Searcharxiv⌕ Search

arXiv subjects

Ying-Cheng Lai

Publications and source records attributed to Ying-Cheng Lai.

At least 19 recordsLinked to original sources
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

Can Transformers predict system collapse in dynamical systems?

Transformer architectures have recently surged as promising solutions for nonlinear dynamical systems, proposed as foundation models capable of zero-shot dynamics reconstruction and forecasting. Despite this success, it remains unclear whether they can truly serve as reliable digital twins of dynamical systems, i.e., whether they capture the underlying physical dynamics in distinct parameter regimes, especially in parameter regimes from which no training data is taken. For parameter-space extrapolation in nonlinear dynamical systems, reservoir computing has demonstrated broad success, as proper training can turn it into an intrinsic dynamical system capable of capturing not only the dynamical climate of the target system but more importantly, how the climate changes with parameter. Transformers, in contrast, rely on permutation-invariant attention mechanisms that can limit their ability to capture how temporal structure changes with parameter. To determine if Transformers have the capability of dynamics extrapolation, we take predicting catastrophic collapse, which occurs when a bifurcation parameter crosses a critical threshold, as a benchmark task. Models are trained on trajectories in normal parameter regimes and then tested on parameters in an unseen regime with system collapse. Our results show that Transformers, across configurations, consistently fail to capture collapse, while reservoir computing reliably predicts the transitions. This surprising finding raises questions about the generalization ability of Transformers to dynamical systems, a topic warranting future research.

nlin.CD↗
arXiv2026

Vestibular reservoir computing

Reservoir computing (RC) is a computational framework known for its training efficiency, making it ideal for physical hardware implementations. However, realizing the complex interconnectivity of traditional reservoirs in physical systems remains a significant challenge. This paper proposes a physical RC scheme inspired by the biological vestibular system. To overcome hardware complexity, we introduce a designed uncoupled topology and demonstrate that it achieves performance comparable to fully coupled networks. We theoretically analyze the difference between these topologies by deriving a memory capacity formula for linear reservoirs, identifying specific conditions where both configurations yield equivalent memory. These analytical results are demonstrated to approximately hold for nonlinear reservoir systems. Furthermore, we systematically examine the impact of reservoir size on predictive statistics and memory capacity. Our findings suggest that uncoupled reservoir architectures offer a mathematically sound and practically feasible pathway for efficient physical reservoir computing.

cs.LG↗
arXiv2026

Anticipating tipping in spatiotemporal systems with machine learning

In nonlinear dynamical systems, tipping refers to a critical transition from one steady state to another, typically catastrophic, steady state, often resulting from a saddle-node bifurcation. Recently, the machine-learning framework of parameter-adaptable reservoir computing has been applied to predict tipping in systems described by low-dimensional stochastic differential equations. However, anticipating tipping in complex spatiotemporal dynamical systems remains a significant open problem. The ability to forecast not only the occurrence but also the precise timing of such tipping events is crucial for providing the actionable lead time necessary for timely mitigation. By utilizing the mathematical approach of non-negative matrix factorization to generate dimensionally reduced spatiotemporal data as input, we exploit parameter-adaptable reservoir computing to accurately anticipate tipping. We demonstrate that the tipping time can be identified within a narrow prediction window across a variety of spatiotemporal dynamical systems, as well as in CMIP5 (Coupled Model Intercomparison Project 5) climate projections. Furthermore, we show that this reservoir-computing framework, utilizing reduced input data, is robust against common forecasting challenges and significantly alleviates the computational overhead associated with processing full spatiotemporal data.

nlin.CD↗
arXiv2025

Optimal sparse networks for synchronization of semiconductor lasers

The inevitable random frequency differences among semiconductor lasers present an obstacle to achieving their collective coherence, but previous worked showed that fully (all-to-all) coupled networks can still be synchronized even in the weakly coupling regime. An outstanding question is whether sparsely coupled network structures exist that lead to strong synchronization. This paper gives an affirmative answer: optimal sparse coupling configurations can be found which enables near-complete synchronization. Quite surprisingly, with respect to synchronization, certain sparse networks can outperform fully coupled networks, when the weights of coupling are placed dominantly on the laser pairs with large frequency differences. The counterintuitive phenomenon can be explained by a thermodynamic potential theory that maps the time-delay-induced phase dynamics to an energy landscape. These findings suggest a scalable and cost-effective approach to achieving robust, steady-state synchronization of semiconductor lasers in the presence of disorder and noise.

physics.optics↗
arXiv2025

Disorder-mediated synchronization resonance in coupled semiconductor lasers

Disorder can profoundly influence synchronization in networks of nonlinear oscillators, sometimes enhancing coherence through external tuning. In semiconductor lasers, however, achieving high-quality steady-state synchronization is desired, while intrinsic and typically uncontrollable disorder poses a major challenge. Under fixed frequency disorder, we investigate homogeneous fully coupled external-cavity semiconductor lasers governed by the complex, time-delayed Lang-Kobayashi equations with experimentally relevant parameters and identify an optimal coupling strength that maximizes steady-state synchronization in the weak-coupling regime, which we term disorder-mediated synchronization resonance. This optimum appears for any fixed configuration of intrinsic frequency detuning and scales inversely with the number of lasers, leading to a linear scaling of the total coupling cost with the number of lasers. A theory based on an effective thermodynamic potential explains this disorder-mediated optimization, revealing a general mechanism by which moderate coupling can overcome static heterogeneity in nonlinear physical systems.

physics.optics↗
arXiv2025

Deficiency of equation-finding approach to data-driven modeling of dynamical systems

Finding the governing equations from data by sparse optimization has become a popular approach to deterministic modeling of dynamical systems. Considering the physical situations where the data can be imperfect due to disturbances and measurement errors, we show that for many chaotic systems, widely used sparse-optimization methods for discovering governing equations produce models that depend sensitively on the measurement procedure, yet all such models generate virtually identical chaotic attractors, leading to a striking limitation that challenges the conventional notion of equation-based modeling in complex dynamical systems. Calculating the Koopman spectra, we find that the different sets of equations agree in their large eigenvalues and the differences begin to appear when the eigenvalues are smaller than an equation-dependent threshold. The results suggest that finding the governing equations of the system and attempting to interpret them physically may lead to misleading conclusions. It would be more useful to work directly with the available data using, e.g., machine-learning methods.

nlin.CD↗
arXiv2025

Optimizing disorder with machine learning to harness synchronization

Disorder is often considered detrimental to coherence. However, under specific conditions, it can enhance synchronization. We develop a machine-learning framework to design optimal disorder configurations that maximize phase synchronization. In particular, utilizing the system of coupled nonlinear pendulums with disorder and noise, we train a feedforward neural network (FNN), with the disorder parameters as input, to predict the Shannon entropy index that quantifies the phase synchronization strength. The trained FNN model is then deployed to search for the optimal disorder configurations in the high-dimensional space of the disorder parameters, providing a computationally efficient replacement of the stochastic differential equation solvers. Our results demonstrate that the FNN is capable of accurately predicting synchronization and facilitates an efficient inverse design solution to optimizing and enhancing synchronization.

nlin.AO↗
arXiv2025

Floquet quantum many-body scars in the tilted Fermi-Hubbard chain

The one-dimensional tilted, periodically driven Fermi-Hubbard chain is a paradigm in the study of quantum many-body physics, particularly for solid-state systems. We uncover the emergence of Floquet scarring states, a class of quantum many-body scarring (QMBS) states that defy random thermalization. The underlying physical mechanism is identified to be the Floquet resonances between these degenerate Fock bases that can be connected by one hopping process. It is the first-order hopping perturbation effect. Utilizing the degenerate Floquet perturbation theory, we derive the exact conditions under which the exotic QMBS states emerge. Phenomena such as quantum revivals and subharmonic responses are also studied. Those results open the possibility of modulating and engineering solid-state quantum many-body systems to achieve nonergodicity.

quant-ph↗
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

Entanglement engineering of optomechanical systems by reinforcement learning

Entanglement is fundamental to quantum information science and technology, yet controlling and manipulating entanglement -- so-called entanglement engineering -- for arbitrary quantum systems remains a formidable challenge. There are two difficulties: the fragility of quantum entanglement and its experimental characterization. We develop a model-free deep reinforcement-learning (RL) approach to entanglement engineering, in which feedback control together with weak continuous measurement and partial state observation is exploited to generate and maintain desired entanglement. We employ quantum optomechanical systems with linear or nonlinear photon-phonon interactions to demonstrate the workings of our machine-learning-based entanglement engineering protocol. In particular, the RL agent sequentially interacts with one or multiple parallel quantum optomechanical environments, collects trajectories, and updates the policy to maximize the accumulated reward to create and stabilize quantum entanglement over an arbitrary amount of time. The machine-learning-based model-free control principle is applicable to the entanglement engineering of experimental quantum systems in general.

quant-ph↗
arXiv2024

Reconstructing dynamics from sparse observations with no training on target system

In applications, an anticipated situation is where the system of interest has never been encountered before and sparse observations can be made only once. Can the dynamics be faithfully reconstructed from the limited observations without any training data? This problem defies any known traditional methods of nonlinear time-series analysis as well as existing machine-learning methods that typically require extensive data from the target system for training. We address this challenge by developing a hybrid transformer and reservoir-computing machine-learning scheme. The key idea is that, for a complex and nonlinear target system, the training of the transformer can be conducted not using any data from the target system, but with essentially unlimited synthetic data from known chaotic systems. The trained transformer is then tested with the sparse data from the target system. The output of the transformer is further fed into a reservoir computer for predicting the long-term dynamics or the attractor of the target system. The power of the proposed hybrid machine-learning framework is demonstrated using a large number of prototypical nonlinear dynamical systems, with high reconstruction accuracy even when the available data is only 20% of that required to faithfully represent the dynamical behavior of the underlying system. The framework provides a paradigm of reconstructing complex and nonlinear dynamics in the extreme situation where training data does not exist and the observations are random and sparse.

cs.LG↗
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↗
arXiv2024

High-order exceptional points and stochastic resonance in pseudo-Hermitian systems

Exceptional points, a remarkable phenomenon in physical systems, have been exploited for sensing applications. It has been demonstrated recently that it can also utilize as sensory threshold in which the interplay between exceptional-point dynamics and noise can lead to enhanced performance. Most existing works focused on second-order exceptional points. We investigate the stochastic dynamics associated with high-order exceptional points with a particular eye towards optimizing sensing performance by developing a theoretical framework based on pseudo-Hermiticity. Our analysis reveals three distinct types of frequency responses to external perturbations. A broad type of stochastic resonance is uncovered where, as the noise amplitude increases, the signal-to-noise ratio reaches a global maximum rapidly but with a slow decaying process afterwards, indicating achievable high performance in a wide range of the noise level. These results suggest that stochastic high-order exceptional-point dynamics can be exploited for applications in signal processing and sensor technologies.

physics.app-ph↗
arXiv2024

Kolmogorov-Arnold Network Autoencoders

Deep learning models have revolutionized various domains, with Multi-Layer Perceptrons (MLPs) being a cornerstone for tasks like data regression and image classification. However, a recent study has introduced Kolmogorov-Arnold Networks (KANs) as promising alternatives to MLPs, leveraging activation functions placed on edges rather than nodes. This structural shift aligns KANs closely with the Kolmogorov-Arnold representation theorem, potentially enhancing both model accuracy and interpretability. In this study, we explore the efficacy of KANs in the context of data representation via autoencoders, comparing their performance with traditional Convolutional Neural Networks (CNNs) on the MNIST, SVHN, and CIFAR-10 datasets. Our results demonstrate that KAN-based autoencoders achieve competitive performance in terms of reconstruction accuracy, thereby suggesting their viability as effective tools in data analysis tasks.

cs.LG↗
arXiv2024

Learning to learn ecosystems from limited data -- a meta-learning approach

A fundamental challenge in developing data-driven approaches to ecological systems for tasks such as state estimation and prediction is the paucity of the observational or measurement data. For example, modern machine-learning techniques such as deep learning or reservoir computing typically require a large quantity of data. Leveraging synthetic data from paradigmatic nonlinear but non-ecological dynamical systems, we develop a meta-learning framework with time-delayed feedforward neural networks to predict the long-term behaviors of ecological systems as characterized by their attractors. We show that the framework is capable of accurately reconstructing the ``dynamical climate'' of the ecological system with limited data. Three benchmark population models in ecology, namely the Hastings-Powell model, a three-species food chain, and the Lotka-Volterra system, are used to demonstrate the performance of the meta-learning based prediction framework. In all cases, enhanced accuracy and robustness are achieved using five to seven times less training data as compared with the corresponding machine-learning method trained solely from the ecosystem data. A number of issues affecting the prediction performance are addressed.

q-bio.QM↗
arXiv2024

Data-driven model discovery with Kolmogorov-Arnold networks

Data-driven model discovery of complex dynamical systems is typically done using sparse optimization, but it has a fundamental limitation: sparsity in that the underlying governing equations of the system contain only a small number of elementary mathematical terms. Examples where sparse optimization fails abound, such as the classic Ikeda or optical-cavity map in nonlinear dynamics and a large variety of ecosystems. Exploiting the recently articulated Kolmogorov-Arnold networks, we develop a general model-discovery framework for any dynamical systems including those that do not satisfy the sparsity condition. In particular, we demonstrate non-uniqueness in that a large number of approximate models of the system can be found which generate the same invariant set with the correct statistics such as the Lyapunov exponents and Kullback-Leibler divergence. An analogy to shadowing of numerical trajectories in chaotic systems is pointed out.

cs.LG↗