Rare events in complex systems: Understanding and prediction

Malik, Nishant; Öztürk, Uğur

doi:10.1063/5.0024145

Cited by 20 publications

(5 citation statements)

References 40 publications

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“…In solving the ML binary classification problem for the rare events, it is important to use the correct metrics, which takes into account the imbalance of the datasets (Mena and Gonzalez 2006;Johnson and Khoshgoftaar 2019;Malik and Ozturk, 2020). Previously, we show that the accuracy is not a good classifier, if there are high TN values.…”

Section: Choosing Appropriate Metrics For the Imbalanced Datasetsmentioning

confidence: 87%

“…Such imbalanced classification poses a problem, as quite often just the minority class is of the major interest-say, in disaster forecast, medical diagnostic, business, etc. (Mena and Gonzales, 2006;Malik and Ozturk, 2020). Some widely used classifiers, such as accuracy, are useless if the data are imbalanced.…”

Section: Moderate and Strong Eq Are Rare Events: The Corresponding Fo...mentioning

confidence: 99%

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Earthquake Forecast as a Machine Learning Problem for Imbalanced Datasets: Example of Georgia, Caucasus

et al. 2022

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In this article, we considered the problem of M≥3 earthquake (EQ) forecasting (hindcasting) using a machine learning (ML) approach, using experimental (training) time series on monitoring water-level variations in deep wells as well as geomagnetic and tidal time series in Georgia (Caucasus). For such magnitudes’, the number of “seismic” to “aseismic” days in Georgia is approximately 1:5 and the dataset is close to the balanced one. However, the problem of forecast is practically important for stronger events—say, events of M≥3.5—which means that the learning dataset of Georgia became more imbalanced: the ratio of seismic to aseismic days for in Georgia reaches the values of the order of 1:20 and more. In this case, some accepted ML classification measures, such as accuracy leads to wrong predictions due to a large number of true negative cases. As a result, the minority class, here—seismically active periods—is ignored at all. We applied specific measures to avoid the imbalance effect and exclude the overfitting possibility. After regularization (balancing) of the training data, we build the confusion matrix and performed receiver operating classification in order to forecast the next day probability of M≥3.5 earthquake occurrence. We found that the Matthews’ correlation coefficient (MCC) is the measure, which gives good results even if the negative and positive classes are of very different sizes. Application of MCC to observed geophysical data gives a good forecast of the next day M≥3.5 seismic event probability of the order of 0.8. After randomization of EQ dates in the training dataset, the Matthews’ coefficient efficiency decreases to 0.17.

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Section: Choosing Appropriate Metrics For the Imbalanced Datasetsmentioning

confidence: 87%

Section: Moderate and Strong Eq Are Rare Events: The Corresponding Fo...mentioning

confidence: 99%

Earthquake Forecast as a Machine Learning Problem for Imbalanced Datasets: Example of Georgia, Caucasus

et al. 2022

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“…In addition, it is worth pointing out that many of the issues we have addressed in here are by no means exclusive to crystal nucleation. The occurrence of rare events is ubiquitous in the natural sciences 147 and quantifying the kinetics characterising these processes is a fundamental open question with reverberations across e.g. climate science 148,149 as well as epidemiology 150,151 .…”

Section: Conclusion and Future Challengesmentioning

confidence: 99%

The Seven Deadly Sins: when computing crystal nucleation rates, the devil is in the details

Blow,

Quigley,

Sosso

2021

Preprint

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The formation of crystals has proven to be one of the most challenging phase transformations to quantitatively model -let alone to actually understand -be it by means of the latest experimental technique or the full arsenal of enhanced sampling approaches at our disposal. One of the most crucial quantities involved with the crystallization process is the nucleation rate, a single, elusive number that is supposed to quantify the average probability for a nucleus of critical size to occur within a certain volume and time span. A substantial amount of effort has been devoted to attempt a connection between the crystal nucleation rates computed by means of atomistic simulations and their experimentally measured counterparts. Sadly, this endeavour almost invariably fails to some extent, with the venerable classical nucleation theory typically blamed as the main culprit. Here, we review some of the recent advances in the field, focusing on a number of perhaps more subtle details that are sometimes overlooked when computing nucleation rates. We believe it is important for the community to be aware of the full impact of aspects such as finite size effects and slow dynamics, that often introduce inconspicuous and yet non-negligible sources of uncertainty into our simulations. In fact, it is key to obtain robust and reproducible trends to be leveraged so as to shed new light on the kinetics of a process, that of crystal nucleation, which is involved into countless practical applications, from the formulation of pharmaceutical drugs to the manufacturing of nano-electronic devices.

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“…Instances where this unlikely-yet-important combination occurs include fade-outs of epidemics [1,2], the extinction of species in ecology [3,4], the dynamics of biological switches [5][6][7][8][9][10], the escape of a Brownian particle from a double-well potential [11,12], large fluctuations in chemical reactions [13], and the detection or prediction of rare natural disasters such as earthquakes, storms, or heavy rains [14,15]. The broad range of these applications justifies the considerable recent effort expended on developing sampling algorithms for rare events in models of stochastic phenomena [16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Sampling rare trajectories using stochastic bridges

et al. 2022

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The numerical quantification of the statistics of rare events in stochastic processes is a challenging computational problem. We present a sampling method that constructs an ensemble of stochastic trajectories that are constrained to have fixed start and end points (so-called stochastic bridges). We then show that by carefully choosing a set of such bridges and assigning an appropriate statistical weight to each bridge, one can focus more processing power on the rare events of a target stochastic process while faithfully preserving the statistics of these rare trajectories. Further, we also compare the stochastic bridges we produce to the Wentzel-Kramers-Brillouin (WKB) optimal paths of the target process, derived in the limit of low noise. We see that the generated paths, encoding the full statistics of the process, collapse onto the WKB optimal path as the level of noise is reduced. We propose that the method can also be used to judge the accuracy of the WKB approximation at finite levels of noise.

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Rare events in complex systems: Understanding and prediction

Cited by 20 publications

References 40 publications

Earthquake Forecast as a Machine Learning Problem for Imbalanced Datasets: Example of Georgia, Caucasus

Earthquake Forecast as a Machine Learning Problem for Imbalanced Datasets: Example of Georgia, Caucasus

The Seven Deadly Sins: when computing crystal nucleation rates, the devil is in the details

Sampling rare trajectories using stochastic bridges

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