arXiv subjects

Ying-Cheng Lai

Publications and source records attributed to Ying-Cheng Lai.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2024

Geometry-induced wavefunction collapse

When a quantum particle moves in a curved space, a geometric potential can arise. In spite of a long history of extensive theoretical studies, to experimentally observe the geometric potential remains to be a challenge. What are the physically observable consequences of such a geometric potential? Solving the Schrodinger equation on a truncated conic surface, we uncover a class of quantum scattering states that bear a strong resemblance with the quasi-resonant states associated with atomic collapse about a Coulomb impurity, a remarkable quantum phenomenon in which an infinite number of quasi-resonant states emerge. A characteristic defining feature of such collapse states is the infinite oscillations of the local density of states (LDOS) about the zero energy point separating the scattering from the bound states. The emergence of such states in the curved (Riemannian) space requires neither a relativistic quantum mechanism nor any Coulomb impurity: they have zero angular momentum and their origin is purely geometrical - henceforth the term geometry-induced wavefunction collapse. We establish the collapsing nature of these states through a detailed comparative analysis of the behavior of the LDOS for both the zero and finite angular-momentum states as well as the corresponding classical picture. Potential experimental schemes to realize the geometry-induced collapse states are articulated. Not only has our study uncovered an intrinsic connection between the geometric potential and atomic collapse, it also provides a method to experimentally observe and characterize geometric potentials arising from different subfields of physics. For example, in nanoscience and nanotechnology, curved geometry has become increasingly common. Our finding suggests that wavefunction collapse should be an important factor of consideration in designing and developing nanodevices.

quant-ph↗

arXiv2024

Irregular Bloch Zener oscillations in two-dimensional flat-band Dirac materials

When a static electrical field is applied to a two-dimensional (2D) Dirac material, Landau-Zener transition (LZT) and Bloch-Zener oscillations can occur. Employing alpha-T3 lattices as a paradigm for a broad class of 2D Dirac materials, we uncover two phenomena. First, due to the arbitrarily small energy gaps near a Dirac point that make it more likely for LZTs to occur than in other regions of the Brillouin zone, the distribution of differential LZT probability in the momentum space can form a complicated morphological pattern. Second, a change in the LZT morphology as induced by a mutual switching of the two distinct Dirac points can lead to irregular Bloch-Zener oscillations characterized by a non-smooth behavior in the time evolution of the electrical current density associated with the oscillation. These phenomena are due to mixed interference of quantum states in multiple bands modulated by the geometric and dynamic phases. We demonstrate that the adiabatic-impulse model describing Landau-Zener-Stuckelberg interferometry can be exploited to calculate the phases, due to the equivalence between the alpha-T3 lattice subject to a constant electrical field and strongly periodically driven two- or three-level systems. The degree of irregularity of Bloch-Zener oscillations can be harnessed by selecting the morphology pattern, which is potentially experimentally realizable.

cond-mat.mes-hall↗

arXiv2024

Spin-dependent edge states in two-dimensional Dirac materials with a flat band

The phenomenon of spin-dependent quantum scattering in two-dimensional (2D) pseudospin-1/2 Dirac materials leading to a relativistic quantum chimera was recently uncovered. We investigate spin-dependent Dirac electron optics in 2D pseudospin-1 Dirac materials, where the energy-band structure consists of a pair of Dirac cones and a flat band. In particular, with a suitable combination of external electric fields and a magnetic exchange field, electrons with a specific spin orientation (e.g., spin-down) can be trapped in a class of long-lived edge modes, generating resonant scattering. The spin-dependent edge states are a unique feature of flat-band Dirac materials and have no classical correspondence. However, electrons with the opposite spin (i.e., spin up) undergo conventional quantum scattering with a classical correspondence, which can be understood in the framework of Dirac electron optics. A consequence is that the spin-down electrons produce a large scattering probability with broad scattering angle distribution in both near- and far-field regions, while the spin-up electrons display the opposite behavior. Such characteristically different behaviors of the electrons with opposite spins lead to spin polarization that can be as high as nearly 100%.

cond-mat.mes-hall↗

arXiv2024

An experimental scheme for determining the Berry phase in two-dimensional quantum materials with a flat band

Experimentally feasible methods to determine the Berry phase, a fundamental quantity characterizing a quantum material, are often needed in applications. We develop an approach to detecting the Berry phase by using a class of two-dimensional (2D) Dirac materials with a flat band, the $α$-$\mathcal{T}_3$ lattices. The properties of this class of quantum materials are controlled by a single parameter $0 \le α\le 1$, where the left and right endpoints correspond to graphene with pseudospin-1/2 and the dice lattice with pseudospin-1 Dirac-Weyl quasiparticles, respectively, and each specific value of $α$ represents a material with a unique Berry phase. Applying a constant electric field to the $α$-$\mathcal{T}_3$ lattice, we calculate the resulting electric current and find a one-to-one correspondence between the current and the Berry phase in both the linear and nonlinear response regimes. In the linear (Kubo) regime, the main physics is the Zitterbewegung effect. In the nonlinear regime, the Schwinger mechanism dominates. Beyond the nonlinear regime, Bloch-Zener oscillations can arise. Measuring the current thus provides an effective and experimentally feasible way to determine the Berry phase for this spectrum of 2D quantum materials.

cond-mat.mes-hall↗

arXiv2024

Deep-learning design of graphene metasurfaces for quantum control and Dirac electron holography

Metasurfaces are sub-wavelength patterned layers for controlling waves in physical systems. In optics, meta-surfaces are created by materials with different dielectric constants and are capable of unconventional functionalities. We develop a deep-learning framework for Dirac-material metasurface design for controlling electronic waves. The metasurface is a configuration of circular graphene quantum dots, each created by an electric potential. Employing deep convolutional neural networks, we show that the original scattering wave can be reconstructed with fidelity over 95$\%$, suggesting the feasibility of Dirac electron holography. Additional applications such as plane wave generation, designing broadband, and multi-functionality graphene metasurface systems are illustrated.

physics.comp-ph↗

arXiv2024

Optical properties of two dimensional Dirac Weyl materials with a flatband

The emergence of a flat band in Dirac-Weyl materials offers new possibilities for electronic transitions, leading to stronger interaction with light. As a result, the optical conductivity can be significantly enhanced in these flat-band materials as compared with graphene, making them potentially better candidates for optical sensing and modulation. Recently, a comprehensive theory for the optical conductivity of a spectrum of flat-band Dirac-Weyl materials has been developed, with explicit formulas for both the real and imaginary parts of the conductivity derived through two independent approaches. This Perspective offers a review of the development. An understanding of the optical properties of the flat-band Dirac-Weyl materials paves the way for optical device applications in the terahertz-frequency domain.

physics.optics↗

arXiv2024

Random forests for detecting weak signals and extracting physical information: a case study of magnetic navigation

It was recently demonstrated that two machine-learning architectures, reservoir computing and time-delayed feed-forward neural networks, can be exploited for detecting the Earth's anomaly magnetic field immersed in overwhelming complex signals for magnetic navigation in a GPS-denied environment. The accuracy of the detected anomaly field corresponds to a positioning accuracy in the range of 10 to 40 meters. To increase the accuracy and reduce the uncertainty of weak signal detection as well as to directly obtain the position information, we exploit the machine-learning model of random forests that combines the output of multiple decision trees to give optimal values of the physical quantities of interest. In particular, from time-series data gathered from the cockpit of a flying airplane during various maneuvering stages, where strong background complex signals are caused by other elements of the Earth's magnetic field and the fields produced by the electronic systems in the cockpit, we demonstrate that the random-forest algorithm performs remarkably well in detecting the weak anomaly field and in filtering the position of the aircraft. With the aid of the conventional inertial navigation system, the positioning error can be reduced to less than 10 meters. We also find that, contrary to the conventional wisdom, the classic Tolles-Lawson model for calibrating and removing the magnetic field generated by the body of the aircraft is not necessary and may even be detrimental for the success of the random-forest method.

eess.SP↗

arXiv2023

Rate-induced tipping in complex high-dimensional ecological networks

In an ecosystem, environmental changes as a result of natural and human processes can cause some key parameters of the system to change with time. Depending on how fast such a parameter changes, a tipping point can occur. Existing works on rate-induced tipping, or R-tipping, offered a theoretical way to study this phenomenon but from a local dynamical point of view, revealing, e.g., the existence of a critical rate for some specific initial condition above which a tipping point will occur. As ecosystems are subject to constant disturbances and can drift away from their equilibrium point, it is necessary to study R-tipping from a global perspective in terms of the initial conditions in the entire relevant phase space region. In particular, we introduce the notion of the probability of R-tipping defined for initial conditions taken from the whole relevant phase space. Using a number of real-world, complex mutualistic networks as a paradigm, we discover a scaling law between this probability and the rate of parameter change and provide a geometric theory to explain the law. The real-world implication is that even a slow parameter change can lead to a system collapse with catastrophic consequences. In fact, to mitigate the environmental changes by merely slowing down the parameter drift may not always be effective: only when the rate of parameter change is reduced to practically zero would the tipping be avoided. Our global dynamics approach offers a more complete and physically meaningful way to understand the important phenomenon of R-tipping.

q-bio.PE↗

arXiv2023

Machine-learning parameter tracking with partial state observation

Complex and nonlinear dynamical systems often involve parameters that change with time, accurate tracking of which is essential to tasks such as state estimation, prediction, and control. Existing machine-learning methods require full state observation of the underlying system and tacitly assume adiabatic changes in the parameter. Formulating an inverse problem and exploiting reservoir computing, we develop a model-free and fully data-driven framework to accurately track time-varying parameters from partial state observation in real time. In particular, with training data from a subset of the dynamical variables of the system for a small number of known parameter values, the framework is able to accurately predict the parameter variations in time. Low- and high-dimensional, Markovian and non-Markovian nonlinear dynamical systems are used to demonstrate the power of the machine-learning based parameter-tracking framework. Pertinent issues affecting the tracking performance are addressed.

cs.LG↗

arXiv2023

Digital twins of nonlinear dynamical systems: A perspective

Digital twins have attracted a great deal of recent attention from a wide range of fields. A basic requirement for digital twins of nonlinear dynamical systems is the ability to generate the system evolution and predict potentially catastrophic emergent behaviors so as to providing early warnings. The digital twin can then be used for system "health" monitoring in real time and for predictive problem solving. In particular, if the digital twin forecasts a possible system collapse in the future due to parameter drifting as caused by environmental changes or perturbations, an optimal control strategy can be devised and executed as early intervention to prevent the collapse. Two approaches exist for constructing digital twins of nonlinear dynamical systems: sparse optimization and machine learning. The basics of these two approaches are described and their advantages and caveats are discussed.

cs.LG↗

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↗

arXiv2023

Validity of Markovian modeling for transient memory-dependent epidemic dynamics

The initial transient phase of an emerging epidemic is of critical importance for data-driven model building, model-based prediction of the epidemic trend, and articulation of control/prevention strategies. In principle, quantitative models for real-world epidemics need to be memory-dependent or non-Markovian, but this presents difficulties for data collection, parameter estimation, computation and analyses. In contrast, the difficulties do not arise in the traditional Markovian models. To uncover the conditions under which Markovian and non-Markovian models are equivalent for transient epidemic dynamics is outstanding and of significant current interest. We develop a comprehensive computational and analytic framework to establish that the transient-state equivalence holds when the average generation time matches and average removal time, resulting in minimal Markovian estimation errors in the basic reproduction number, epidemic forecasting, and evaluation of control strategy. Strikingly, the errors depend on the generation-to-removal time ratio but not on the specific values and distributions of these times, and this universality will further facilitate estimation rectification. Overall, our study provides a general criterion for modeling memory-dependent processes using the Markovian frameworks.

physics.soc-ph↗

arXiv2022

Generating extreme quantum scattering in graphene with machine learning

Graphene quantum dots provide a platform for manipulating electron behaviors in two-dimensional (2D) Dirac materials. Most previous works were of the "forward" type in that the objective was to solve various confinement, transport and scattering problems with given structures that can be generated by, e.g., applying an external electrical field. There are applications such as cloaking or superscattering where the challenging problem of inverse design needs to be solved: finding a quantum-dot structure according to certain desired functional characteristics. A brute-force search of the system configuration based directly on the solutions of the Dirac equation is computational infeasible. We articulate a machine-learning approach to addressing the inverse-design problem where artificial neural networks subject to physical constraints are exploited to replace the rigorous Dirac equation solver. In particular, we focus on the problem of designing a quantum dot structure to generate both cloaking and superscattering in terms of the scattering efficiency as a function of the energy. We construct a physical loss function that enables accurate prediction of the scattering characteristics. We demonstrate that, in the regime of Klein tunneling, the scattering efficiency can be designed to vary over two orders of magnitudes, allowing any scattering curve to be generated from a proper combination of the gate potentials. Our physics-based machine-learning approach can be a powerful design tool for 2D Dirac material-based electronics.

cond-mat.mes-hall↗

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↗

arXiv2022

Machine learning prediction of network dynamics with privacy protection

Predicting network dynamics based on data, a problem with broad applications, has been studied extensively in the past, but most existing approaches assume that the complete set of historical data from the whole network is available. This requirement presents a great challenge in applications, especially for large, distributed networks in the real world, where data collection is accomplished by many clients in a parallel fashion. Often, each client only has the time series data from a partial set of nodes and the client has access to only partial timestamps of the whole time series data and partial structure of the network. Due to privacy concerns or license related issues, the data collected by different clients cannot be shared. To accurately predict the network dynamics while protecting the privacy of different parties is a critical problem in the modern time. Here, we propose a solution based on federated graph neural networks (FGNNs) that enables the training of a global dynamic model for all parties without data sharing. We validate the working of our FGNN framework through two types of simulations to predict a variety of network dynamics (four discrete and three continuous dynamics). As a significant real-world application, we demonstrate successful prediction of State-wise influenza spreading in the USA. Our FGNN scheme represents a general framework to predict diverse network dynamics through collaborative fusing of the data from different parties without disclosing their privacy.

physics.soc-ph↗