Research

Based on a recurrent neural network (RNN) framework called reservoir computing (RC), we develop a 'parameter-aware RC' approach. We use it to learn the dynamics of nonlinear systems in a parameter range and to extrapolate their dynamics to nearby parameter regions to anticipate potential qualitative changes in the system dynamics caused by small parameter drifts. Our approach has been applied in anticipating critical transition, transient chaos, synchronization, and amplitude death in various simulated models.

Relevant Publications:

Kong, Ling-Wei, Hua-Wei Fan, Celso Grebogi, and Ying-Cheng Lai. "Machine learning prediction of critical transition and system collapse." Physical Review Research 3, no. 1 (2021): 013090.

Fan, Huawei, Ling-Wei Kong, Ying-Cheng Lai, and Xingang Wang. "Anticipating synchronization with machine learning." Physical Review Research 3, no. 2 (2021): 023237.

Kong, Ling-Wei, Huawei Fan, Celso Grebogi, and Ying-Cheng Lai. "Emergence of transient chaos and intermittency in machine learning." Journal of Physics: Complexity 2, no. 3 (2021): 035014.

Xiao, Rui, Ling-Wei Kong, Zhong-Kui Sun, and Ying-Cheng Lai. "Predicting amplitude death with machine learning." Physical Review E 104, no. 1 (2021): 014205.

Machine learning has opened new possibilities for developing long-term memory devices by aritifical neural networks. The dynamics of memory retrieval process have not yet been well understood, with open issues such as how different memory states compete and how a desired memory state can be recalled. 

We study memory devices based on reservoir computing, a general class of recurrent neural networks (RNN), under two distinct settings: with or without an explicit index/address channel, corresponding to the “location-addressable” and “context-addressable” scenarios, respectively. We demonstrate that, for the location-addressable scenario, a single reservoir computer can restore more than a dozen sophisticated memory states such as chaotic attractors, which are sustained and can be successfully recalled. The dynamics of the memory are studied with a focus on the transition success rates when switching among different memory states. Control strategies to enhance the success rates are articulated. For the “context-addressable” setting without an index channel, we exploit multi-stability to recall, with the aid of some cue signals, different memory states that can be coexisting asymptotic attractors or transient states. A surprising transition phenomenon in the retrieval success rate emerges as the length of the cue signal varies. The dynamical behaviors associated with memory retrieval uncovered in this work provide foundational insights into developing artificial intelligence based long-term memory devices.

Relevant Publication:

Kong, Ling-Wei, Gene A. Brewer, and Ying-Cheng Lai. "Reservoir-computing based associative memory for complex dynamical attractors." Nature Communications. (Accepted)

Most realistic systems are not operating in isolated states. Instead, they are constantly driven or perturbed by exogenous variables such as some environmental factors. We study the problem of how the system may behave under driving signals unseen before (e.g. different amplitude, frequency, or waveform) in a data-driven approach. Of special interest is to anticipate potential qualitative changes in the system behavior, which may result in serious system malfunctioning.

Relevant Publication:

Kong, Ling-Wei, Yang Weng, Bryan Glaz, Mulugeta Haile, and Ying-Cheng Lai. "Digital twins of nonlinear dynamical systems." Chaos, 33(3), 033111 (2023).

Synthetic gene circuits are powerful tools with various medical and agricultural applications. However, the interactions among these synthetic components with the complicated environments inside the host cell may cause malfunctioning for the gene circuits. We study the dynamical mechanisms behind possible functional failures of gene circuits under growth feedback, which is an important type of host-circuit interaction, through massive simulations. In total, about 85,000,000 different gene circuits are simulated and tested. We are still analyzing this data set.

Kong, Ling-Wei, Wenjia Shi, Xiao-Jun Tian, and Ying-Cheng Lai. "Effects of growth feedback on gene circuits: A dynamical understanding." eLife. (To be published)

Inter-dependency among nodes in complex networks is ubiquitous in the real world. However, the dependency is not always complete and homogeneous. We studied how weak and heterogeneous inter-dependency affected the stability of complex networks in percolation processes and determined the mathematical formulas for the first-order and second-order transition points. We also proved the benefit of heterogeneity in the inter-dependency, which can postpone the collapses in ER networks.

Relevant Publication:

Kong, Ling-Wei, Ming Li, Run-Ran Liu, and Bing-Hong Wang. "Percolation on networks with weak and heterogeneous dependency." Physical Review E 95, no. 3 (2017): 032301.

How would the chimera state in a ring of Kuramoto phase oscillators behave if their dimensionality is changed? In our work published in Physical Review Research, we found that the transient lifetime of the manifold of the chimera state with usual two-dimensional Kuramoto oscillators becomes extremely short with three-dimensional models, where it scales with the magnitude of the perturbation only logarithmically.

Relevant Publication:

Kong, Ling-Wei, and Ying-Cheng Lai. "Scaling law of transient lifetime of chimera states under dimension-augmenting perturbations." Physical Review Research 2, no. 2 (2020): 023196.

Kong, Ling-Wei, and Ying-Cheng Lai. "Lai. Short-lived chimera states." Chaos, 33(6) (2023).