Ying-Cheng Lai

• Doctor of Philosophy
• Regents Professor at Arizona State University

The successful integration of engineered gene circuits into host cells remains a significant challenge in synthetic biology due to circuit–host interactions, such as growth feedback, where the circuit influences cell growth and vice versa. Understanding the dynamics of circuit failures and identifying topologies resilient to growth feedback are cru...

In complex dynamical networks, the resilience of the individual nodes against perturbation and their influence on the network dynamics are of great interest and have been actively investigated. We consider situations where the coupling dynamics are separable, which arise in certain classes of dynamical processes including epidemic spreading, popula...

In nonautonomous dynamical systems, rate-induced tipping (R-tipping) is a critical transition triggered by the rate of change of a time-varying parameter, rather than its absolute value. In recent years, there is a growing interest in R-tipping due to its relevance to significant problems of current interest, such as potential, catastrophic collaps...

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 feedf...

Data-driven model discovery of complex dynamical systems can be 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 functions. Examples where sparse optimization fails abound, including the classic Ikeda or optic...

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 t...

Finding optimal control strategies to suppress quantum thermalization for arbitrarily initial states, the so-called quantum nonergodicity control, is important for quantum information science and technologies. Previous control methods relied largely on theoretical model of the target quantum system, but invertible model approximations and inaccurac...

In the study of nonlinear dynamics and chaos, analytically solvable physical models are rare. We investigate the classical motion of a trapped relativistic particle, subject to an electric and a magnetic field. When the directions of the electric and magnetic fields coincide, the dynamics are integrable. As the magnetic field rotates away from the...

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 dee...

The ever-increasing complexity of modern power grids makes them vulnerable to cyber and/or physical attacks. To protect them, accurate attack detection is essential. A challenging scenario is that a localized attack has occurred on a specific transmission line but only a small number of transmission lines elsewhere can be monitored. That is, full s...

In applications, an anticipated issue 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? We address this challenge by developing a hybrid transformer and reservoir-computing scheme. The transformer is trained without using data from the targe...

The successful integration of engineered gene circuits into host cells remains a significant challenge in synthetic biology due to circuit-host interactions, such as growth feedback, where the circuit influences cell growth and vice versa. Understanding the dynamics of circuit failures and identifying topologies resilient to growth feedback are cru...

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...

A foundational machine-learning architecture is reinforcement learning, where an outstanding problem is achieving an optimal balance between exploration and exploitation. Specifically, exploration enables the agents to discover optimal policies in unknown domains of the environment for gaining potentially large future rewards, while exploitation re...

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 oscill...

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 a...

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 p...

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...

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 da...

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 optic...

The Atlantic Meridional Overturning Circulation (AMOC) is a significant component of the global ocean system, which has so far ensured a relatively warm climate for the North Atlantic and mild conditions in regions, such as Western Europe. The AMOC is also critical for the global climate. The complexity of the dynamical system underlying the AMOC i...

Metasurfaces are sub-wavelength patterned layers for controlling waves in physical systems. In optics, metasurfaces 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 metasurfa...

Finding optimal control strategies to suppress quantum thermalization for arbitrarily initial states, the so-called quantum nonergodicity control, is important for quantum information science and technologies. Previous control methods largely relied on theoretical model of the target quantum system, but invertible model approximations and inaccurac...

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−T3 lattices. The properties of this class of quantum materials...

Identifying and understanding various causal relations are fundamental to climate dynamics for improving the predictive capacity of Earth system modeling. In particular, causality in Earth systems has manifest temporal periodicities, like physical climate variabilities. To unravel the characteristic frequency of causality in climate dynamics, we de...

Traditional neural network models of associative memories were used to store and retrieve static patterns. We develop reservoir-computing based memories for complex dynamical attractors, under two common recalling scenarios in neuropsychology: location-addressable with an index channel and content-addressable without such a channel. We demonstrate...

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 deep rei...

Reinforcement learning (RL) has been employed to devise the best course of actions in defending the critical infrastructures, such as power networks against cyberattacks. Nonetheless, even in the case of the smallest power grids, the action space of RL experiences exponential growth, rendering efficient exploration by the RL agent practically unatt...

A problem in nonlinear and complex dynamical systems with broad applications is forecasting the occurrence of a critical transition based solely on data without knowledge about the system equations. When such a transition leads to system collapse, as often is the case, all the available data are from the pre-critical regime where the system still f...

Reconstructing complex networks and predicting the dynamics are particularly challenging in real-world applications because the available information and data are incomplete. We develop a unified collaborative deep-learning framework consisting of three modules: network inference, state estimation, and dynamical learning. The complete network struc...

Identifying hidden states in nonlinear physical systems that evade direct experimental detection is important as disturbances and noises can place the system in a hidden state with detrimental consequences. We study a cavity magnonic system whose main physics is photon and magnon Kerr effects. Sweeping a bifurcation parameter in numerical experimen...

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. Quantitative models for real-world epidemics need to be memory-dependent or non-Markovian, but this presents difficulties for data collection,...

It has been 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 corre...

Global climate change has been shown to cause longer, more intense, and frequent heatwaves, of which anthropogenic stressors concentrated in urban areas are a critical contributor. In this study, we investigate the causal interactions during heatwaves across 520 urban sites in the U.S. combining complex network and causal analysis. The presence of...

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 in...

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-T3 lattices. The properties of this class of quantum materials...

The emergence of a flatband 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 flatband materials as compared with graphene, making them potentially better candidates for optical sensing and modulation....

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 dynami...

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 par...

The integration of computing and communication capabilities into the power grid has led to vulnerabilities enabling attackers to launch cyberattacks on the grid. The resources that can be deployed to protect a power grid are limited, rendering the need to impose preferences and priorities in optimal resource allocation. Due to the complexity of mod...

Traditional neural-network models of associative memories were for storing and retrieving static patterns. We develop reservoir-computing based memories for complex dynamical attractors, under two common recalling scenarios in neuropsychology: location-addressable with an index channel and context-addressable without such a channel. We demonstrate...

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 provide early warnings. The digital twin can then be used for system “health”...

In our modern time, travel has become one of the most significant factors contributing to global epidemic spreading. A deficiency in the literature is that travel has largely been treated as a Markovian process: it occurs instantaneously without any memory effect. To provide informed policies such as determining the mandatory quarantine time, the n...

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 tw...

The challenging problem of network reconstruction from dynamical data can in general be formulated as an optimization task of solving multiple linear equations. Existing approaches are of the two types: Point-by-point (PBP) and global methods. The local PBP method is computationally efficient, but the accuracies of its solutions are somehow low, wh...

Traditionally, mathematical modelling of population dynamics was focused on long-term, asymptotic behaviour (systems attractors), whereas the effects of transient regimes were largely disregarded. However, recently there has been a growing appreciation of the role of transients both in empirical ecology and theoretical studies. Among the main chall...

The benefits of noise to applications of nonlinear dynamical systems through mechanisms such as stochastic and coherence resonances have been well documented. Recent years have witnessed a growth of research in exploiting machine learning to predict nonlinear dynamical systems. It has been known that noise can act as a regularizer to improve the tr...

The successful integration of engineered gene circuits into host cells remains a significant challenge in synthetic biology due to circuit-host interactions, such as growth feedback, where the circuit influences cell growth and vice versa. Understanding the dynamics of circuit failures and identifying topologies resilient to growth feedback are cru...

The successful integration of engineered gene circuits into host cells remains a significant challenge in synthetic biology due to circuit-host interactions, such as growth feedback, where the circuit influences cell growth and vice versa. Understanding the dynamics of circuit failures and identifying topologies resilient to growth feedback are cru...

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 dat...

A remarkable phenomenon in contemporary physics is quantum scarring in systems whose classical dynamics are chaotic, where certain wave functions tend to concentrate on classical periodic orbits of low periods. Quantum scarring has been studied for more than four decades, but detecting quantum scars still mostly relies on human visualization of the...

The successful integration of engineered gene circuits into host cells remains a significant challenge in synthetic biology due to circuit-host interactions, such as growth feedback, where the circuit influences cell growth and vice versa. Understanding the dynamics of circuit failures and identifying topologies resilient to growth feedback are cru...

In the classic Kuramoto system of coupled two-dimensional rotators, chimera states characterized by the coexistence of synchronous and asynchronous groups of oscillators are long-lived because the average lifetime of these states increases exponentially with the system size. Recently, it was discovered that, when the rotators in the Kuramoto model...

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 tw...

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 α−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...

Detecting a weak physical signal immersed in overwhelming noises entails separating the two, a task for which machine learning is naturally suited. In principle, such a signal is generated by a nonlinear dynamical system of intrinsically high dimension for which a mathematical model is not available, rendering unsuitable traditional linear or nonli...

We articulate the design imperatives for machine learning based digital twins for nonlinear dynamical systems, which can be used to monitor the “health” of the system and anticipate future collapse. The fundamental requirement for digital twins of nonlinear dynamical systems is dynamical evolution: the digital twin must be able to evolve its dynami...

Plain Language Summary Successful detection of causality in complex systems is important to unraveling the underlying mechanisms of system dynamics. The dynamic interactions in Earth's climate system are often nonlinear, weakly or moderately coupled, and essentially non‐separable, which renders conventional approaches of causal inference, such as s...

In the field of quantum chaos, spectral statistics is one of the most extensively investigated characteristics. Despite a large body of existing literature, the effects of many-body interactions on the spectral statistics of relativistic quantum systems remain poorly understood. Treating electron-electron interactions through the one-orbital mean-f...

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. T...

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. Th...

A key to ensuring the security of smart electrical power grids is to devise and deploy effective defense strategies against cyberattacks. To achieve this goal, an essential task is to simulate and understand the dynamic interplay between the attacker and defender, for which stochastic game theory and reinforcement learning stand out as a powerful m...

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 i...

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...

The quantification of cross-regional interactions for the atmospheric transport processes is of crucial importance to improve the predictive capacity of climatic and environmental system modeling. The dynamic interactions in these complex systems are often nonlinear and non-separable, making conventional approaches of causal inference, such as stat...

Quantum many-body scarring (QMBS) is a recently discovered form of weak ergodicity breaking in strongly interacting quantum systems, which presents opportunities for mitigating thermalization-induced decoherence in quantum information processing applications. However, the existing experimental realizations of QMBS are based on systems with specific...

A tipping point presents perhaps the single most significant threat to an ecological system as it can lead to abrupt species extinction on a massive scale. Climate changes leading to the species decay parameter drifts can drive various ecological systems towards a tipping point. We investigate the tipping-point dynamics in multi-layer ecological ne...

It is evident that increasing the intensive-care-unit (ICU) capacity and giving priority to admitting and treating patients will reduce the number of COVID-19 deaths, but the quantitative assessment of these measures has remained inadequate. We develop a comprehensive, non-Markovian state transition model, which is validated through the accurate pr...

Symmetries, due to their fundamental importance to dynamical processes on networks, have attracted a great deal of current research. Finding all symmetric nodes in large complex networks typically relies on automorphism groups from algebraic-group theory, which are solvable in quasipolynomial time. We articulate a conceptually appealing and computa...

Thirty-five years ago, Sir Michael Berry and his collaborator Mondragon studied the behaviors of neutrino, a massless relativistic quantum particle, in a classically chaotic billiard - the neutrino billiard problem. To celebrate Sir Michael Berry's eightieth birthday, here we report results on the role of geometric symmetries of the billiard system...

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 a challenge. What are the physically observable consequences of such a geometric potential? Solving the Schrödinger equation on a truncated conic sur...

Boolean networks introduced by Kauffman, originally intended as a prototypical model for gaining insights into gene regulatory dynamics, have become a paradigm for understanding a variety of complex systems described by binary state variables. However, there are situations, e.g., in biology, where a binary state description of the underlying dynami...

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...

The inverse problem of estimating the background potential from measurements of the local density of states (LDOS) is a challenging issue in quantum mechanics. Even harder is doing this estimation using approximate methods such as scanning gate microscopy (SGM). Here we propose a machine-learning-based solution by exploiting adaptive cellular neura...

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...

Previous efforts on data-based reconstruction focused on complex networks with pairwise or two-body interactions. There is a growing interest in networks with higher-order or many-body interactions, raising the need to reconstruct such networks based on observational data. We develop a general framework combining statistical inference and expectati...

Data based detection and quantification of causation in complex, nonlinear dynamical systems is of paramount importance to science, engineering and beyond. Inspired by the widely used methodology in recent years, the cross-map-based techniques, we develop a general framework to advance towards a comprehensive understanding of dynamical causal mecha...

The mathematical framework of stochastically adaptive feedback control, which is generally applicable to significant problems in nonlinear dynamics such as stabilization and synchronization, has been previously established but only for systems whose vector fields satisfy the global Lipschitzian condition. Nonlinear dynamical systems arising from ph...

We develop a framework based on the deep convolutional neural network (DCNN) for model-free prediction of the occurrence of extreme events both in time (“when”) and in space (“where”) in nonlinear physical systems of spatial dimension two. The measurements or data are a set of two-dimensional snapshots or images. For a desired time horizon of predi...

Two-dimensional Dirac materials with a flat band have been demonstrated to possess a plethora of unusual electronic properties, but the optical properties of these materials are less studied. Utilizing α−T3 lattice as a prototypical system, where 0≤α≤1 is a tunable parameter and a flat band through the conic intersection of two Dirac cones arises f...

We uncover a phenomenon in coupled nonlinear networks with a symmetry: as a bifurcation parameter changes through a critical value, synchronization among a subset of nodes can deteriorate abruptly, and, simultaneously, perfect synchronization emerges suddenly among a different subset of nodes that are not directly connected. This is a synchronizati...

We develop a deep convolutional neural network (DCNN) based framework for model-free prediction of the occurrence of extreme events both in time ("when") and in space ("where") in nonlinear physical systems of spatial dimension two. The measurements or data are a set of two-dimensional snapshots or images. For a desired time horizon of prediction,...