简并参量放大器中时间算符出现的全新讨论。主题： 量子物理 (quant-ph) ; 量子气体 (cond-mat.quant-gas) ; 广义相对论与量子宇宙学 (gr-qc) ; 模式形成与孤子 (nlin.PS) ; 光学 (physics.optics)
我们提出一种基于量子黑洞激光器的时间晶体，其中对称性破缺的真正自发性来源于霍金辐射的自增强效应。 由此产生的霍金时间晶体（HTC）以时空密度-密度关联函数的周期性依赖为特征，而等时可观测量是时间不变的，因为它们体现了不同实现的平均值，具有随机振荡相位。 HTC可以被视为安德烈夫-霍金效应的非线性周期类比，表现出由于向上下游区域自发量子发射色散波和孤子对而产生的反相关带。 值得注意的是，时间晶体的形成被理解为两个时间算符：一个与初始黑洞激光器相关，另一个与最终的自发弗洛凯态相关。
We propose a time crystal based on a quantum black-hole laser, where the genuinely spontaneous character of the symmetry breaking stems from the self-amplification of spontaneous Hawking radiation. The resulting Hawking time crystal (HTC) is characterized by the periodic dependence of the out-of-time density-density correlation function, while equal-time observables are time-independent because they embody averages over different realizations with a random oscillation phase. The HTC can be regarded as a nonlinear periodic analogue of the Andreev-Hawking effect, exhibiting anticorrelation bands resulting from the spontaneous, quantum emission of pairs of dispersive waves and solitons into the upstream and downstream regions. Remarkably, the time-crystal formation is understood in terms of two time operators: one associated to the initial black-hole laser and another associated to the final spontaneous Floquet state.
- [9] arXiv:2507.12858 (替换) [中文pdf, pdf, html, 其他]
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标题： 通过循环神经网络中的互信息最小化出现功能分化结构标题： Emergence of Functionally Differentiated Structures via Mutual Information Minimization in Recurrent Neural Networks主题： 神经与认知 (q-bio.NC) ; 适应性与自组织系统 (nlin.AO)
大脑中的功能分化随着不同区域的专门化而出现，这是理解大脑作为复杂系统功能的关键。 先前的研究使用具有特定约束的人工神经网络对这一过程进行了建模。 在此，我们提出了一种新方法，通过最小化神经子群之间的互信息，利用互信息神经估计在循环神经网络中诱导功能分化。 我们将该方法应用于一个2位工作记忆任务和一个涉及Lorenz和Rössler时间序列的混沌信号分离任务。 对网络性能、相关性模式和权重矩阵的分析表明，互信息最小化在实现高任务性能的同时，还表现出清晰的功能模块性和中等程度的结构模块性。 重要的是，我们的结果表明，通过相关性结构测量的功能分化，在由突触权重定义的结构模块性之前出现。 这表明功能专业化先于并可能驱动发育中的神经网络内的结构重组。 我们的发现为信息论原则如何在人工和生物大脑发育过程中支配专门功能和模块化结构的出现提供了新的见解。
Functional differentiation in the brain emerges as distinct regions specialize and is key to understanding brain function as a complex system. Previous research has modeled this process using artificial neural networks with specific constraints. Here, we propose a novel approach that induces functional differentiation in recurrent neural networks by minimizing mutual information between neural subgroups via mutual information neural estimation. We apply our method to a 2-bit working memory task and a chaotic signal separation task involving Lorenz and R\"ossler time series. Analysis of network performance, correlation patterns, and weight matrices reveals that mutual information minimization yields high task performance alongside clear functional modularity and moderate structural modularity. Importantly, our results show that functional differentiation, which is measured through correlation structures, emerges earlier than structural modularity defined by synaptic weights. This suggests that functional specialization precedes and probably drives structural reorganization within developing neural networks. Our findings provide new insights into how information-theoretic principles may govern the emergence of specialized functions and modular structures during artificial and biological brain development.