Collection of some Early Warning Signals / Resilience Indicators / Regime Shift Identifiers / Transition Identifiers

[Datseris]

EDIT: These algorithms will live in https://github.com/JuliaDynamics/TransitionIdentifiers.jl

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In the near future we'll be adding a module in DynamicalSystems.jl about functionality related to "early warning signals, resilience indicators, tipping indicators, precurson signals, quantities that identify regime shifts" and similar functionality that is typically used in tipping points analysis. The plan is to have both timeseries analysis tools, but also dynamical-system-based tools (similarly to how you can compute a lyapunov exponent from a dynamical system / ODE with lyapunov or use a reconstructed signal and get the exponent from data with lyapunov_from_data).

The purpose of this Issue is to collect existing functionality online and in the current literature, and serve both as a starting point, but also as an indicator of what new research directions are useful to be pursued in the future.

(will be editing frequently this issue to add more stuff)

Methodologies/Methods/Quantities

• Physical precursor signals. Such signals are context-specific, and depend on the physics and causal connections of the signal at hand. They can be utilized to anticipate (TODO: write more).
• Critical Slowing Down indicators. In the specific case of a sadle-node bifurcation in a 1D (or, quasi-1D-potential) case driven by weak, Gaussian noise, it has been showing that the autocorrelation and variance of a signal (computed via a sliding window) increase the closer the system gets to the bifurcation. TODO; Add references.
• Kolmogorov-Smirnov difference. TODO: write more, Witold's work.
• Recurrence quantificaiton analysis. TODO: write more (also Witold's work).
• basins fractions. TODO: Write more (Menck2013 and our work with Alex).

Existing code bases

• Vasilis Dakos toolbox/software TODO write more

[johannes-lohmann]

Here is a method I came across in recent literature. From time series they fit a 1D quadratic map in a moving window, and extrapolate when the fixed point of this map disappears.
http://dx.doi.org/10.1098/rsif.2020.0566

[johannes-lohmann]

Here is another method I came across in also recent literature. They use dynamic mode decomposition to approximate the eigenmodes of a system. They track the performance of this approximation and detect a regime transition that occurs as this approximation fails, due to fast dynamics as the system transitions to another attractor.
https://doi.org/10.1007/s10955-019-02392-3

[johannes-lohmann]

Even another method aiming to deal with very high-dimensional, but short data uses the dynamic network marker method to determine when certain modes in the system become dominant as a critical transition is approached.
https://doi.org/10.1111/jcmm.13943

[jbuxt]

For critical slowing down indicators, Dakos et al. (2012) is a great resource for temporal indicators and Kefi et al. (2014) is the version for spatial indicators.

Dakos et al. (2012) - https://doi.org/10.1371/journal.pone.0041010
Kefi et al. (2014) - https://doi.org/10.1371/journal.pone.0092097

I believe that a lot of these methods were then coded up in an early warning 'toolkit', so that could be a good place to start.

[Datseris]

Links with software implementations:

https://cran.r-project.org/web/packages/earlywarnings/index.html

https://ewstools.readthedocs.io/en/latest/