A time-aware conformal uncertainty calibration method for burnup evolution curve

Abstract

The application discloses a time-aware conformal uncertainty calibration method for burnup evolution curve, and belongs to the field of fusion nuclear engineering. The method constructs a prediction model by taking time as an explicit input, calibrates the calibration residual by using a validation set or cross-validation, groups the calibration according to time bins, operating stages and their combinations, or performs local calibration based on feature space neighbors, and obtains a calibration quantity that changes with time. The prediction interval is adaptively expanded to meet the preset confidence level. For nuclides / physical quantities that meet the first-order decay equation in the cooling stage, an analytical decay expansion is introduced, the anchor value at the shutdown time is extrapolated according to the decay law, and the interval endpoints are output in cooperation with the conformal calibration. The method also provides audit outputs such as coverage, error binning and access control conclusions.

Description

Technical Field

[0001] This invention relates to the field of fusion nuclear engineering, and more specifically to a time-aware conformal uncertainty calibration method for burnup evolution curves. Background Technology

[0002] In the design and evaluation of the breeding blanket and related components of fusion reactors, it is often necessary to obtain burnup / activation response curves that evolve over time, such as the nuclide stockpile in the breeding region, tritium generation and decay, structural material activity, decay heat, and contact dose rate. These curves are usually derived from neutronics-activation coupling calculations, which are computationally expensive and not conducive to design iteration. Therefore, machine learning or response surface methodology is often introduced in engineering for rapid prediction.

[0003] Existing rapid prediction methods often focus on point prediction accuracy or use empirical methods to give uncertainty (e.g., globally fixed multipliers, uniform residual variance over time), making it difficult to provide stable, interpretable, and auditable confidence intervals over the time dimension. On the one hand, the error distribution of the curve varies significantly across different time scales and different operational stages (irradiation and cooling); on the other hand, when the sample size is limited, directly learning the variance or using high-dimensional Bayesian models is prone to instability, making it difficult to meet the coverage and tail risk requirements for engineering acceptance.

[0004] Conformal calibration can provide coverage guarantees under limited sample conditions, but if a global single calibration quantity is used, there will be an overly conservative problem where "abnormal residuals at certain time points affect the entire time axis"; if pure time point grouping is used, the calibration will be unstable due to too few samples in each group.

[0005] Meanwhile, existing technologies suffer from the following problems: 1) providing a time-varying uncertainty range with controllable coverage for the burnup / activation evolution curve under limited sample conditions; 2) avoiding excessive cross-time propagation expansion caused by global conformal calibration, while also avoiding small-sample instability caused by precise time grouping; 3) providing stable point predictions and interval endpoints in the tail time range for nuclides / physical quantities that satisfy the first-order decay equation during the cooling stage; 4) providing auditable outputs for engineering acceptance, including configuration snapshots, grouping coverage, bin tail factor indices, and gate conclusions. Therefore, there is an urgent need for a time-aware conformal uncertainty calibration scheme for burnup evolution curves that can: operate stably in time bins of engineering interest; be more robust in scenarios where the first-order decay law of nuclides is satisfied in the cooling tail; and output verifiable coverage, error binning, and auditable evidence. Summary of the Invention

[0006] To address the above problems, the present invention provides the following technical solution.

[0007] A time-aware conformal uncertainty calibration method for fuel consumption evolution curves includes:

[0008] Step 1: Obtain sample characteristics of fusion nuclear engineering objects Multiple time points and target physical quantity or calculation label The target physical quantity includes at least the number of nuclide atoms / stock, activity, decay heat, dose rate, multiplication ratio, or a combination thereof;

[0009] Step 2: Extract time features As explicit input, a time-aware prediction model is constructed, resulting in... Point prediction or interval prediction, wherein the time feature includes at least and One or more of the following; the This is an absolute time value in years. Its commonly used logarithmic transformation;

[0010] Step 3: Calculate the conformal score on the calibration set based on the point prediction or interval prediction, and use the conformal score as the basis for calculation. quantiles obtain calibration values ,in Preset coverage rate;

[0011] Step 4: Obtain the calibration amount that changes over time by using group conformal calibration and / or local nearest neighbor conformal calibration, and expand the point prediction or interval prediction accordingly to obtain the calibrated prediction interval.

[0012] Step 5: Output the calibrated prediction range and / or output audit information related to the calibration process.

[0013] Compared with the prior art, the present invention has at least the following beneficial effects:

[0014] 1) Under limited sample conditions, conformal calibration enables controllable interval coverage and allows for adaptive changes over time.

[0015] 2) By employing strategies such as time binning, phase grouping, or local proximity, the problem of excessive conservatism in "abnormal time points affecting the whole" can be reduced, and the effectiveness of the engineering focus area can be improved.

[0016] 3) Analytical extrapolation is introduced for nuclides / physical quantities that satisfy the first-order decay law during the cooling stage, which significantly enhances tail stability and interpretability;

[0017] 4) Generate audit outputs such as coverage, error binning, access control conclusions and configuration snapshots to facilitate project acceptance and reproduction experiments. Attached Figure Description

[0018] Figure 1This is a schematic diagram of the overall process of the method of the present invention;

[0019] Figure 2 A schematic flowchart for group conformal calibration;

[0020] Figure 3 A schematic flowchart illustrating local nearest neighbor conformal calibration and OOD rollback;

[0021] Figure 4 This is a schematic diagram of the first-order decay propagation (analytical extrapolation) during the cooling stage;

[0022] Figure 5 This is a schematic diagram for audit output and engineering access control assessment. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other. To achieve the above objectives, this invention adopts the following technical solution.

[0024] The parameters of this invention are explained as follows:

[0025]

[0026] This invention provides a time-aware conformal uncertainty calibration method for fuel consumption evolution curves, such as... Figure 1 As shown, it includes:

[0027] Step 1: Construct a time-aware prediction model, including: obtaining samples of fusion nuclear engineering objects. Multiple time points and target physical quantity The target physical quantity includes at least the number of nuclide atoms / stock, activity, decay heat, dose rate, multiplication ratio, or a combination thereof;

[0028] Step 2: Extract time features As an explicit input time-aware prediction model, the following is obtained: Point prediction or interval prediction, wherein the time feature includes at least and One or more of the following; the This is an absolute time value in years. Its commonly used logarithmic transformation;

[0029] Step 3: Calculate the conformal score on the calibration set based on the point prediction or interval prediction, and use the conformal score as the basis for calculation. Conformal calibration values ​​were obtained at quantile sites. ,in Preset coverage rate;

[0030] Step 4: Obtain the calibration amount that changes over time by using group conformal calibration and / or local nearest neighbor conformal calibration, and expand the point prediction or interval prediction accordingly to obtain the calibrated prediction interval.

[0031] Step 5: Output the calibrated prediction range and / or output audit information related to the calibration process.

[0032] Furthermore, the time-aware prediction model described in step 2 is learned in a logarithmic space or a log-ratio space, wherein the logarithmic space or log-ratio space at least satisfies:

[0033] ; and / or

[0034] ;

[0035] in, An engineering stability term is introduced to avoid numerical problems caused by zero or minimum values ​​in logarithmic operations. A typical value is... ; For reference physical quantity values, the mean, median, or target value of a specified benchmark design at the same time point can be taken.

[0036] Furthermore, the conformal fraction mentioned in step 3 includes one of the following:

[0037] Interval violation fraction ;

[0038] residuals ;

[0039] Asymmetric fractions constructed based on upper and lower residuals respectively. Let be the conformal fraction of the i-th calibration sample; , These are the lower and upper interval endpoints predicted by the model for the i-th sample, respectively. Let i be the true target physical quantity of the i-th sample; This is the model's predicted value for the i-th sample.

[0040] Furthermore, the grouping key used in the group conformal calibration includes at least one or more of the following: precise time point, time bin, running phase, or phase × time bin.

[0041] Furthermore, the time bins are defined by a right-closed interval time boundary and include at least a time bin of 100 years or more for characterizing the risk of cooling tail.

[0042] Furthermore, the local nearest neighbor conformal calibration includes: imputing missing values ​​and normalizing the scale of the feature vectors of the calibration set and the query point; selecting k nearest neighbor calibration samples in the normalized feature space; and using their conformal scores... quantiles as local calibration parameters .

[0043] Furthermore, the local nearest neighbor conformal calibration imposes a temporal consistency constraint at discrete time points, specifically: prioritizing or selecting nearest neighbor samples from the same set of discrete time points as the query point for calculation. .

[0044] Furthermore, it also includes the determination of out-of-distribution samples: when the nearest neighbor distance from the query point to the calibration set exceeds a preset threshold, it is determined as an out-of-distribution sample, and a more conservative nearest neighbor number, calibration scaling factor, or fallback to the group / global calibration value is applied to the out-of-distribution sample.

[0045] Furthermore, the calibration set mentioned in step 3 is generated through cross-validation, specifically by performing grouped multi-fold cross-validation on the sample label dimension of the training and validation sets, and using extrapolation prediction to generate conformal scores, thereby obtaining a more stable calibration quantity. Furthermore, the calibration quantity that varies over time mentioned in step 4 includes multiple values ​​calculated separately at precise time points, by time binning, or by stage × time binning. And during inference, the corresponding group is selected based on the group to which the query point belongs. .

[0046] Furthermore, the operating phase includes at least an irradiation phase and a cooling phase, and the operating phase is determined by an explicit phase identifier and / or by operating parameters and threshold rules characterizing the source term intensity or power.

[0047] Furthermore, this occurs when the target nuclide / physical quantity satisfies the first-order decay equation during the cooling phase. At that time, it further includes:

[0048] Determine the shutdown time ;

[0049] by The predicted point or interval endpoint is used as the anchor value;

[0050] right Using formula Extrapolation point prediction and interval endpoints.

[0051] Furthermore, the decay constant From half-life Equivalence is determined, satisfying And the Sources include nuclide databases, configuration files, or parameter tables.

[0052] Furthermore, the nuclide that satisfies the first-order decay equation is tritium H-3.

[0053] Furthermore, the audit information includes at least one or more of the following: runtime configuration snapshot information; calibration group and sample size information; calibration amount for each group. Coverage and interval width statistics; error factor index for time-based binning; access control pass / fail conclusions; data and configuration integrity verification information.

[0054] More specifically, the following specific embodiments are provided:

[0055] (a) Time-aware prediction model:

[0056] Using time as an explicit input, construct a time-aware prediction model:

[0057] ;

[0058] in, Design features that are constant or slowly changing over time. As a time feature, the time feature includes at least the following: and One or more of the following; the This is an absolute time value in years. It uses a commonly used logarithmic transformation; optionally, it also includes stage identifiers (irradiation / cooling) and time characteristics within the stage.

[0059] To improve numerical stability, the target physical quantity can be learned in logarithmic space or logarithmic ratio space, for example:

[0060] Logarithmic space: ;

[0061] Logarithmic ratio space: ;

[0062] in, An engineering stability term is introduced to avoid numerical problems caused by zero or minimum values ​​in logarithmic operations. Its typical value is 1×10⁻³⁰. For reference physical quantity values, the mean, median, or target value of a specified benchmark design at the same time point can be taken.

[0063] (ii) Conformal calibration:

[0064] In obtaining the uncalibrated region Or point prediction Then, the conformal score is calculated on the calibration set (validation set or extrapolation set for cross-validation). and take it quantiles as calibration parameters .

[0065] When using interval conformal (CQR class), the following can be chosen: ;

[0066] in, Let be the conformal fraction of the i-th calibration sample; , These are the lower and upper interval endpoints predicted by the model for the i-th sample, respectively. Let i be the true target physical quantity of the i-th sample; This is the model's predicted value for the i-th sample.

[0067] When using conformal residuals, either symmetric or asymmetric fractions can be taken:

[0068] ;

[0069] Alternatively, quantile points can be taken from the upper and lower residuals to form an asymmetric expansion.

[0070] To adapt to the time structure, this invention supports one or a combination of the following calibration strategies:

[0071] Grouped Conformal Calibration: Group the calibration samples according to the grouping key. The grouping key includes at least one of the following: precise time point, time bin, operation phase, and phase × time bin; calculations are performed within each group. And use the corresponding group when making predictions. Perform interval expansion; where To sample A function that maps to group identifiers; This is the 1-α quantile calibration value calculated within group g.

[0072] Local conformal calibration: for each query point in the feature space Select k calibration nearest neighbors, and obtain the local calibration value based on the quantile of the nearest neighbor scores. Optionally, a Mondrian constraint of "nearest neighbor priority" can be imposed at discrete time points.

[0073] Out-of-Distribution (OOD) handling: When the query point is more than the nearest neighbor distance of the calibration set (e.g., the quantile of the 1-NN distance within the calibration set), it is judged as OOD and a more conservative k, a larger scaling factor, or a fallback to the group / global calibration amount is adopted.

[0074] Output range after calibration:

[0075] ;

[0076] Or in the conformal residual:

[0077] ;

[0078] And map back to the original dimensional space when needed; where , These are the lower and upper bounds of the calibrated prediction interval, respectively, located in the original dimensional space.

[0079] (III) First-order decay propagation during the cooling stage:

[0080] For nuclides / physical quantities that satisfy the first-order decay equation, analytical decay extrapolation can be used during the cooling stage to enhance tail stability.

[0081] Let the shutdown / irradiation end time be At any time during the cooling phase, ( The nuclide / physical quantity satisfies:

[0082] ;

[0083] Its analytical solution is:

[0084] ;

[0085] in, The decay constant (or the decay constant determined by the half-life) Equivalently given: ),in This represents the number of atoms of the target nuclide at time t; if the target physical quantity is not the number of atoms (such as activity), then replace it with the symbol of the corresponding physical quantity.

[0086] This solution can The point prediction or interval endpoint is used as the anchor value, and the above analytical decay extrapolation is applied synchronously to the point prediction and interval endpoint during the cooling period; conformal calibration can be performed during the irradiation period or throughout the entire period, and outputs the final interval in conjunction with the analytical extrapolation.

[0087] The present invention will be further described below with reference to the accompanying drawings. It should be understood that the specific embodiments of the present invention are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.

[0088] Implementation Method 1: Time-Aware Modeling and Target Space.

[0089] Step 1, Data Organization: Identify each design sample as sample_id, which forms a long table data row at multiple time points (which can be the entire irradiation / cooling period);

[0090] Step 2, Feature Construction:

[0091] Design Features Geometric and material composition, volume fraction, operating parameters, source terms or equivalent operating parameters, etc.

[0092] Time characteristics At least including With log10_time_years and Optionally, when phase metadata exists, add is_cooling, phase_elapsed_years, and log10_phase_elapsed_years; where is_cooling is a Boolean or 0 / 1 type feature, and a value of 1 indicates that the current stage is cooling; phase_elapsed_years is a floating-point feature, representing the number of years that have passed since the start of the current running stage; log10_phase_elapsed_years is a common logarithmic transformation of phase_elapsed_years, i.e., log10(phase_elapsed_years).

[0093] Step 3, Target Space: For targets with dynamic ranges spanning orders of magnitude (e.g., number of nuclides, activity, decay heat, dose rate), learning in logarithmic space is preferred.

[0094] ;

[0095] in, For engineering stability; or to learn in the logarithmic ratio space to reduce system bias.

[0096] Implementation Method 2: Generation of Uncalibrated Intervals.

[0097] Uncalibrated regions can be generated in one of the following ways:

[0098] Quantile Regression: Direct Learning (For example ), and obtain in model space ;

[0099] Point prediction + residual interval: Learning point estimation And use residual conformal construction to construct intervals.

[0100] Mapping the model space interval back to the original space yields the uncalibrated interval. .

[0101] in, Let q be the model prediction value of the qth quantile in logarithmic space; The uncalibrated prediction interval in logarithmic space; These are point predictions in logarithmic space. This represents the uncalibrated prediction interval after mapping back to the original dimensional space.

[0102] Implementation Method 3: For example Figure 2 As shown, the group conformal calibration specifically involves:

[0103] Calibration score: based on calibration set samples calculate ;

[0104] Grouping key:

[0105] Precise time point: (right Stable rounding is performed to avoid floating-point errors.

[0106] Time binning: Divide according to preset boundaries Mapped to discrete-time bins (time_bin);

[0107] Operation phase: For example, irradiation / cooling;

[0108] Grouping: .

[0109] Within-group threshold: Take within each group of quantiles, obtaining within groups quantile calibration value ;

[0110] Reasoning: Apply corresponding groups to the query points Expand the interval and output group-level coverage and interval width statistics.

[0111] in, To calibrate the feature vector, time, and true target value of the i-th sample in the set; This is the conformal score of the sample. This is the calibration value within its respective group g.

[0112] Implementation Method Four: (e.g.) Figure 3 As shown, local nearest neighbor conformal and OOD fallback.

[0113] Standardize the calibration feature vector (e.g., fill in missing values ​​with the median, normalize the standard deviation);

[0114] For each query point, find the k nearest neighbor calibration samples in the normalized space and take their scores. quantiles as ;

[0115] OOD determination: Calculate the 1-NN distance for the query point. When the distance exceeds the preset quantile threshold of the 1-NN distance within the calibration set, it is judged as OOD. Here, NN is the abbreviation for Nearest Neighbor; k is the number of selected nearest neighbors; and 1-NN distance is the Euclidean distance from the query point to the nearest calibration sample in the normalized feature space.

[0116] OOD rollback: Apply a larger k, a larger scaling factor to the OOD point, or roll back to grouping / global. .

[0117] Implementation Method 5: (e.g.) Figure 4 As shown, the first-order decay propagation occurs during the cooling phase.

[0118] When the target nuclide / physical quantity satisfies the first-order decay equation during the cooling phase:

[0119] Determine the shutdown time : It can be given directly by the stage identifier, or automatically detected through the time grid gap / running parameter threshold;

[0120] exist Obtaining anchor values: Model pairs can be used. The predicted points or interval endpoints are used as anchor values;

[0121] Arbitrary cooling stage ,according to:

[0122] ;

[0123] Extrapolation point prediction and interval endpoints; if necessary, [further details needed]. Configuration-based management or provided by the nuclide library;

[0124] Collaboration with conformal calibration: Conformal calibration can be performed during the irradiation phase followed by extrapolation, or group calibration can be performed on the extrapolated cooling prediction.

[0125] Implementation method six: such as Figure 5 As shown, audit outputs and access control assessments.

[0126] The present invention preferably outputs one or more of the following audit fields:

[0127] Run configuration snapshot (dataset identifier, feature list, model type, random seed, time window, , Grouping strategies, nearest neighbor parameters, OOD thresholds, etc.

[0128] Calibration evidence (sample size of each group, (such as coverage, median interval width, etc.)

[0129] Binning error indicators (such as the quantile factor for time-based binning, the maximum tail factor, etc.).

[0130] Access control result (pass / fail) and its threshold comparison;

[0131] Integrity information (hash digest / digital fingerprint / signature) is used to prove the consistency of configuration, data, and results.

[0132] Example Implementation (Example Diameter):

[0133] The following is a non-restrictive example of a total nuclide amount curve for the breeding region of a fusion reactor breeding blanket:

[0134] Time window: t∈[0,100] years;

[0135] Target: Number of nuclides (including tritium-related targets);

[0136] Time bin boundaries (years): [0, 1 / 365, 1, 10, 100, 1000, 10000, ∞);

[0137] Calibration confidence level: 90% (α=0.1);

[0138] Grouping strategy: Phase × Time binning;

[0139] Local conformal (optional): k=50, OOD threshold is taken as 0.99 quantile of the calibrated internal 1-NN distance;

[0140] Cooling extension: Analytical extrapolation is used for targets that satisfy the first-order decay equation during the cooling stage.

[0141] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A time-aware conformal uncertainty calibration method for fuel consumption evolution curves, characterized in that, include: Step 1: Obtain sample characteristics of fusion nuclear engineering objects Multiple time points and target physical quantity or calculation label The target physical quantity includes at least the number of nuclide atoms / stock, activity, decay heat, dose rate, multiplication ratio, or a combination thereof; Step 2: Extract time features As explicit input, a time-aware prediction model is constructed, resulting in... Point prediction or interval prediction, wherein the time feature includes at least and One or more of the following; the This is an absolute time value in years. Its commonly used logarithmic transformation; Step 3: Calculate the conformal score on the calibration set based on the point prediction or interval prediction, and use the conformal score as the basis for calculation. quantiles obtain calibration values ,in Preset coverage rate; Step 4: Obtain the calibration amount that changes over time by using group conformal calibration and / or local nearest neighbor conformal calibration, and expand the point prediction or interval prediction accordingly to obtain the calibrated prediction interval. Step 5: Output the calibrated prediction range and / or output audit information related to the calibration process.

2. The method according to claim 1, characterized in that, In step 2, the time-aware prediction model learns in a logarithmic space or a log-ratio space, wherein the logarithmic space or log-ratio space satisfies at least the following: ; and / or ； in An engineering stability term introduced to avoid numerical problems caused by zero or minimum values ​​in logarithmic operations; For reference physical quantity values, the target value at the same time point is taken from the mean, median, or specified benchmark design of the training set.

3. The method according to claim 1, characterized in that, The conformal fraction mentioned in step 3 includes one of the following: Interval violation fraction ; residuals ; Asymmetric fractions constructed based on upper and lower residuals respectively; where , These are the lower and upper interval endpoints predicted by the model for the i-th sample, respectively. Let i be the true target physical quantity of the i-th sample. This is the model's predicted value for the i-th sample.

4. The method according to claim 1, characterized in that, The calibration quantity is calculated as follows: missing value imputation and scale normalization are performed on the feature vectors of the calibration set and the query point. In the normalized feature space, the k nearest neighbor calibration samples are selected, and their conformal fraction 1-α quantiles are used as the local calibration quantity. Furthermore, at discrete time points, nearest neighbor samples are selected preferentially or only from the set of discrete time points that are the same as the query point.

5. The method according to claim 4, characterized in that, It also includes out-of-distribution sample judgment: when the nearest neighbor distance from the query point to the calibration set exceeds a preset threshold, it is judged as an out-of-distribution sample, and a more conservative nearest neighbor number, calibration scaling factor, or fallback to the group / global calibration value is applied to the out-of-distribution sample.

6. The method according to claim 1, characterized in that, The calibration set mentioned in step 3 is generated through cross-validation: grouped multi-fold cross-validation is performed on the sample label dimension of the training set and the validation set, and conformal scores are generated by extrapolation prediction.

7. The method according to claim 1, characterized in that, Furthermore, the grouping key used in the grouping conformal calibration includes at least one or more of the following: precise time point, time bin, operation phase, or phase × time bin; the time bin adopts the time boundary of a right-closed interval and includes at least a time bin of more than 100 years for characterizing the risk of cooling tail.

8. The method according to claim 7, characterized in that, When the target physical quantity satisfies the first-order decay equation during the cooling phase, the following further includes: determining the shutdown time. ;by The predicted point or interval endpoint is used as the anchor value; for according to Extrapolation point prediction and interval endpoints; where λ is the decay constant, derived from the half-life. Equivalence is determined, satisfying The Sources include nuclide databases, configuration files, or parameter tables; Let be the number of atoms of the target nuclide at time t.

9. The method according to claim 1, characterized in that, The audit information mentioned above includes at least one or more of the following: runtime configuration snapshot information; calibration group and sample size information; calibration amount for each group. Coverage and interval width statistics; error factor index for time-based binning; access control pass / fail conclusions; data and configuration integrity verification information.

10. The method according to claim 7, characterized in that, The operation phase includes at least an irradiation phase and a cooling phase, and the operation phase is determined by an explicit phase identifier and / or by operation parameters and threshold rules characterizing the source term intensity or power.

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