arXiv subjects

Ling-Wei Kong

Publications and source records attributed to Ling-Wei Kong.

13 recordsLinked to original sources

arXiv2026

A Continuous-Time and State-Space Relaxation of the Linear Threshold Model with Nonlinear Opinion Dynamics

The Linear Threshold Model (LTM) is widely used to study the propagation of collective behaviors as complex contagions. However, its dependence on discrete states and timesteps restricts its ability to capture the multiple time-scales inherent in decision-making, as well as the effects of subthreshold signaling. To address these limitations, we introduce a continuous-time and state-space relaxation of the LTM based on the Nonlinear Opinion Dynamics (NOD) framework. By replacing the discontinuous step-function thresholds of the LTM with the smooth bifurcations of the NOD model, we map discrete cascade processes to the continuous flow of a dynamical system. We prove that, under appropriate parameter choices, activation in the discrete LTM guarantees activation in the continuous NOD relaxation for any given seed set. We establish computable conditions for equivalence: by sufficiently bounding the social coupling parameter, the continuous NOD cascades exactly recover the cascades of the discrete LTM. We then illustrate how this NOD relaxation provides a richer analytical framework than the LTM, allowing for the exploration of cascades driven by strictly subthreshold inputs and the role of temporally distributed signals.

eess.SY↗

arXiv2026

Basin Geometry and Reliable Recall of Dynamical Memories in Reservoir Computing

Reliable attractor recall conventionally requires broad basins of attraction. However, in reservoir-computing based associative memory, temporal cues reliably recover dynamical memories despite basins dominated by unpredictable, riddled-like regions. We reveal that memory basins exhibit an ``octopus-like'' structure: a robust ``head'' near the attractor and thin, intertwined ``tentacles'' spanning state space. Initial states in tentacular regions yield near-zero uncertainty exponents, making the recalled memory effectively unpredictable at finite precision. Yet, cue-driven generalized synchronization bypasses this unpredictability, driving the system into the robust basin head. This mechanism yields a quantitative relation linking minimum cue duration, synchronization rate, and basin-head radius. Trained recurrent neural networks exhibit similar geometry, suggesting this phenomenon extends beyond reservoir computing.

nlin.CD↗

arXiv2026

Messaging strategies and the emergence of echo chambers in collective decision-making

Collective decision-making arises from individual agents integrating their own personal observations with information obtained from social partners. In many biological systems that exhibit collective decision-making, the process by which social information is produced, transmitted, and used is subject to two key constraints. First, individuals often do not observe the internal states or personal observations of their neighbors; instead, they observe neighbors' discrete actions. Second, agents often have limited attention, such that, at any given moment, only a subset of social partners influences decisions. Using methods from nonlinear dynamics, we show that either of these constraints can cause collective accuracy to become extremely sensitive to the weight individuals place on the information they receive from others. This sensitivity arises from the spontaneous formation of echo chamber-like states in which individuals receive and transmit homogeneous social messages. Under such conditions, collectives become locked in self-reinforcing states that prevent them from tracking changes in the environment. We reveal the mathematical basis of this phenomenon, and show that it emerges not only in generic models of collective decision-making but also in models developed to describe specific biological systems, including neural circuits, eusocial insect colonies, and mobile animal groups. Finally, we identify biologically plausible mechanisms through which individuals may reduce the risk of echo chamber formation and achieve robust yet sensitive collective decisions without requiring fine-tuning parameters. Our results reveal how fundamental constraints on communication shape the dynamics and reliability of collective decisions across diverse biological systems.

q-bio.QM↗

arXiv2025

Unsupervised learning for anticipating critical transitions

For anticipating critical transitions in complex dynamical systems, the recent approach of parameter-driven reservoir computing requires explicit knowledge of the bifurcation parameter. We articulate a framework combining a variational autoencoder (VAE) and reservoir computing to address this challenge. In particular, the driving factor is detected from time series using the VAE in an unsupervised-learning fashion and the extracted information is then used as the parameter input to the reservoir computer for anticipating the critical transition. We demonstrate the power of the unsupervised learning scheme using prototypical dynamical systems including the spatiotemporal Kuramoto-Sivashinsky system. The scheme can also be extended to scenarios where the target system is driven by several independent parameters or with partial state observations.

nlin.CD↗

arXiv2024

Machine-learning prediction of tipping with applications to the Atlantic Meridional Overturning Circulation

Anticipating a tipping point, a transition from one stable steady state to another, is a problem of broad relevance due to the ubiquity of the phenomenon in diverse fields. The steady-state nature of the dynamics about a tipping point makes its prediction significantly more challenging than predicting other types of critical transitions from oscillatory or chaotic dynamics. Exploiting the benefits of noise, we develop a general data-driven and machine-learning approach to predicting potential future tipping in nonautonomous dynamical systems and validate the framework using examples from different fields. As an application, we address the problem of predicting the potential collapse of the Atlantic Meridional Overturning Circulation (AMOC), possibly driven by climate-induced changes in the freshwater input to the North Atlantic. Our predictions based on synthetic and currently available empirical data place a potential collapse window spanning from 2040 to 2065, in consistency with the results in the current literature.

physics.ao-ph↗

arXiv2023

Model-free tracking control of complex dynamical trajectories with machine learning

Nonlinear tracking control enabling a dynamical system to track a desired trajectory is fundamental to robotics, serving a wide range of civil and defense applications. In control engineering, designing tracking control requires complete knowledge of the system model and equations. We develop a model-free, machine-learning framework to control a two-arm robotic manipulator using only partially observed states, where the controller is realized by reservoir computing. Stochastic input is exploited for training, which consists of the observed partial state vector as the first and its immediate future as the second component so that the neural machine regards the latter as the future state of the former. In the testing (deployment) phase, the immediate-future component is replaced by the desired observational vector from the reference trajectory. We demonstrate the effectiveness of the control framework using a variety of periodic and chaotic signals, and establish its robustness against measurement noise, disturbances, and uncertainties.

cs.RO↗

arXiv2022

Emergence of a stochastic resonance in machine learning

Can noise be beneficial to machine-learning prediction of chaotic systems? Utilizing reservoir computers as a paradigm, we find that injecting noise to the training data can induce a stochastic resonance with significant benefits to both short-term prediction of the state variables and long-term prediction of the attractor of the system. A key to inducing the stochastic resonance is to include the amplitude of the noise in the set of hyperparameters for optimization. By so doing, the prediction accuracy, stability and horizon can be dramatically improved. The stochastic resonance phenomenon is demonstrated using two prototypical high-dimensional chaotic systems.

cs.LG↗

arXiv2022

Digital twins of nonlinear dynamical systems

We articulate the design imperatives for machine-learning based digital twins for nonlinear dynamical systems subject to external driving, which can be used to monitor the ``health'' of the target system and anticipate its future collapse. We demonstrate that, with single or parallel reservoir computing configurations, the digital twins are capable of challenging forecasting and monitoring tasks. Employing prototypical systems from climate, optics and ecology, we show that the digital twins can extrapolate the dynamics of the target system to certain parameter regimes never experienced before, make continual forecasting/monitoring with sparse real-time updates under non-stationary external driving, infer hidden variables and accurately predict their dynamical evolution, adapt to different forms of external driving, and extrapolate the global bifurcation behaviors to systems of some different sizes. These features make our digital twins appealing in significant applications such as monitoring the health of critical systems and forecasting their potential collapse induced by environmental changes.

nlin.AO↗

arXiv2021

Anticipating synchronization with machine learning

In applications of dynamical systems, situations can arise where it is desired to predict the onset of synchronization as it can lead to characteristic and significant changes in the system performance and behaviors, for better or worse. In experimental and real settings, the system equations are often unknown, raising the need to develop a prediction framework that is model free and fully data driven. We contemplate that this challenging problem can be addressed with machine learning. In particular, exploiting reservoir computing or echo state networks, we devise a "parameter-aware" scheme to train the neural machine using asynchronous time series, i.e., in the parameter regime prior to the onset of synchronization. A properly trained machine will possess the power to predict the synchronization transition in that, with a given amount of parameter drift, whether the system would remain asynchronous or exhibit synchronous dynamics can be accurately anticipated. We demonstrate the machine-learning based framework using representative chaotic models and small network systems that exhibit continuous (second-order) or abrupt (first-order) transitions. A remarkable feature is that, for a network system exhibiting an explosive (first-order) transition and a hysteresis loop in synchronization, the machine learning scheme is capable of accurately predicting these features, including the precise locations of the transition points associated with the forward and backward transition paths.

nlin.AO↗

arXiv2020

Machine learning prediction of critical transition and system collapse

To predict a critical transition due to parameter drift without relying on model is an outstanding problem in nonlinear dynamics and applied fields. A closely related problem is to predict whether the system is already in or if the system will be in a transient state preceding its collapse. We develop a model free, machine learning based solution to both problems by exploiting reservoir computing to incorporate a parameter input channel. We demonstrate that, when the machine is trained in the normal functioning regime with a chaotic attractor (i.e., before the critical transition), the transition point can be predicted accurately. Remarkably, for a parameter drift through the critical point, the machine with the input parameter channel is able to predict not only that the system will be in a transient state, but also the average transient time before the final collapse.

cs.LG↗

arXiv2020

Synchronization within synchronization: transients and intermittency in ecological networks

Transients are fundamental to ecological systems with significant implications to management, conservation, and biological control. We uncover a type of transient synchronization behavior in spatial ecological networks whose local dynamics are of the chaotic, predator-prey type. In the parameter regime where there is phase synchronization among all the patches, complete synchronization (i.e., synchronization in both phase and amplitude) can arise in certain pairs of patches as determined by the network symmetry - henceforth the phenomenon of "synchronization within synchronization." Distinct patterns of complete synchronization coexist but, due to intrinsic instability or noise, each pattern is a transient and there is random, intermittent switching among the patterns in the course of time evolution. The probability distribution of the transient time is found to follow an algebraic scaling law with a divergent average transient lifetime. Based on symmetry considerations, we develop a stability analysis to understand these phenomena. The general principle of symmetry can also be exploited to explain previously discovered, counterintuitive synchronization behaviors in ecological networks.

q-bio.PE↗

arXiv2020

Scaling law of transient lifetime of chimera states under dimension-augmenting perturbations

Chimera states arising in the classic Kuramoto system of two-dimensional phase coupled oscillators are transient but they are "long" transients in the sense that the average transient lifetime grows exponentially with the system size. For reasonably large systems, e.g., those consisting of a few hundreds oscillators, it is infeasible to numerically calculate or experimentally measure the average lifetime, so the chimera states are practically permanent. We find that small perturbations in the third dimension, which make system "slightly" three-dimensional, will reduce dramatically the transient lifetime. In particular, under such a perturbation, the practically infinite average transient lifetime will become extremely short, because it scales with the magnitude of the perturbation only logarithmically. Physically, this means that a reduction in the perturbation strength over many orders of magnitude, insofar as it is not zero, would result in only an incremental increase in the lifetime. The uncovered type of fragility of chimera states raises concerns about their observability in physical systems.

nlin.AO↗

arXiv2017

Percolation on networks with weak and heterogeneous dependency

In real networks, the dependency between nodes is ubiquitous; however, the dependency is not always complete and homogeneous. In this paper, we propose a percolation model with weak and heterogeneous dependency; i.e., dependency strengths could be different between different nodes. We find that the heterogeneous dependency strength will make the system more robust, and for various distributions of dependency strengths both continuous and discontinuous percolation transitions can be found. For Erdős-Rényi networks, we prove that the crossing point of the continuous and discontinuous percolation transitions is dependent on the first five moments of the dependency strength distribution. This indicates that the discontinuous percolation transition on networks with dependency is determined not only by the dependency strength but also by its distribution. Furthermore, in the area of the continuous percolation transition, we also find that the critical point depends on the first and second moments of the dependency strength distribution. To validate the theoretical analysis, cases with two different dependency strengths and Gaussian distribution of dependency strengths are presented as examples.

cond-mat.stat-mech↗