Related papers: Deep Learning for predicting rate-induced tipping

A Hopf bifurcation is prevalent in many nonlinear dynamical systems. When a system prior to a Hopf bifurcation is exposed to a sufficient level of noise, its noise-induced dynamics can provide valuable information about the impending…

We study the problem of predicting rare critical transition events for a class of slow-fast nonlinear dynamical systems. The state of the system of interest is described by a slow process, whereas a faster process drives its evolution and…

This study employs scientific machine learning to identify transient time series of dynamical systems near a fold bifurcation of periodic solutions. The unique aspect of this work is that a convolutional neural network (CNN) is trained with…

We consider how breakdown of the quasistatic approximation for attractors can lead to rate-induced tipping, where a qualitative change in tracking/tipping behaviour of trajectories can be characterised in terms of a critical rate.…

Machine learning plays an essential role in preventing financial losses in the banking industry. Perhaps the most pertinent prediction task that can result in billions of dollars in losses each year is the assessment of credit risk (i.e.,…

Prediction of climate tipping is challenging due to the lack of recent observation of actual climate tipping. Despite many previous efforts to accurately predict the existence and timing of climate tippings under specific climate scenarios,…

To discover intrinsic inter-class transition probabilities underlying data, learning with noise transition has become an important approach for robust deep learning on corrupted labels. Prior methods attempt to achieve such transition…

This paper shows that the variance of load bus voltage magnitude in a small power system test case increases monotonically as the system approaches a Hopf bifurcation. This property can potentially be used as a method for monitoring…

In applications of dynamical systems, situations can arise where it is desired to predict the onset of synchronization as it can lead to characteristic and significant changes in the system performance and behaviors, for better or worse. In…

The possibility of rate-induced tipping (R-tipping) away from an attracting fixed point has been thoroughly explored in 1-dimensional systems. In these systems, it is impossible to have R-tipping away from a path of quasi-stable equilibria…

We propose self-adaptive training -- a unified training algorithm that dynamically calibrates and enhances training processes by model predictions without incurring an extra computational cost -- to advance both supervised and…

Many dynamical systems exhibit abrupt transitions or tipping as the control parameter is varied. In scenarios where the parameter is varied continuously, the rate of change of control parameter greatly affects the performance of early…

This paper investigates biological models that represent the transition equation from a system in the past to a system in the future. It is shown that finite-time Lyapunov exponents calculated along a locally pullback attractive solution…

Detecting critical transitions in complex, noisy time-series data is a fundamental challenge across science and engineering. Such transitions may be anticipated by the emergence of a low-dimensional order parameter, whose signature is often…

Social behaviour models are increasingly integrated into climate change studies, and the significance of climate tipping points for `runaway' climate change is well recognised. However, there has been insufficient focus on tipping points in…

There is an emerging trend in applying deep learning methods to control complex nonlinear systems. This paper considers enhancing the runtime safety of nonlinear systems controlled by neural networks in the presence of disturbance and…

Tipping points have been actively studied in various applications as well as from a mathematical viewpoint. A main technique to theoretically understand early-warning signs for tipping points is to use the framework of fast-slow stochastic…

A large variety of complex systems in ecology, climate science, biomedicine and engineering have been observed to exhibit tipping points, where the internal dynamical state of the system abruptly changes. For example, such critical…

Social tipping points are promising levers to achieve net-zero greenhouse gas emission targets. They describe how social, political, economic or technological systems can move rapidly into a new state if cascading positive feedback…

Real-world complex systems such as the climate, ecosystems, stock markets, and combustion engines are prone to dynamical transitions from one state to another, with catastrophic consequences. State variables of such systems often exhibit…