A precipitation nowcast reliable prediction method based on multi-strategy consistency risk control calibration

Abstract

The present application relates to a kind of precipitation near reliable prediction method based on multi-strategy consistency risk control calibration, comprising: S1, the pre-processing of original observation data;S2, construct and train precipitation near prediction model;S3, complete multi-strategy risk control calibration.The present application does not change the structure and training process of the existing high-precision point prediction model under the premise, through post-processing calibration mechanism, give the model distribution independent, limited sample, provable risk control ability, and support multiple data division strategies and stratified risk assessment, applicable to the business warning of high-impact weather such as severe convection.

Description

Technical Field

[0001] This invention belongs to the field of meteorological radar technology, specifically relating to a method for reliable nowcasting of precipitation based on multi-strategy consistency risk control calibration. Background Technology

[0002] Precipitation nowcasting plays a crucial role in meteorological forecasting, flood prevention, and other disaster prevention and mitigation systems. In recent years, with the development of deep learning technology, precipitation nowcasting models based on convolutional neural networks, recurrent neural networks, and their variants such as ConvLSTM and U-Net have made significant progress. These models typically use radar echo sequences (especially those fusing three-dimensional radar reflectivity and multi-dimensional environmental field elements) as input, and achieve high-precision point predictions of precipitation fields for the next hour through model training. They have demonstrated superior performance compared to traditional optical flow methods or numerical model post-processing methods in multiple operational scenarios and public datasets.

[0003] However, despite continuous improvements in point prediction accuracy, existing deep learning models still suffer from fundamental flaws: they only provide deterministic outputs, cannot quantify prediction uncertainty, and cannot answer the crucial question of "whether the prediction is reliable." In extreme weather events, models are prone to generating "illusionary" heavy precipitation, which, without reliable assurance, could lead to false alarms or missed alarms, resulting in serious consequences.

[0004] To improve model credibility, some studies have attempted to introduce frameworks such as Conformal Risk Control (CRC) to ensure statistical risk under limited samples by constructing prediction intervals. However, such methods usually require: (1) the model output to be in the form of a set (such as a two-sided interval); and (2) the loss function to satisfy monotonicity (i.e., the larger the prediction set, the smaller the loss). In actual business, precipitation is non-negative, and more attention is paid to whether heavy precipitation is missed (i.e. the true value is not covered), so one-sided prediction intervals are often used. At the same time, risk measurement usually adopts the average uncovered proportion of the whole map (i.e. the proportion of pixels not included in the interval), or the weighted underreporting rate consistent with the masked weighted mean square error (MWMSE) - whose weight is positively correlated with the true precipitation intensity (e.g., a higher penalty is given to areas with heavy precipitation). Although such losses are bounded, they do not meet the monotonicity condition required by traditional CRC because they are coupled with the true value and depend on the one-sided interval structure, causing existing traditional risk control methods to fail.

[0005] Furthermore, current calibration strategies are mostly limited to a single data partitioning method (such as the fixed leaveout method), which neither systematically evaluates the stability of different strategies (such as split, oob, cross) under limited samples, nor do they have a refined evaluation of the risk control effect of different precipitation interval prediction lengths, making it difficult to support differentiated decision-making needs oriented towards business.

[0006] Therefore, there is an urgent need for a precipitation nowcasting method that does not rely on model structure modification, is compatible with unilateral intervals and non-monotonic losses, supports multi-strategy calibration, and can evaluate risk control performance by grouping according to the size of the forecast interval. This method would provide distribution-independent, provable, and operationally oriented uncertainty quantification and risk protection while retaining high-precision point forecasting capabilities. Summary of the Invention

[0007] The purpose of this invention is to address the shortcomings and deficiencies of existing technologies by providing a reliable nowcasting method for precipitation based on multi-strategy consistency risk control calibration. Without altering the structure and training process of existing high-precision point prediction models, this invention endows the model with distribution-independent, finite-sample, and provable risk control capabilities through a post-processing calibration mechanism. It also supports multiple data partitioning strategies and hierarchical risk assessments, making it suitable for operational early warning of high-impact weather such as severe convection.

[0008] The technical problem solved by this invention is achieved through the following technical solution: A reliable nowcasting method for precipitation based on multi-strategy consistency risk control calibration is proposed. This method relies on a trained precipitation nowcasting model. The model takes radar reflectivity volume scan data and environmental field elements collected every 6 minutes within one hour as input, and the cumulative precipitation grid field for the following hour as output. The model employs a 3D ConvLSTM fusion CBAM attention mechanism. During training, masked weighted mean square error (MWMSE) is used as the loss function. Multi-strategy risk control calibration is performed on the model to achieve a transition from "point prediction" to "risk-controllable interval prediction." The steps of the method are as follows: S1. Preprocess the raw observation data by collecting radar reflectivity volume scan data at 6-minute intervals, environmental field elements, and hourly cumulative precipitation data recorded by automatic weather stations. Convert the radar reflectivity volume scan data from polar coordinates to Cartesian coordinates to generate a three-dimensional grid field with a horizontal resolution of 4 km × 4 km and a vertical interval of 0.5 km. Match the environmental field elements to the radar resolution using spatiotemporal interpolation to ensure strict spatial and temporal alignment. Use inverse range weighted interpolation to generate a two-dimensional grid field with the same resolution as the radar field from the cumulative precipitation data, and nonnegate all negative values ​​to conform to the physical characteristics of precipitation. Simultaneously, construct a land mask to shield the ocean and invalid areas, preventing them from interfering with model training and risk assessment. S2. Construct and train a precipitation nowcasting model, using 3D ConvLSTM as the backbone network and integrating the CBAM (Convolutional Block Attention Module) attention mechanism to effectively capture the spatiotemporal evolution characteristics of radar echoes and the influence of the environmental field. The input of the precipitation nowcasting model is the three-dimensional radar reflectivity sequence of the past hour and its corresponding environmental field, and the output is the precipitation grid field of the next hour. The spatial size of the precipitation grid field is 128×128. During training, the masked weighted mean square error (MWMSE) is used as the main loss function. ; in: For the observed image located in Precipitation intensity at the location; To predict the image Precipitation intensity at the location; This is a land mask, where land points within the radar scanning range are marked as 1, and all other points are marked as 0. The weight corresponding to this point is set differently depending on the actual precipitation. S3. Complete multi-strategy risk control calibration: During the inference phase, a calibration set is constructed through different data partitioning strategies to obtain a stable and robust integrated prediction model; and the integrated test model is used to perform complete inference on the calibration set and the test set respectively to execute risk control calibration.

[0009] Moreover, S3 specifically refers to: (1) On a fixed historical dataset, implement three strategies: split, oob, and cross respectively; For the split strategy, the data is divided into a training set and an independent calibration set according to a certain ratio, and a single model is trained and then directly used for calibration. For the OOB strategy, the number of ensemble members is set to M=5. Five sub-training sets are generated by Bootstrap resampling. The out-of-bag samples that did not participate in the training automatically constitute the calibration set of the ensemble prediction model. Finally, the prediction results of all models on the calibration set are merged by averaging to form a global calibration package. For the cross strategy, the data is divided into 5 folds, and the data is trained in turn with 4 folds and calibrated with 1 fold, for a total of 5 sub-models. The final prediction result is the arithmetic mean of the 5 outputs. (2) The ensemble prediction model was used to perform complete inference on the calibration set and the test set respectively, and two sets of key data packages were systematically collected: one is the calibration package, which contains the predicted value and the corresponding true label of each sample on the calibration set; the other is the test package, which contains the predicted value of each sample on the test set. With real labels The aforementioned data packets are stored in the form of a structured dictionary to provide complete input for subsequent calibration. Considering the non-negativity of precipitation and focusing more on whether heavy precipitation is missed (i.e., the actual value is higher than the upper limit of the forecast), a one-sided forecast interval format is adopted: ; in: For the optimal calibration scaling factor, For image The prediction interval at that point, The predicted value is the maximum of 0; Task loss is calculated using the average uncovered percentage across the entire map: ; in: This represents the average loss due to uncovered areas across the entire map. For indicator functions; The actual value; Predict the reciprocal of the sum of the total number of pixels in the entire image; Optimal calibration scaling factor The search method is as follows: in: To maximize losses, The average loss for n samples, For definition in On the power set, the output is a search function for a given element in its input set, and the average loss on the calibration set is defined as follows: ; Obtain the optimal calibration scaling factor Then, it is applied to the test set to construct the final risk-controllable range forecast, and the actual empirical risk on the test set is calculated to verify whether it is effectively controlled within the preset risk level. the following.

[0010] The advantages and beneficial effects of this invention are as follows: 1. The strategy of this invention is comprehensive. It can use the spilt, oob, and cross strategies to divide the samples, so as to make full use of the limited sample library, avoid the problem of reducing the training data due to the special division of the calibration set, and prevent overfitting on a specific dataset during the calibration process. 2. The process of this invention forms a closed loop, from division → integration → collection → calibration → verification → hierarchical evaluation. Each module has a clear division of labor, which allows the risk control module to run independently of the main model like a plug-in, making it plug-and-play. 3. This invention provides a refined assessment method that addresses the significant differences in uncertainty between different intensities of precipitation in precipitation forecasts. Instead of relying on a single global accuracy assessment, it proposes a refined assessment method that verifies risk control in four categories based on the length of the forecast interval. 4. This invention adopts a post-processing calibration paradigm, which is significantly non-invasive and does not alter the original model; 5. This invention introduces the concept of consistent risk calibration, constructs a theoretically provable risk control framework that can be proven in theory, and does not rely on searching for the optimal calibration scaling factor. Mathematically, this ensures that, under limited sample conditions, the empirical risk on the test set is effectively controlled within a preset risk level; it not only significantly improves the reliability and interpretability of precipitation nowcasting, but also provides a reusable technical paradigm for other high-risk artificial intelligence applications. Attached Figure Description

[0011] Figure 1 This is a flowchart of the present invention; Figure 2 The present invention provides three different strategies at different risk levels. A diagram illustrating the risk control level below; Figure 3 The present invention provides three different strategies at different risk levels. A quantitative comparison diagram of the predicted interval length; Figure 4 The three different strategies of this invention are at different risk levels A schematic diagram illustrating the risk control level for grouping prediction interval lengths; Figure 5 This is a case study of precipitation nowcasting in an embodiment of the present invention. Detailed Implementation

[0012] The present invention will be further described in detail below through specific embodiments. The following embodiments are merely descriptive and not limiting, and should not be used to limit the scope of protection of the present invention.

[0013] This embodiment is based on observation data from 15 meteorological radars in North China from 2015 to 2016. However, it should be understood that this method is not limited to this region or time period, and can also be extended to other meteorological regions or precipitation nowcasting tasks at different time scales.

[0014] like Figure 1 As shown, a reliable nowcasting method for precipitation based on multi-strategy consistency risk control calibration is innovative in that: First, the raw observation data were systematically preprocessed. Radar reflectivity volume scan data at 6-minute intervals, divergence in environmental field elements, and hourly cumulative precipitation data recorded by ground automatic weather stations were collected.

[0015] The radar reflectivity volume scan data was converted from polar coordinates to Cartesian coordinates to generate a three-dimensional gridded field with a horizontal resolution of 4 km × 4 km and a vertical spacing of 0.5 km. Environmental field elements were matched to the radar resolution through spatiotemporal interpolation to ensure strict spatial and temporal alignment. Cumulative precipitation data were generated using inverse range-weighted interpolation to produce a two-dimensional gridded field with the same resolution as the radar field, and all negative values ​​were non-negatively processed to conform to the physical characteristics of precipitation. In addition, a land mask was constructed to shield the ocean and invalid areas, preventing them from interfering with model training and risk assessment.

[0016] Based on this data, a high-precision precipitation nowcasting model is constructed and trained. This embodiment uses a 3D ConvLSTM as the backbone network, integrating a CBAM (Convolutional Block Attention Module) attention mechanism to effectively capture the spatiotemporal evolution characteristics of radar echoes and the influence of the environmental field. The model input consists of a 3D radar reflectivity sequence of 10 samples from the past hour and their corresponding environmental field; the output is a gridded precipitation field for the next hour, with a spatial size of 128×128. During training, the masked weighted mean square error (MWMSE) is used as the main loss function. ; In the formula: The representative observation image is located in The intensity of precipitation at that location In the predicted image The intensity of precipitation at that location This is a land mask. Land points within the radar scanning range are represented as 1, and all other points are represented as 0. The weights corresponding to this point are set differently depending on the actual precipitation, so that the model pays more attention to areas of heavy precipitation.

[0017] After the model structure is determined, the core multi-strategy risk control calibration phase begins. The key to this invention is that, without modifying the model itself, a calibration set is constructed during the inference phase using different data partitioning strategies, and ensemble inference is used to improve stability. Specifically, on a fixed historical dataset, three strategies—split, out-of-bounds (OOB), and cross—are implemented respectively.

[0018] For the split strategy, the data is proportionally divided into a training set and an independent calibration set. After training a single model, it is directly used for calibration. For the out-of-bag (OOB) strategy, the number of ensemble members is set to M=5. Five sub-training sets are generated through Bootstrap resampling. After the model corresponding to each sub-training set is trained, the out-of-bag samples that did not participate in the training automatically constitute the calibration set of the ensemble prediction model. Finally, the prediction results of all sub-models on the calibration set are merged by averaging to form a global calibration package. For the cross strategy, the data is divided into 5 folds, and training is performed alternately with 4 folds and calibration with 1 fold, for a total of 5 sub-models. The final prediction result is the arithmetic mean of the 5 outputs. Regardless of the strategy used, a stable and robust ensemble prediction model is obtained.

[0019] Subsequently, the ensemble prediction model was used to perform complete inference on both the calibration and test sets, and two sets of key data packages were systematically collected: one is the calibration package, which contains the predicted value and corresponding true label for each sample on the calibration set; the other is the test package, which contains the predicted value for each sample on the test set. With real labels These data packets are stored in the form of a structured dictionary to provide complete input for subsequent calibration, ensuring that the entire process is reproducible and verifiable.

[0020] Based on this, risk control calibration is performed. Considering that precipitation is non-negative, and that operations are more concerned with whether heavy precipitation is missed (i.e., the actual value is higher than the forecast upper limit), this invention adopts a one-sided forecast interval form: ; in: For the optimal calibration scaling factor, For image The prediction interval at that point, The predicted value is the maximum of 0; Task loss is calculated using the average uncovered percentage across the entire map: ; in: This represents the average loss due to uncovered areas across the entire map. For indicator functions; The actual value; Predict the reciprocal of the sum of the total number of pixels in the entire image; Optimal calibration scaling factor The search method is as follows: ; in: To maximize losses, The average loss for n samples, For definition in On the power set, the output is a search function for a given element in its input set, and the average loss on the calibration set is defined as follows: ; Obtain the optimal calibration scaling factor Then, it is applied to the test package to construct the final risk-controllable range prediction, and the actual empirical risk on the test set is calculated to verify whether it is effectively controlled within the preset level. the following.

[0021] To further evaluate the uniformity of calibration results, this invention proposes a tiered verification mechanism based on prediction interval length: the prediction interval widths of all pixels in the test set are divided into four categories according to their numerical values, for example, short, medium-short, medium-long, and long intervals based on quartiles, and the average uncovered proportion of each category is calculated. This analysis can answer whether the corresponding risks are effectively controlled regardless of the predicted value size. If a certain type of risk significantly exceeds the limit, it indicates that there is a calibration deviation, and the strategy needs to be adjusted.

[0022] Ultimately, the system outputs two results: first, a point prediction field completely consistent with the original model, which can be directly used by business systems; second, a one-sided interval field with controllable risk, which can be further visualized as an uncertainty heatmap, where red represents low uncertainty and yellow represents high uncertainty, such as... Figure 5 As shown, the four images from left to right are: precipitation forecast, visualization of uncertainty in interval proportion, absolute error, and actual precipitation. In the precipitation forecast and actual precipitation images, black areas represent rainless areas, and blue areas represent precipitation areas; the darker the color, the greater the precipitation. The visualization of uncertainty in interval proportion visualizes the size of the precipitation forecast interval; the highlighted areas at the bottom of the image represent high uncertainty, while areas with precipitation but low precipitation represent low uncertainty, i.e., higher certainty. The absolute error image visualizes the absolute difference between the precipitation forecast and actual precipitation images. Comparing the model's prediction results with the labels, we can see that the overall distribution trend is generally consistent, especially in the central and southern regions with higher precipitation. However, after introducing the consistency risk control framework, the model exhibits higher uncertainty in the southern and peripheral regions of the prediction results, indicating that the model is hesitant in its judgment of these areas. Therefore, a significant correction is applied to maximize the inclusion of the true precipitation in the final output interval. We can see that the high error areas of absolute error and interval uncertainty have strong spatial consistency, indicating that corrections have been made based on the consistency risk control framework. By comparing uncertainty and error plots, it can be seen that uncertainty can, to some extent, indicate areas where the model may err. This is very valuable in practical applications.

[0023] like Figure 2As shown, blue represents the risk control level of the split strategy, brown represents the risk control level of the cross strategy, and green represents the risk control level of the OOB strategy. Figure 2 From left to right: Risk Level The risk control levels corresponding to the three strategies: split, cross, and out-of-bounds. When the risk control effect of the cross strategy is the best, the risk control is the lowest, around 0.04. The OOB performance is worse than expected, slightly exceeding the preset risk level, at about 0.055. The split strategy performs moderately, effectively controlling the risk below the preset risk level, at about 0.048. At this time, the cross strategy remains optimal, with an actual risk of approximately 0.08, significantly lower than the preset risk level. The split and OOB strategies perform similarly, with actual risks around 0.095, both effectively controlled below the preset risk level of 0.1. At that time, the actual risk control of the three strategies were close to the preset risk level, with the cross strategy at about 0.135, the split strategy at about 0.145, and the OOB strategy at about 0.14. The cross strategy still maintained a relative advantage.

[0024] like Figure 3 As shown, blue represents the average prediction interval length of the split strategy, brown represents the average prediction interval length of the cross strategy, and green represents the average prediction interval length of the OOB strategy. Figure 3 From left to right: Risk Level The average length of the prediction interval for the three strategies. At that time, the cross strategy generated the longest interval length, exceeding 1.0, indicating that it adopted the most conservative strategy to ensure low risk. The oob strategy generated the shortest interval length, approximately 0.5, indicating that its prediction strategy was the most aggressive. This also corresponds to... Figure 2 middle At that time, the OOB strategy slightly exceeded the preset risk level, while the Split strategy fell between the two, close to 1.0; when When the interval length predicted by all three strategies decreased significantly, the interval length predicted by the cross strategy was approximately 0.48, the interval length predicted by the OOB strategy was approximately 0.35, and the interval length predicted by the split strategy was approximately 0.42; when At that time, the interval length further shortened, with the cross strategy predicting an interval length of approximately 0.28, the OOB strategy predicting an interval length of approximately 0.20, and the split strategy predicting an interval length of approximately 0.25. Overall, with the preset risk level... The interval lengths predicted by all three strategies show a decreasing trend, with the cross strategy consistently maintaining the longest interval to achieve the highest security, while the oob strategy consistently maintaining the shortest interval to achieve higher information efficiency.

[0025] like Figure 4 As shown, displayed in Under the given conditions, samples were categorized into four groups—Short, Short-Medium, Medium-Long, and Long—based on the predicted interval length. The dashed line represents the target risk level of 0.1. For the `cross` strategy, as the interval length increased, the risk gradually rose from 0.05 in the Short group to 0.105 in the Long group. Although the Long group slightly exceeded the target, the overall increase was relatively gradual, indicating the best control effect. For the `oob` strategy, the risk was lowest in the Short group (approximately 0.04), but it rose sharply to 0.165 in the Long group, significantly exceeding the preset level, indicating insufficient risk control capability when handling high-uncertainty samples. For the `split` strategy, the risk rose from 0.055 in the Short group to 0.145 in the Long group, falling between the performance of `cross` and `oob`. These results show that although the `cross` strategy performed best in terms of overall risk, its advantage mainly stemmed from its good coverage of the simple Short group. However, all three strategies faced challenges in the extremely difficult Long group, with the `cross` strategy exhibiting the strongest robustness.

[0026] Overall, each of the three strategies has its advantages: the cross strategy is the most robust in overall risk control and is suitable for scenarios with extremely high safety requirements; the OOB strategy performs best in terms of prediction interval length efficiency and has excellent control over simple samples, making it suitable for routine forecasts; the split strategy provides a compromise. This invention, through parallel evaluation of multiple strategies, can flexibly select the optimal strategy based on whether actual business needs prioritize safety or forecast accuracy, achieving an effective balance between risk control and forecast efficiency.

[0027] In summary, this embodiment fully implements the technical solution of the present invention, and fully verifies its feasibility, effectiveness, and operational applicability in achieving high-precision, highly reliable, and provable precipitation near-term forecasts through multi-strategy calibration and hierarchical evaluation without altering the original high-precision model.

[0028] Although embodiments and drawings of the present invention have been disclosed for illustrative purposes, those skilled in the art will understand that various substitutions, variations and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the scope of the present invention is not limited to the contents disclosed in the embodiments and drawings.

Claims

1. A method for reliable nowcasting of precipitation based on multi-strategy consistency risk control calibration, characterized in that: The forecasting method relies on a trained precipitation nowcasting model. The model takes radar reflectivity volume scan data and environmental field elements collected every 6 minutes within one hour as input, and the cumulative precipitation grid field for the next hour as output. The model adopts a 3D ConvLSTM fusion CBAM attention mechanism. During training, masked weighted mean square error (MWMSE) is used as the loss function; the model is calibrated with multi-strategy risk control to achieve a leap from "point prediction" to "risk-controllable interval prediction". The steps of the method are as follows: S1. Preprocess the raw observation data by collecting radar reflectivity volume scan data at 6-minute intervals, environmental field elements, and hourly cumulative precipitation data recorded by automatic weather stations. Convert the radar reflectivity volume scan data from polar coordinates to Cartesian coordinates to generate a three-dimensional grid field with a horizontal resolution of 4 km × 4 km and a vertical interval of 0.5 km. Match the environmental field elements to the radar resolution using spatiotemporal interpolation to ensure strict spatial and temporal alignment. Use inverse range weighted interpolation to generate a two-dimensional grid field with the same resolution as the radar field from the cumulative precipitation data, and nonnegate all negative values ​​to conform to the physical characteristics of precipitation. Simultaneously, construct a land mask to shield the ocean and invalid areas, preventing them from interfering with model training and risk assessment. S2. Construct and train a precipitation nowcasting model, using 3D ConvLSTM as the backbone network and integrating the CBAM (Convolutional Block Attention Module) attention mechanism to effectively capture the spatiotemporal evolution characteristics of radar echoes and the influence of the environmental field. The input of the precipitation nowcasting model is the three-dimensional radar reflectivity sequence of the past hour and its corresponding environmental field, and the output is the precipitation grid field of the next hour. The spatial size of the precipitation grid field is 128×128. During training, the masked weighted mean square error (MWMSE) is used as the main loss function. ； in: For the observed image located in Precipitation intensity at the location; To predict the image Precipitation intensity at the location; This is a land mask, where land points within the radar scanning range are marked as 1, and all other points are marked as 0. The weight corresponding to this point is set differently depending on the actual precipitation. S3. Complete multi-strategy risk control calibration: During the inference phase, a calibration set is constructed through different data partitioning strategies to obtain a stable and robust integrated prediction model; and the integrated test model is used to perform complete inference on the calibration set and the test set respectively to execute risk control calibration.

2. The method for reliable nowcasting of precipitation based on multi-strategy consistency risk control calibration according to claim 1, characterized in that: Specifically, S3 is: (1) On a fixed historical dataset, implement three strategies: split, oob, and cross respectively; For the split strategy, the data is divided into a training set and an independent calibration set according to a certain ratio, and a single model is trained and then directly used for calibration. For the OOB strategy, the number of ensemble members is set to M=5. Five sub-training sets are generated by Bootstrap resampling. The out-of-bag samples that did not participate in the training automatically constitute the calibration set of the ensemble prediction model. Finally, the prediction results of all models on the calibration set are merged by averaging to form a global calibration package. For the cross strategy, the data is divided into 5 folds, and the data is trained in turn with 4 folds and calibrated with 1 fold, for a total of 5 sub-models. The final prediction result is the arithmetic mean of the 5 outputs. (2) Use the integrated prediction model to perform complete inference on the calibration set and the test set respectively, and systematically collect two sets of key data packages: one is the calibration package, which contains the predicted value and the corresponding true label of each sample on the calibration set; Second is the test package, which contains the predicted value for each sample in the test set. With real labels The aforementioned data packets are stored in the form of a structured dictionary to provide complete input for subsequent calibration. Considering the non-negativity of precipitation and focusing more on whether heavy precipitation is missed (i.e., the actual value is higher than the upper limit of the forecast), a one-sided forecast interval format is adopted: ； in: For the optimal calibration scaling factor, For image The prediction interval at that point, The predicted value is the maximum of 0; Task loss is calculated using the average uncovered percentage across the entire map: ； in: This represents the average loss due to uncovered areas across the entire map. For indicator functions; The actual value; Predict the reciprocal of the sum of the total number of pixels in the entire image; Optimal calibration scaling factor The search method is as follows: in: To maximize losses, The average loss for n samples, For definition in On the power set, the output is a search function for a given element in its input set, and the average loss on the calibration set is defined as follows: ； Obtain the optimal calibration scaling factor Then, it is applied to the test set to construct the final risk-controllable range forecast, and the actual empirical risk on the test set is calculated to verify whether it is effectively controlled within the preset risk level. the following.

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