3.1 Neural Networks

Artificial neural network (ANN) has many advantages such as nonlinearity, adaptability, parallelism, robustness, and strong computing power [54], and have been applied in many fields for prediction, such as economic growth estimation [55, 56], stock price prediction [57, 58], and exchange rate prediction [59, 60]. The numerical experiment indicates that the performance of various neural networks with different network structures varies and is suitable for different situations [38].

For instance, BPNN is a classic network in time series analysis. Even many scholars use heuristic optimization algorithms to optimize its initial weights and thresholds in order to improve model accuracy. However, it still has drawbacks such as slow convergence speed, low running efficiency and poor generalization ability [11, 61, 62].

RNN is a typical algorithm. In RNN, the hidden layer endows memory function by connecting nodes in different components, but it has a divergence issue over a long period of time. Therefore, LSTM was proposed by introducing gate components. Furthermore, it was improved by redesigning the gate structure [63], such as bidirectional LSTM and GRU.

Additionally, GRNN performs well in small sample fitting [64].

3.2 Support Vector Machine

Support Vector Machine (SVM) is a new type of machine learning method, which has many strengths to process nonlinear data, global optimization, strong adaptability, and strong generalization ability, especially for complex problems such as small samples, nonlinearity, and high-dimensional. Compared with neural network models, support vector machine models require less training data [6]. Therefore, it is an effective tool and more suitable for simulating and predicting disaster loss sequences [65].

Based on traditional SVM and by combining regularization theory, Least Squares Support Vector Machine (LSSVM) is developed, which transforms inequality constraints into equality constraints, and uses quadratic programming method to solve function estimation problems, greatly improving convergence speed [66]. Overall, LSSVM can not only solve problems with few samples and nonlinearity, but also has many advanced properties (such as simple operation, fast convergence speed and high prediction accuracy, etc.), which can be used for disaster loss prediction [6, 11]. However, it should also be noted that non-stationary time series have a significant impact on their prediction accuracy [11].

3.3 Application of Machine Learning Algorithms in Disaster Loss Prediction

At present, researches on disaster loss prediction are mainly focused on earthquakes [67, 68, 69], tropical cyclones [70, 71, 72, 73], floods [74, 75, 76, 77], storm surges [78],Wang et al. [79] and forest fires [16, 80].

Loss prediction models include two forms, i.e. single and combined models.

Here are some cases of single model. Wang et al. [79] estimate direct losses of storm surges by using GIS and open data. Yin et al. [78] established a grey correlation model of storm surge disaster losses in coastal areas of China. Jin et al. [4] using SVM to predicted storm surge disaster loss with small sample data. Feng et al. [81] forecasted the direct economic losses and sufferers of storm surges separately based on SVM and BPNN. Zhang et al. [82] evaluated the accuracy of five models, including BPNN, one-dimensional convolutional neural network, decision tree (DT), random forest (RF), and extreme gradient enhancement (XGBoost), in constructing mudslides prediction models. Lou et al. [83] constructed a loss assessment model of tropical cyclone based on SVM. Cao et al. [84] used an improved grey model to assess the direct economic losses caused by marine disasters in coastal cities of China. He et al. [85] used dynamic recurrent neural networks to predict flood disaster losses. Ye et al. [86] discussed the feasibility of artificial neural networks, nonlinear regression, and EI Niño for predicting storm surge disasters. Yang et al. [87] utilized the extended Kalman filter to forecast the economic losses and casualties caused by storm surge. Wu et al. [11] applied LSSVM to predict the economic losses of waterlogging in the subway station project. As research deepens, more and more models are available, but choosing the appropriate model still poses challenges [88].

Besides single model, many researchers proposed a combination model to improve the prediction accuracy [89, 90]. For example, Chen et al. [91] combined GA Elman neural network (ENN), support vector regression (SVR), and GRNN into a comprehensive evaluation model for predicting tropical cyclone losses. Feng and Liu [81] believe that the joint model of BP and SVM can better predict the economic losses by storm surges. Zhao et al. [15] combined the results of ENN and GRNN to achieve interval prediction of economic losses caused by storm surge disasters. They think that the performance of the combined model is better than that of the single model. Meng et al. [92] used four machine learning models to predict the direct economic losses caused by tropical cyclones in Guangdong Province. Yang et al. [93] predicted the affected population caused by tropical cyclones based on a mixed model of the generalized additive model(GAM) and XGBoost.

4.1 Small Sample Size and Its Solution

The small sample size problem often led to large errors and poor performance in loss estimation model. It inevitably brings some limitations to machine learning based loss rate estimation models, such as easy overfitting and poor generalization ability [7, 37]. Therefore, in this case, choosing a suitable learning algorithm, or finding a method to enhance the information of the original data, is currently urgently needed [2].

Some researchers proposed data augmentation technology to address the issue [37], such as virtual sample generation (VSG) [94, 95]. The strategy of VSG is to extract prior information from a given small sample data, and then generate new virtual samples to fill the information gap between the original samples, which can obtain more samples containing the original data features [37]. These virtual samples have similarity. Its data distribution and statistical characteristics are the same as the original sample [37].

There are also many VSG techniques applied in small samples. For example, Li et al. [96] use an information diffusion model (IDM) to generate virtual loss samples. Huang [97] also proposed an information diffusion model, which is a fuzzy statistical technique that converts single point samples into set valued samples, which can effectively utilize fuzzy information in small samples to fill information gaps. Additionally, Sun [2] proposed a new data augmentation technique called k-nearest neighbor Gaussian noise method (KNN-GN), which generates virtual samples by adding Gaussian noise to the original sample. Rogoza [98] proposed local extrapolation to simulate small samples less than ten. Yuan et al. [1] and Sun et al. [2] generate virtual samples through interpolation.

Presently, some scholars have conducted researches on small sample prediction. For example, Dan et al. [99] established a small sample preprocessing model to enhance data stationarity, and then used simulated annealing algorithm and SVM for prediction. Rajesh et al. [100] and Deng et al. [101] also applied grey theory to traditional small sample prediction. Sun et al. [2] combined KNN-GN with XGBoost to construct a prediction model, which can quickly and accurately estimate direct economic losses in a short period of time after a storm surge occurs.

4.2 Data Non-stationary and Its Solutions

On this issue, some studies have shown that the Empirical Mode Decomposition (EMD) can decompose the original sequence into a set of IMF (Intrinsic Mode Function) components with different frequencies and residuals. After decomposition, these subsequences are relatively stationary, which are easy to simulate, can fully mine data information, better reflect the physical characteristics of the original data, and extract linear features from nonlinear time series. Further, this method shows strong universality in processing non-stationary data [97].

This technology has also been applied to loss prediction. For instance, Chai et al. [6] decomposed the time series of ship collision conflicts into combinations of different frequency subsequences. Each subsequence displayed a more regular frequency range than the original conflict sequence. Subsequently, different LSSVMs were established for each IMF components. The final prediction result of the ship collision conflict number was obtained by summarizing the prediction results of each subsequence. After this step, the prediction accuracy was greatly improved [6].

4.3 Other Solutions

Besides the above solutions in a single model, some ensemble learning strategies that use multiple machine learners also begun to emerge [9, 20, 37, 102, 103, 104, 105]. Ensemble learning is a learning strategy that combines multiple learners together to reduce bias, achieve superior generalization ability, improve the accuracy and reliability of prediction, and has already achieved excellent performance for predication [2, 106, 107]. Compared to a single machine learning model, it can absorb the advantages of a single method and more effectively extract the features of data. In addition to single and combined models, ensemble learning and optimization algorithms are gradually gaining attention in agricultural disaster prediction. For example, integrating optimization techniques such as Genetic Algorithms (GA) and Particle Swarm Optimization (PSO) with machine learning models for crop yield prediction, livestock loss estimation, and food supply chain forecasting further improves the model's accuracy. Additionally, the prediction results can directly support agricultural insurance pricing, disaster risk zoning, and food emergency reserve management.

Especially for small sample data, it can effectively fit nonlinear functions, and comprehensively extract high-dimensional and temporal features of data. Even for the loss prediction, whether it is the affected populations or economic losses, the composite prediction has a smaller error than the two single predictions. For instance, Du et al., [7] constructed a new combination model, namely Elman neural network-Generalized regression neural network-Definite integral model (ENN-GRNN-DI), for interval prediction of disaster losses [2, 7, 15].

In addition, some researches combined optimization algorithms and machine learning model. They adopted optimization methods to optimize the hyperparameters of machine learning algorithms to improve prediction accuracy. For example, Wang et al. [108] and Yuan et al. [1] respectively used the Beetle Antenna Search (BAS) algorithm and Levenberg Marquardt (LM) algorithm to optimize the BPNN, and used the optimized BPNN model to predict the economic losses of storm surges, and found that the prediction accuracy is significantly improved. Lin et al. [42] used a Vector Space Model (VSM) to correct the results of BPNN. Chen et al. [91] combined genetic algorithm (GA) with Elman neural network, SVR, and GRNN models to predict tropical cyclone losses. Liu et al. [109] proposed a hybrid model that combines wavelet transform (WT), genetic algorithm, and support vector machine. Wu et al. [11] established a new intelligent prediction model for economic losses of subway station caused by rainstorm and flood using sparrow search algorithm (SSA), mean impact value (MIV) and LSSVM. The results showed that SSA algorithms has the advantages of good stability, strong global search ability, and fewer parameters. This fusion method can not only improve the prediction accuracy, but also have strong interpretability.

Furthermore, some researchers adopted a strategy of combining machine learning algorithms with strong predictors, such as Zhao [31] combining an adaptive boosting algorithm with BPNN (Adaboost-BPNN) to predict direct economic losses from marine disasters [2, 11]. Moreover, other researchers combined machine learning algorithms with attention mechanisms to improve prediction accuracy.