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Description
Predicting nonlinear dynamical systems has been a long-standing challenge in science. This field is currently witnessing a revolution with the advent of machine learning methods. Concurrently, the analysis of dynamics in various nonlinear complex systems continues to be crucial. Guided by these directions, I conduct the following studies. Predicting critical transitions and transient states in nonlinear dynamics is a complex problem. I developed a solution called parameter-aware reservoir computing, which uses machine learning to track how system dynamics change with a driving parameter. I show that the transition point can be accurately predicted while trained in a sustained functioning regime before the transition. Notably, it can also predict if the system will enter a transient state, the distribution of transient lifetimes, and their average before a final collapse, which are crucial for management. I introduce a machine-learning-based digital twin for monitoring and predicting the evolution of externally driven nonlinear dynamical systems, where reservoir computing is exploited. Extensive tests on various models, encompassing optics, ecology, and climate, verify the approach’s effectiveness. The digital twins can extrapolate unknown system dynamics, continually forecast and monitor under non-stationary external driving, infer hidden variables, adapt to different driving waveforms, and extrapolate bifurcation behaviors across varying system sizes. Integrating engineered gene circuits into host cells poses a significant challenge in synthetic biology due to circuit-host interactions, such as growth feedback. I conducted systematic studies on hundreds of circuit structures exhibiting various functionalities, and identified a comprehensive categorization of growth-induced failures. I discerned three dynamical mechanisms behind these circuit failures. Moreover, my comprehensive computations reveal a scaling law between the circuit robustness and the intensity of growth feedback. A class of circuits with optimal robustness is also identified. Chimera states, a phenomenon of symmetry-breaking in oscillator networks, traditionally have transient lifetimes that grow exponentially with system size. However, my research on high-dimensional oscillators leads to the discovery of ’short-lived’ chimera states. Their lifetime increases logarithmically with system size and decreases logarithmically with random perturbations, indicating a unique fragility. To understand these states, I use a transverse stability analysis supported by simulations.
ContributorsKong, Lingwei (Author) / Lai, Ying-Cheng (Thesis advisor) / Tian, Xiaojun (Committee member) / Papandreou-Suppappola, Antonia (Committee member) / Alkhateeb, Ahmed (Committee member) / Arizona State University (Publisher)
Created2023
Description
Complex dynamical systems are the kind of systems with many interacting components that usually have nonlinear dynamics. Those systems exist in a wide range of disciplines, such as physical, biological, and social fields. Those systems, due to a large amount of interacting components, tend to possess very high dimensionality. Additionally, due to the intrinsic nonlinear dynamics, they have tremendous rich system behavior, such as bifurcation, synchronization, chaos, solitons. To develop methods to predict and control those systems has always been a challenge and an active research area.
My research mainly concentrates on predicting and controlling tipping points (saddle-node bifurcation) in complex ecological systems, comparing linear and nonlinear control methods in complex dynamical systems. Moreover, I use advanced artificial neural networks to predict chaotic spatiotemporal dynamical systems. Complex networked systems can exhibit a tipping point (a “point of no return”) at which a total collapse occurs. Using complex mutualistic networks in ecology as a prototype class of systems, I carry out a dimension reduction process to arrive at an effective two-dimensional (2D) system with the two dynamical variables corresponding to the average pollinator and plant abundances, respectively. I demonstrate that, using 59 empirical mutualistic networks extracted from real data, our 2D model can accurately predict the occurrence of a tipping point even in the presence of stochastic disturbances. I also develop an ecologically feasible strategy to manage/control the tipping point by maintaining the abundance of a particular pollinator species at a constant level, which essentially removes the hysteresis associated with tipping points.
Besides, I also find that the nodal importance ranking for nonlinear and linear control exhibits opposite trends: for the former, large degree nodes are more important but for the latter, the importance scale is tilted towards the small-degree nodes, suggesting strongly irrelevance of linear controllability to these systems. Focusing on a class of recurrent neural networks - reservoir computing systems that have recently been exploited for model-free prediction of nonlinear dynamical systems, I uncover a surprising phenomenon: the emergence of an interval in the spectral radius of the neural network in which the prediction error is minimized.
My research mainly concentrates on predicting and controlling tipping points (saddle-node bifurcation) in complex ecological systems, comparing linear and nonlinear control methods in complex dynamical systems. Moreover, I use advanced artificial neural networks to predict chaotic spatiotemporal dynamical systems. Complex networked systems can exhibit a tipping point (a “point of no return”) at which a total collapse occurs. Using complex mutualistic networks in ecology as a prototype class of systems, I carry out a dimension reduction process to arrive at an effective two-dimensional (2D) system with the two dynamical variables corresponding to the average pollinator and plant abundances, respectively. I demonstrate that, using 59 empirical mutualistic networks extracted from real data, our 2D model can accurately predict the occurrence of a tipping point even in the presence of stochastic disturbances. I also develop an ecologically feasible strategy to manage/control the tipping point by maintaining the abundance of a particular pollinator species at a constant level, which essentially removes the hysteresis associated with tipping points.
Besides, I also find that the nodal importance ranking for nonlinear and linear control exhibits opposite trends: for the former, large degree nodes are more important but for the latter, the importance scale is tilted towards the small-degree nodes, suggesting strongly irrelevance of linear controllability to these systems. Focusing on a class of recurrent neural networks - reservoir computing systems that have recently been exploited for model-free prediction of nonlinear dynamical systems, I uncover a surprising phenomenon: the emergence of an interval in the spectral radius of the neural network in which the prediction error is minimized.
ContributorsJiang, Junjie (Author) / Lai, Ying-Cheng (Thesis advisor) / Papandreou-Suppappola, Antonia (Committee member) / Wang, Xiao (Committee member) / Zhang, Yanchao (Committee member) / Arizona State University (Publisher)
Created2020