Substitute training machine learning early warning method based on historical data

Abstract

The invention discloses a historical data-based substitute training machine learning early warning method, which comprises the following steps of: on the basis of a small amount of historical data of a real world system, generating substitute data of a plurality of time sequences with the same statistical attribute as the real historical data; and then training a machine learning classifier based on the generated substitute data to identify different dynamic characteristics between a pre-critical-transition stage and a critical stage, thereby detecting an early warning signal of a critical state or phase change. The detection method is applied to experience and experimental data sets of geology, climatic, sociology and cardiology, the effectiveness of the detection method is verified, and the sensitivity and the specificity of the detection method are higher than those of two widely used general early warning signals. Therefore, the method is not limited by partial bifurcation hypothesis in the conventional method; the method based on the specific system can improve the early warning signal.

Description

Technical Field

[0001] The present invention relates to the technical field of complex systems, and particularly to an early warning method for training machine learning based on historical data surrogates Background Art

[0002] In recent years, deep learning classifiers have been used for the detection of early warning signals. These classifiers require large amounts of data, but in the context of critical transitions, this data is often difficult to obtain; thus, researchers have chosen to use synthetic data generated from bifurcation simulations of mathematical models, which can be generated on a sufficiently large scale as needed; given the general nature of bifurcations, these classifiers have been shown to be effective in predicting bifurcations in real systems, outperforming variance and lag-1 autocorrelation in many cases. However, the performance of machine learning classifiers depends on the quality of their training data - this approach relies on the real-world system having characteristics similar to a particular bifurcation trajectory in the training set. In fact, this approach assumes the presence of bifurcations in the system - which is not inherent to real-world systems, but rather an attribute of the mathematical model of the relevant system

[0003] Ideally, machine learning classifiers should be trained directly on data from real-world systems; to address the problem of limited data availability, a method of training machine learning based on historical data surrogates (SDML) for predicting critical transitions has been proposed to identify early warning signals of critical transitions; the machine learning method based on surrogate data has been tested on empirical data in geology, climatology, sociology, and cardiology, and its performance has been compared with widely used general early warning signals (variance and lag-1 autocorrelation); in addition, the robustness of the machine learning method based on surrogate data to different surrogate data generation methods has been evaluated Summary of the Invention

[0004] To solve the above technical problems, the present invention designs an early warning method for training machine learning based on historical data surrogates

[0005] To achieve the above technical effects, the present invention is realized through the following technical solutions: an early warning method for training machine learning based on historical data surrogates, characterized by including the following steps

[0006] S1. Generating a training data set consisting of a number of surrogate data samples based on data in a real system that is close to and far from a critical transition: splitting a time series containing a critical transition at the midpoint, with the first half regarded as "neutral" and the second half regarded as "pre-transition"; then, using a variety of surrogate data methods to generate surrogate data for the "neutral" and "pre-transition" parts to preserve the histogram distribution and / or power spectrum of the original data, and the surrogate data is labeled according to whether they are far from neutral or close to the pre-transition critical transition, constituting a binary classification data set

[0007] S2. Machine learning algorithm selection: Select Support Vector Machine (SVM), Long Short-Term Memory Network (LSTM), Convolutional Neural Network (CNN), and Multi-Head Convolutional Neural Network (Multi-HeadCNN).

[0008] S3. For the LSTM, CNN, and Multi-HeadCNN algorithms, use binary cross-entropy as the loss function and adopt the Adam optimizer to efficiently update the network weights; and train and validate the selected machine learning algorithm models.

[0009] S4. Verify the effectiveness of the device: Select the historical experience data of rapid transition events, input it into the machine learning algorithm models selected in S2 for verification, and select the machine learning algorithm with the best performance for each rapid transition event, and finally obtain the prediction results.

[0010] S5. Compare the prediction results in S4 with the true results: Compare its performance with variance and lag-1 autocorrelation; at the same time, use the Receiver Operating Characteristic (ROC) curve to compare the performance of these methods in terms of true positives and false positives.

[0011] Furthermore, in S1, the multiple alternative data methods are one of random permutation (RP) replacement, Fourier transform (FT) replacement, amplitude-adjusted Fourier transform (AAFT) replacement, iterative amplitude-adjusted Fourier transform (IAAFT1 and IAAFT2) replacement.

[0012] Furthermore, in S3, the training and validation of the selected machine learning algorithm models are as follows: All models use a batch size of 64, train for 100 epochs, and adopt a 0.8 / 0.2 training / validation dataset division; use early stopping to prevent overfitting. When the accuracy on the validation set does not improve within 5 epochs, stop training; then select the model with the highest validation accuracy as the best model and report its F1 score on the validation set to measure the performance of the model; this is a metric that considers both sensitivity and specificity; note that the test data used to generate the ROC curve is not involved in the training process.

[0013] Further, in S4, the machine learning algorithms that perform best for each rapid transition event are as follows: for the MS66 sediment core and ice core data, the best classifier is the Support Vector Machine (SVM), with F1 scores of 1.0 and 1.0 respectively; for the 64PE406E1 sediment core, the best performer is the Long Short-Term Memory Network (LSTM), with an F1 score of 0.99; for the MS21 sediment core, the best algorithm is the Convolutional Neural Network (CNN), with an F1 score of 0.99; for the chicken heart data and construction activity data, the best algorithm is the Multi-Head Convolutional Neural Network (Multi-HeadCNN), with F1 scores of 1.0 and 0.99 respectively.

[0014] Further, in S4, the historical empirical data of the rapid transition events include: using publicly available experimental data of chicken embryo heart cell aggregates; using the past oxygen dynamics of three sediment cores, MS21, MS66, and 64PE406E1, in the Eastern Mediterranean region; using publicly available ice core data from Vostok, Antarctica; using the annually resolved time series of the number of tree cuttings in the former Pueblo society in Spain.

[0015] The beneficial effects of the present invention are as follows:

[0016] The present invention trains and tests the SDML classifier on the empirical and experimental data in the fields of ecology, climatology, sociology, and cardiology, and compares its performance with variance and lag-1 autocorrelation. It can be seen that the SDML method may have an advantage over general metrics in providing early warning signals; compared with general early warning signals that rely on the phenomenon of critical slowing down, the SDML method does not assume the existence of bifurcations, but observes past transitions and attempts to extract relevant features close to the transitions; it can open up a new direction for the research of early warning signals and can be applied to fields such as ecology, climatology, finance, energy, human and biological activities, and other complex dynamic systems, which is crucial for improving the ability to predict or avoid critical transitions. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0018] Figure 1 It is a schematic diagram of the prediction framework of the machine learning early warning method based on historical data surrogates of the present invention;

[0019] Figure 2It is a schematic diagram of the time series of rapid transition events in the Mediterranean hypoxia transition, paleoclimate transition, and the transition of human activities in the pre-Spanish Pueblo society of the present invention;

[0020] Figure 3 It is a schematic diagram of the index trend before the critical transition in the empirical data using the amplitude-adjusted Fourier transform AAFT substitution method of the present invention;

[0021] Figure 4 It is the performance ROC curve of the index in the historical empirical data of the present invention;

[0022] Figure 5 It is the algorithm for generating Fourier transform surrogate data in the embodiments of the present invention. Detailed implementation manners

[0023] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts belong to the scope of protection of the present invention.

[0024] Embodiment 1

[0025] A surrogate training machine learning early warning method based on historical data, characterized by including the following steps:

[0026] Step 1: Generate a training data set consisting of several surrogate data samples based on the data close to and far from the critical transition in the real system: The time series containing the critical transition is split at the midpoint, the first half is regarded as "neutral", and the second half is regarded as "before transition"; then, multiple surrogate data methods are used to generate surrogate data for the "neutral" and "before transition" parts to preserve the histogram distribution and / or power spectrum of the original data. The surrogate data are labeled according to whether they are far from neutral or close to the critical transition before transition, constituting a binary classification data set; The methods used to generate surrogate data are listed below:

[0027] 1) Random permutation RP substitution: RP surrogate data are obtained by randomly shuffling the original time series. They retain the same mean, variance, and histogram distribution as the original signal, but any time structure is removed. Therefore, the power spectrum and autocorrelation function of the RP surrogate data are different from those of the original signal, and are usually used to test the time structure in the signal.

[0028] 2) Fourier Transform (FT) surrogate: FT surrogate data retains the power spectrum of the original signal but not necessarily the histogram distribution. They are generated by first performing a discrete Fourier transform on the original signal, randomizing the phase, and then transforming back to the time domain. This method retains all linear information but removes non-linear dependencies and is thus commonly used to test for non-linear structures in signals. The Fourier transform surrogate generation algorithm is based on the null hypothesis that the data is derived from a linear stochastic process. This hypothesis implies the absence of non-linearity in both the dynamics and data observations. The surrogate data should have the same power spectrum as the original data and, according to the Wiener-Khintchine theorem, the same autocorrelation function; as Figure 5 shown, Algorithm 1 for generating Fourier transform surrogate data is given.

[0029] 3) Amplitude Adjusted Fourier Transform (AAFT) surrogate: AAFT surrogate data aims to retain both the power spectrum and the histogram distribution. It is generated in a similar manner to FT surrogate data, but a histogram transformation step is added during the process to match the histogram of the surrogate data to that of the original signal. However, this process may introduce spurious harmonics in the power spectrum. Thus, AAFT surrogate data perfectly retains the histogram distribution, but the power spectrum will be slightly distorted.

[0030] 4) Iterative Amplitude Adjusted Fourier Transform (IAAFT1 and IAAFT2) surrogate: IAAFT surrogate data was proposed by Schreiber and Schmitz to address the distortion of the power spectrum in AAFT surrogate data. They better match the histogram distribution and the power spectrum by iteratively replacing the Fourier amplitudes. The IAAFT algorithm cannot precisely retain both the histogram distribution and the power spectrum simultaneously and has two versions: IAAFT1 can precisely retain the histogram distribution, while IAAFT2 can precisely retain the power spectrum.

[0031] Step 2: Selection of machine learning algorithms: Select Support Vector Machine (SVM), Long Short-Term Memory Network (LSTM), Convolutional Neural Network (CNN), and Multi-Head Convolutional Neural Network (Multi-HeadCNN); and use binary cross-entropy as the loss function for the LSTM, CNN, and Multi-HeadCNN algorithms, and use the Adam optimizer to efficiently update the network weights; and train and validate the selected machine learning algorithm models for LSTM, CNN, and Multi-HeadCNN;

[0032] In each case, the default hyperparameter values were used without hyperparameter tuning. The implementation details of each algorithm are provided below.

[0033] 1) SVM: This is a supervised machine learning algorithm suitable for classification tasks in high-dimensional spaces; SVM separates different classes in the feature space by finding the optimal hyperplane; for time series classification, each data point serves as a feature; the SVM model architecture includes an input feature normalization layer MinMaxScaler and a support vector classifier SupportVectorClassifier, which are connected through a pipeline for training. The model uses a 5-fold 3-repetition cross-validation method and uses AUC as the performance evaluation metric to improve the generalization ability of the classifier and the reliability of the evaluation.

[0034] 2) LSTM: This is a recurrent neural network (RNN) designed to address the vanishing gradient problem in traditional RNNs; LSTM is very effective in capturing the temporal dependencies of sequential data and is well-suited for time series classification. The LSTM architecture is first connected through a fully connected layer to an LSTM layer with 128 neurons; to mitigate overfitting, a Dropout layer with a dropout rate of 0.5 is added, followed by another LSTM layer; then a fully connected layer with 128 neurons and a ReLU activation function is added;. Finally, a fully connected layer with a Sigmoid activation function is added to output the probabilities of two classes.

[0035] 3) CNN: This learns features through convolutional operations and is commonly used in image and time series classification: The CNN architecture has two one-dimensional convolutional layers, where each convolutional layer has 64 filters, a kernel size of 3, and uses a ReLU activation function; followed by a Dropout layer with a dropout rate of 0.5 and a MaxPooling layer to reduce the dimension; then, a fully connected layer with a ReLU activation function and 128 neurons is used. Finally, a fully connected layer with a Sigmoid activation function is used to output the probabilities of two classes.

[0036] 4) Multi-Head CNN: This algorithm aims to capture features of different scales in the input data through CNNs with different convolutional kernel sizes and different heads; the present invention uses a three-head CNN; the first head is a one-dimensional convolutional layer with 32 filters and 3 convolutional kernel sizes, batch normalization to standardize the input, and a ReLU activation function; subsequently, there is a Dropout layer for regularization, a MaxPooling layer for dimensionality reduction, and a flattening layer; the second head is similar, but uses a one-dimensional convolutional layer with 5 convolutional kernel sizes, aiming to capture patterns in a wider window of the input data; it also uses the same batch normalization, ReLU activation function, Dropout layer, MaxPooling layer, and flattening layer; the third head uses a larger convolutional kernel size of 11 and 64 filters, aiming to capture wider patterns. The outputs of the flattening layers from all three heads are concatenated into a vector, and then passed through a fully connected layer with 128 neurons (using ReLU activation). Finally, the probabilities of two classes are output through a fully connected layer with a Sigmoid activation function.

[0037] Step 3. Verify the effectiveness of the device: Select the historical empirical data of rapid transition events, bring it into the machine learning algorithm model selected in S2 for verification, and select the machine learning algorithm with the best performance for each rapid transition event, and finally obtain the prediction result;

[0038] The historical empirical data of the rapid transition events are as follows:

[0039] 1) Aggregates of chicken embryo heart cells: Use publicly available experimental data of aggregates of chicken embryo heart cells, which studied the process of the transition of aggregates of chicken embryo heart cells to arrhythmia; these aggregates were given the drug E4031 at a concentration of 0.5 mol to 2.5 mol, which can block the human Ether-α`-go-go-Related gene (hERG) potassium channel; after administration, the time interval between two heartbeats of some aggregates began to alternate, that is, it showed period-doubling bifurcation; a similar transition may also occur in the human heart as T-wave alternans, increasing the risk of sudden cardiac death in patients. The heart rate interval was obtained by calculating the time between two consecutive heartbeats and was used for further analysis.

[0040] The dataset contains 23 aggregate time series that experienced period-doubling bifurcation and 23 aggregate time series that did not experience any transition; a Gaussian filter with a bandwidth of 20 heartbeats was used; the early warning signal was calculated through a rolling window with a window size of 0.5; in this study, the Python package ewstools was used to smooth the data and calculate the general early warning signal.

[0041] 2) Sedimentary archives of the Mediterranean Sea: Adopt the past oxygen dynamics of three sediment cores MS21, MS66, and 64PE406E1 in the existing East Mediterranean region; in the geological history, rapid transitions between aerobic and anaerobic states often occurred in this region; the MS21 core contains 2 anaerobic events, the MS66 core contains 4 anaerobic events, and the 64PE406E1 core contains 7 anaerobic events; in this study, the SDML method was tested separately for each core; the sampling rate varies according to the core, providing a resolution of approximately 10 to 50 years, and the interval between data points is almost uniform; the residual data was obtained by using Gaussian kernel smoothing with a bandwidth of 900 years, and the early warning signal was calculated using a rolling window of 0.5.

[0042] 3) Ice core records of paleoclimate transitions: Use ice core data from Vostok, Antarctica, which records paleoclimate transitions from 420,000 years ago to the present; the data preprocessing methods: perform linear interpolation to make the data equidistant, and use a Gaussian filter for detrending.

[0043] 4) Building activities of the pre - Hispanic Pueblo society: This data records the annual - resolution time series of the number of tree cuttings in the pre - Hispanic Pueblo society as a proxy indicator of building activities; the data shows 5 collapse transitions of building activities and the subsequent formation of different archaeological periods; the data preprocessing method: the time series was detrended using a Gaussian filter with a default bandwidth of 30 years, and the early warning signal was calculated using a default rolling window size of 60 years.

[0044] Step 4: Compare the prediction results of S4 with the true results: Compare its performance with variance and lag - 1 autocorrelation; at the same time, use the receiver operating characteristic (ROC) curve to compare the performance of these methods in terms of true positives and false positives.

[0045] See Figure 2 It can be seen that the rapid transition events in the continuous records of the three empirical systems are brought into the SDML method for predicting critical transitions: specifically, the historical experience data of the rapid transition events in the continuous records of the three empirical systems are brought into S1 to obtain substitute data, as shown in the green part of Figure 2 ; the blue - part data is used to predict the situation in future periods;

[0046] The prediction results after bringing the rapid transition events in the continuous records of the three empirical systems into the SDML method are specifically as follows:

[0047] 1) Mediterranean oxygenation transition: Due to rising temperatures and excessive nutrient inputs into coastal areas, the ocean is losing oxygen; in geological history, large-scale oxygenation events have occasionally triggered mass extinction events, and the current reduction in oceanic oxygen has raised concerns about the recurrence of such events; to understand oceanic oxygenation events, high-resolution oxygenation records based on molybdenum (Mo), as shown in Figure 2 a - 2c, show a rapid aerobic to anaerobic transition at the beginning of each sediment layer; in addition, oxygenation events in the eastern Mediterranean occur regularly on a multi-century time scale and exhibit critical point behavior when the system suddenly transitions to anoxic conditions.

[0048] 2) Paleoclimate transition: The completion of drilling at Vostok Station in East Antarctica has extended the ice core records of atmospheric composition and climate back to the past four glacial - interglacial periods; glacial - interglacial climate changes have been recorded through complementary climate records from deep - sea sediments, continental plants, animal deposits, loess deposits, and ice cores. The Vostok ice core record covers four climate cycles, with an ice layer depth of 3310 meters and an age slightly greater than 400 thousand years, covering a period comparable to the time range of many oceanic and continental records; Figure 2 d shows the relationship between the deuterium content of the ice core (i.e., a proxy for local temperature changes) and the GT4 time scale of the ice core; a notable feature of glacial - interglacial periods is the sudden end of most glacial periods.

[0049] 3) Transformation of pre - Hispanic Puebloan social activities: Using an extremely long and high - resolution time series of tree - cutting by the Pueblo people as a proxy for construction activities, as shown in Figure 2 e; this time series spans eight centuries and has undergone five transformations; the annual - resolution time series of construction activities indicates that signals of critical slowing down preceded multiple catastrophic transformations in the pre - Hispanic Pueblo culture of the southwestern United States.

[0050] In summary, the present invention trains and tests the SDML classifier on empirical and experimental data in the fields of ecology, climatology, sociology, and cardiology, and compares its performance with variance and lag - 1 autocorrelation; as more time series are revealed, these metrics are gradually monitored; if the variance and lag - 1 autocorrelation show strong trends, they are considered to provide early warning signals, and such trends are quantified by the Kendall tau statistic; for variance, an upward trend is considered an early warning signal.

[0051] For lag - 1 autocorrelation, the direction of the trend depends on the oscillation frequency (θ) of the critical point; when θ ∈ [0, π / 2), the lag - 1 autocorrelation is expected to increase; while when θ ∈ (π / 2, π], it is expected to decrease;

[0052] The variances and lag-1 autocorrelations of the predicted results and the actual results of rapid transition events in the continuous records of three empirical systems were compared:

[0053] In the chicken embryo heart aggregate experiment, an increase in variance and a decrease in lag-1 autocorrelation were observed before the transition, which can serve as an early warning signal. For the test trajectories in the three empirical datasets ( Figure 2 , blue), the variances and lag-1 autocorrelations performed inconsistently in providing early warning signals; in 9 out of 12 cases, the variance increased before the transition ( Figure 3 , orange), while the lag-1 autocorrelation increased in only 7 cases ( Figure 3 , green).

[0054] The SDML classifier assigns probabilities to two possible classes: neutral (i.e., far from the transition state) and pre-transition (i.e., close to the transition state); an increase in the pre-transition class probability is regarded as an early warning signal ( Figure 3 , purple); in each case, the probability of the pre-transition state increases over time, thus providing an early warning signal; when approaching the critical point, the classifier's judgment probability of the pre-transition state approaches 1; these results demonstrate that: ① the history and future trajectories before the critical transition have similar dynamic characteristics; ② the trajectories far from the critical transition (labeled "neutral") and those close to the critical transition (labeled "pre-transition") have different dynamic characteristics; ③ the SDML method performs well among five different surrogate data methods, indicating its strong robustness to different method selections.

[0055] The receiver operating characteristic (ROC) curve was used to compare the performance of these methods in terms of true positives and false positives: by predicting the "pre-transition" time series (i.e., close to the critical transition) and the "neutral" time series (i.e., far from the critical transition); as Figure 4 shown, the ROC curves of the variance, lag-1 autocorrelation (AC), and SDML classifier for six evaluations in four different complex systems are presented. For the chicken embryo heart data ( Figure 4 A), both the SDML classifier and the lag-1 autocorrelation performed better than the variance; for the other empirical datasets, except for the sediment data of the 64PE406E1 core ( Figure 4 D), the lag-1 autocorrelation was proven to be the best indicator, and in all other cases, the SDML classifier performed better than the variance and the lag-1 autocorrelation.

[0056] In summary, the SDML method described in the present invention has more advantages than general indicators in providing early warning signals; the SDML method does not assume the existence of bifurcations and does not rely on the phenomenon of critical slowing down. Instead, by observing past transitions and attempting to extract relevant features near the transitions, the early warning signals will not fail in cases such as global bifurcations, non-equilibrium (transient) dynamics, and rate-induced mutations.

[0057] Example 2

[0058] This example further explains Figure 1 、 Figure 2 、 Figure 3 and Figure 4 as follows:

[0059] Figure 1 In, A shows two trajectories (blue) of chicken embryo heart aggregates and their smoothed curves (grey) before the critical transition. The vertical dashed line marks the start of the transition; the green background represents the part of the time series far from the transition (neutral), and the red represents the part close to the transition (pre-transition); these trajectories are divided into training trajectories (left) and test trajectories (right); B shows that thousands of surrogate time series are generated from the training trajectories of neutral (left) and pre-transition (right) respectively; C shows the binary classification problem where a machine learning classifier is used to distinguish neutral and pre-transition time series; D shows the changing trends of pre-transition metrics in the test trajectories, including variance, lag-1 autocorrelation (AC), and the probability assigned by the SDML classifier; the arrow indicates the rolling window (50% of the time series) used to calculate the early warning signal.

[0060] Figure 2 In A - C show three cores from the Mediterranean sediment archive: Core MS21 at a depth of 1,022 meters (A), Core MS66 at a depth of 1,630 meters (B), and Core 64PE406E1 at a depth of 1,760 meters (C); D shows the paleoclimate transition, with δD representing the deuterium content (‰ represents per mille relative to standard mean ocean water); the time unit is years before present (BP); E shows the construction activities of the pre-Hispanic Pueblo society, represented by the number of trees cut down per year; the vertical dashed line indicates the start of the rapid transition event; the green time series is the historical trajectory used to generate surrogate data; the red time series is the transformed trajectory and is not used; the blue time series is the trajectory used to test the early warning signal.

[0061] Figure 3 The trajectory in corresponds to the blue trajectory in Figure 2 ; Figure 3In it, A represents the anoxic transition (Sapropel S1) obtained from the MS21 core data; B-C represent the anoxic transitions (Sapropels S1 and S3) obtained from the MS66 core data; D-G represent the anoxic transitions (Sapropels S3-S6) obtained from the 64PE406E1 core data; H represents the end of glacial period I (i.e., the end of the last glacial period); I represents the end of glacial period II; J represents the archaeological PII period; K represents the archaeological Early PIII period; L represents the archaeological Late PIII period; (top) time series trajectory (blue) and Gaussian smoothing curve (gray); (second layer) variance; (third layer) lag-1 autocorrelation (AC); (bottom) critical transition probability predicted by the SDML classifier; the line and the shaded area represent the mean and the 95% confidence interval, respectively; the arrow represents the width of the rolling window used to calculate the early warning signal; the gray band represents the transition stage.

[0062] Figure 4 In it, the ROC curve shows the performance of the SDML classifier (SDML, purple), variance (Var, orange), and lag-1 autocorrelation (AC, green) under the following conditions: Figure 4 In it, A represents that the chicken embryo heart aggregates experience period-doubling bifurcations; B represents the sedimentation data of the MS21 core; C represents the sedimentation data of the MS66 core; D represents the sedimentation data of the 64PE406E1 core; these data from A-D show the process of the Mediterranean Sea rapidly turning into an anoxic state; E represents that the ice core record shows a rapid change in paleoclimate; F represents the change in the construction activities of the pre-Hispanic Pueblo society; 10 classifiers are used to make predictions for each dataset, and 40 predictions are made at equal intervals between 60%-100% (a, b, e, and f) or 80%-100% (c and d) of the data before the critical transition; the area under the curve (AUC), denoted by A, is an indicator to measure the performance of the classifier. The inset shows the proportion of the classifier correctly predicting the trajectory before the critical transition; "before transition" means close to the critical transition, and "neutral" means far from the critical transition.

Claims

1. An early warning method based on surrogate training of historical data, characterized in that: The following steps are involved: S1. Generate a training dataset consisting of several surrogate data samples based on data close to and far from the critical transition in the real system: split the time series containing the critical transition at the midpoint, with the first half regarded as "neutral" and the second half regarded as "before the transition"; then, use a variety of surrogate data methods to generate surrogate data for the "neutral" and "before the transition" parts to preserve the histogram distribution and / or power spectrum of the original data. The surrogate data are labeled according to whether they are far from neutral or close to the critical transition before the transition, forming a binary classification dataset; S2. Machine learning algorithm selection: select support vector machine (SVM), long short-term memory (LSTM), convolutional neural network (CNN), and multi-head convolutional neural network (Multi-Head CNN); S3. For SVM, LSTM, CNN and Multi-Head CNN algorithms, binary cross entropy is used as the loss function, and the Adam optimizer is used to efficiently update the network weights; and the selected machine learning algorithm models are trained and verified; S4, verifying the effectiveness of the device: select historical experience data of rapid transition events, bring it into the machine learning algorithm model selected in S2 for verification, and select the machine learning algorithm with the best performance for each rapid transition event, and finally obtain the prediction results; S5. Comparing the predictions of S4 with the true results: The performance was compared with the variance and lag 1 autocorrelation; the receiver operating characteristic (ROC) curve was used to compare the performance of these methods in terms of true positives and false positives.

2. The early warning method of machine learning based on substitute training of historical data according to claim 1 is characterized in that: In S1, the multiple data substitution methods are one of random permutation (RP) substitution, Fourier transform (FT) substitution, amplitude adjusted Fourier transform (AAFT) substitution, and iterative amplitude adjusted Fourier transform (IAAFT1 and IAAFT2) substitution.

3. The early warning method of machine learning based on substitute training of historical data according to claim 1 is characterized in that: In S3, the selected machine learning algorithm model is trained and validated as follows: all models use a batch size of 64, train for 100 epochs, and adopt a training / validation data set split of 0.8 / 0.2; the early stopping method is used to prevent overfitting, and the training is stopped when the accuracy on the validation set does not improve within 5 epochs; then the model with the highest validation accuracy is selected as the best model, and its F1 score on the validation set is reported to measure the performance of the model.

4. The early warning method of machine learning based on substitute training of historical data according to claim 1 is characterized in that: In S4, the best performing machine learning algorithm for each rapid transition event is selected: the best performing classifier in the MS66 sediment core and ice core data is the support vector machine SVM, with F1 scores of 1.0 and 1.0, respectively; for the 64PE406E1 sediment core, the best performing one is the long short-term memory network LSTM, with an F1 score of 0.99; for the MS21 sediment core, the best algorithm is the convolutional neural network CNN, with an F1 score of 0.99; for the chicken heart data and construction activity data, the best algorithm is the multi-head convolutional neural network Multi-Head CNN, with F1 scores of 1.0 and 0.99, respectively.

5. The early warning method of machine learning based on substitute training of historical data according to claim 1 is characterized in that: In S4, the historical empirical data of rapid transition events include: using publicly available experimental data of chicken embryo heart cell aggregates; using publicly available past oxygen dynamics of three sedimentary cores MS21, MS66, and 64PE406E1 in the eastern Mediterranean region; using publicly available ice core data from Vostok in Antarctica; and using publicly available annual-resolution time series of the number of trees cut down in pre-Hispanic Pueblo societies.

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