Method and system for quantifying uncertainty in leaf area index inversion

Abstract

The application provides a leaf area index inversion uncertainty quantification method and system, and belongs to the technical field of remote sensing data processing, and comprises the following steps: extracting target spectral features according to a remote sensing image; generating a simulation sample set based on a radiation transfer model; combining model sensitivity and parameter prior calculation to obtain a first uncertainty degree derived from physical parameter transmission; repeatedly training and constructing a machine learning model set by using the simulation sample set; calculating a second uncertainty degree derived from algorithm randomness according to the statistical dispersion degree of model set prediction values; and obtaining a total uncertainty degree according to the first and second uncertainty degrees. By quantifying physical modeling errors and algorithm randomness errors respectively, end-to-end decoupling and comprehensive of the uncertainty are realized, so that the accuracy of the confidence evaluation of the leaf area index inversion result is improved.

Description

Technical Field

[0001] This invention relates to the field of remote sensing data processing technology, and in particular to a method and system for quantifying uncertainty in leaf area index inversion. Background Technology

[0002] Leaf area index (LAI) is a key parameter characterizing vegetation growth. Using remote sensing technology combined with physical models and machine learning algorithms to retrieve LAI is currently the mainstream method for obtaining large-scale vegetation parameters and is widely used in agricultural monitoring and ecological assessment.

[0003] Existing techniques typically utilize radiative transfer models to generate training data, train machine learning models to establish a mapping relationship between the spectrum and leaf area index, and directly output prediction results or include globally uniform error statistics when applied. This approach primarily focuses on the inversion accuracy of the leaf area index value itself, usually assuming ideal input parameters or evaluating model performance through simple statistical validation.

[0004] However, existing technologies overlook the complexity of different error sources during the inversion process, failing to effectively distinguish between systematic biases introduced by assumptions about physical model parameters and instabilities caused by the randomness of machine learning algorithms. The lack of decoupling and comprehensive quantification of these two distinct error sources makes it difficult for existing methods to accurately reflect the true reliability of each pixel's inversion result, thus reducing the accuracy of confidence assessment for leaf area index inversion results. Summary of the Invention

[0005] This invention provides a method and system for quantifying the uncertainty of leaf area index inversion, which addresses the shortcomings of existing technologies and improves the accuracy of confidence assessment of leaf area index inversion results.

[0006] This invention provides a method for quantifying the uncertainty of leaf area index inversion, comprising the following steps: Extract target spectral feature data from remote sensing images of the area to be measured; Based on the radiative transfer model, a simulated sample set containing simulated spectral feature data and corresponding true values ​​of leaf area index is generated. Calculate the sensitivity of the spectral response of the radiative transfer model to the input parameters, and, in conjunction with the prior uncertainty of the input parameters, calculate the first uncertainty arising from the propagation of the physical model parameters; A machine learning inversion model is constructed, and the machine learning inversion model is repeatedly trained using the simulated sample set to obtain a model set consisting of multiple trained sub-models. The target spectral feature data is input into each sub-model in the model set to obtain the leaf area index prediction value output by each sub-model. Based on the statistical dispersion of the multiple leaf area index prediction values, the second uncertainty arising from the randomness of the machine learning training process is calculated. Based on the first uncertainty and the second uncertainty, the total uncertainty of the leaf area index inversion of the region to be measured is obtained.

[0007] According to the leaf area index inversion uncertainty quantification method provided by the present invention, the step of constructing a machine learning inversion model involves repeatedly training the machine learning inversion model using the simulated sample set to obtain a model set consisting of multiple trained sub-models, including: Constructing a machine learning inversion model with a neural network structure; The weight parameters and bias parameters of the neural network are encoded as chromosomes using real values ​​to generate an initial population. Using the training and validation data in the simulated sample set, the fitness function value of individuals in the initial population is calculated; Based on the fitness function value, the initial population is subjected to selection, crossover, and mutation operations, and the population is iteratively updated until the stopping condition is met to obtain the trained sub-model; Repeat the above process until a preset number of trained sub-models are obtained, thus generating the model set.

[0008] According to the leaf area index inversion uncertainty quantification method provided by the present invention, the step of calculating the fitness function value of individuals in the initial population using training data and validation data in the simulated sample set includes: Calculate the first root mean square error of the current individual on the training data and the second root mean square error on the validation data, respectively; The fitness function value is obtained by weighted summation of the first root mean square error and the second root mean square error.

[0009] According to the leaf area index inversion uncertainty quantification method provided by the present invention, the calculation of the sensitivity of the spectral response of the radiative transfer model to the input parameters includes: The partial derivatives of the radiative transfer model are approximated using the central difference method; For each target parameter in the input parameters, a small perturbation step size is set; Calculate the change in spectral reflectance output by the radiative transfer model when the target parameter is increased and the perturbation step size is decreased, respectively; The sensitivity of the spectral response to the target parameter is determined based on the ratio of the change to twice the perturbation step size.

[0010] According to the leaf area index inversion uncertainty quantification method provided by the present invention, the calculation of the first uncertainty originating from the parameter propagation of the physical model, in conjunction with the prior uncertainty of the input parameters, includes: Determine the standard uncertainty of each input parameter; Calculate the error covariance between correlated input parameters; Based on the sensitivity, the standard uncertainty, and the error covariance, the simulated uncertainty of each band is calculated using the uncertainty propagation law. The simulated uncertainty of each band is calculated by weighted sum of squares based on the bandwidth of each band, and the square root of the calculation result is obtained to obtain the first uncertainty.

[0011] According to the leaf area index inversion uncertainty quantification method provided by the present invention, the step of calculating a second uncertainty arising from the randomness of the machine learning training process based on the statistical dispersion of multiple leaf area index prediction values ​​includes: Based on the leaf area index predictions output by all the sub-models, the prediction mean and prediction standard deviation are calculated. The second uncertainty is obtained by calculating the ratio of the predicted standard deviation to the predicted mean.

[0012] According to the leaf area index inversion uncertainty quantification method provided by the present invention, the step of obtaining the total uncertainty of leaf area index inversion of the region to be measured based on the first uncertainty and the second uncertainty includes: Calculate the sum of the square of the first uncertainty and the square of the second uncertainty; The total uncertainty of the leaf area index inversion for the region to be measured is obtained by calculating the square root of the sum of the squares.

[0013] This invention also provides a system for quantifying the uncertainty of leaf area index inversion, comprising the following modules: The first processing module is used to extract target spectral feature data based on remote sensing images of the area to be measured; The second processing module is used to generate a simulated sample set containing simulated spectral feature data and corresponding true values ​​of leaf area index based on the radiative transfer model. The third processing module is used to calculate the sensitivity of the spectral response of the radiative transfer model to the input parameters, and, in combination with the prior uncertainty of the input parameters, calculate the first uncertainty arising from the parameter propagation of the physical model. The fourth processing module is used to construct a machine learning inversion model, and to repeatedly train the machine learning inversion model using the simulated sample set to obtain a model set consisting of multiple trained sub-models. The fifth processing module is used to input the target spectral feature data into each sub-model in the model set to obtain the leaf area index prediction value output by each sub-model, and to calculate the second uncertainty caused by the randomness of the machine learning training process based on the statistical dispersion of the multiple leaf area index prediction values. The sixth processing module is used to obtain the total uncertainty of leaf area index inversion of the region to be measured based on the first uncertainty and the second uncertainty.

[0014] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the leaf area index inversion uncertainty quantification method as described above.

[0015] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the leaf area index inversion uncertainty quantification method as described above.

[0016] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the leaf area index inversion uncertainty quantification method as described above.

[0017] In summary, one or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages: This application addresses the problem of insufficient sample representativeness by generating a simulated sample set containing simulated spectral feature data and corresponding true values ​​of leaf area index based on a radiative transfer model. It constructs a complete physical prior knowledge base. By calculating the sensitivity of the spectral response of the radiative transfer model to input parameters and combining this with the prior uncertainty of the input parameters, it calculates the first uncertainty arising from the transmission of physical model parameters, thus accurately quantifying the error propagation at the physical mechanism level. By constructing a machine learning inversion model and repeatedly training it using the simulated sample set, it obtains a model set composed of multiple trained sub-models, thereby capturing the random fluctuations during algorithm training using ensemble learning. By inputting the target spectral feature data into the model set to obtain multiple predicted values ​​and calculating the second uncertainty arising from the randomness of the machine learning training process, it accurately quantifies the randomness error inherent in the data-driven algorithm itself. By obtaining the total uncertainty of leaf area index inversion for the test area based on the first and second uncertainties, it provides an end-to-end error range with clear physical meaning for the inversion results, improving the accuracy of the confidence assessment of the leaf area index inversion results. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0019] Figure 1 This is one of the flowcharts of the leaf area index inversion uncertainty quantification method provided by the present invention.

[0020] Figure 2 This is the second flowchart of the leaf area index inversion uncertainty quantification method provided by the present invention.

[0021] Figure 3 This is a schematic diagram of the uncertainty quantification system for leaf area index inversion provided by the present invention.

[0022] Figure 4 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0024] It should be noted that in the description of this invention, the terms "comprising," "including," or any other variations thereof are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element. The terms "upper," "lower," etc., indicating orientation or positional relationships according to the accompanying drawings, are only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the system or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0025] The terms "first," "second," etc., used in this invention are used to distinguish similar objects, not to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that embodiments of the invention can be implemented in orders other than those illustrated or described herein, and the objects distinguished by "first," "second," etc., are generally of the same class, without limiting the number of objects; for example, a first object can be one or more. Furthermore, "and / or" indicates at least one of the connected objects, and the character " / " generally indicates that the preceding and following objects are in an "or" relationship.

[0026] The following is combined with Figures 1 to 4 This invention describes the leaf area index inversion uncertainty quantification method, system, electronic device, storage medium, and computer program product provided by the present invention.

[0027] This application provides a method for quantifying the uncertainty of leaf area index (LAI) inversion. The executing entity in this embodiment is a remote sensing data processing device. This remote sensing data processing device includes, but is not limited to, a high-performance computer, a server, or a cloud computing cluster. Through this method for quantifying the uncertainty of LAI inversion, the remote sensing data processing device can achieve end-to-end uncertainty assessment that combines physical mechanisms with data-driven approaches.

[0028] Reference Figure 1 , Figure 1 This is a flowchart illustrating the uncertainty quantification method for leaf area index inversion provided by the present invention, as shown below. Figure 1 As shown, the uncertainty quantification method for leaf area index inversion includes steps 101 to 106: Step 101: Extract target spectral feature data based on remote sensing images of the area to be measured; Step 102: Based on the radiative transfer model, generate a simulated sample set containing simulated spectral feature data and corresponding true values ​​of leaf area index; Step 103: Calculate the sensitivity of the spectral response of the radiative transfer model to the input parameters, and calculate the first uncertainty arising from the propagation of the physical model parameters, taking into account the prior uncertainty of the input parameters. Step 104: Construct a machine learning inversion model, and repeatedly train the machine learning inversion model using the simulated sample set to obtain a model set consisting of multiple trained sub-models; Step 105: Input the target spectral feature data into each sub-model in the model set to obtain the leaf area index prediction value output by each sub-model, and calculate the second uncertainty due to the randomness of the machine learning training process based on the statistical dispersion of the multiple leaf area index prediction values. Step 106: Based on the first uncertainty and the second uncertainty, obtain the total uncertainty of the leaf area index inversion of the region to be measured.

[0029] Specifically, firstly, the remote sensing data processing equipment extracts target spectral feature data from the remote sensing imagery of the area to be measured. The equipment acquires the original remote sensing imagery covering the area and performs preprocessing operations on it. These preprocessing operations include radiometric calibration, atmospheric correction, and geometric correction. In the radiometric calibration stage, the equipment uses the gain and offset values ​​from the satellite sensor parameters to convert the digital number (DN) values ​​of the original imagery into radiance values. The calculation formula is as follows: .

[0030] In the geometric correction stage, remote sensing data processing equipment uses ground control points combined with image-to-map registration methods, or based on the accompanying geometric projection information, to eliminate geometric distortions in the images.

[0031] In the atmospheric correction stage, remote sensing data processing equipment uses atmospheric radiative transfer models (such as the FLAASH module or 6S model) to eliminate the effects of atmospheric scattering and absorption, converting radiance values ​​into surface reflectance data.

[0032] After preprocessing, the remote sensing data processing equipment extracts image data from the image as target spectral feature data.

[0033] In this step, as an optional implementation, the remote sensing data processing equipment can directly use multi-band reflectance values ​​as target spectral feature data. Alternatively, to enhance sensitivity to vegetation signals and reduce background noise, the remote sensing data processing equipment can also calculate a vegetation index using preprocessed reflectance data and use the calculated vegetation index as target spectral feature data. This vegetation index includes, but is not limited to, the Normalized Difference Vegetation Index (NDVI), the Modified Normalized Difference Vegetation Index (MNDVI), the SimpleRatio (SR), or the Perpendiculars Vegetation Index (PVI). For example, when using NDVI, the remote sensing data processing equipment calculates the vegetation index based on the red band reflectance... R and near-infrared reflectivity NIR calculate NDVI =( NIR -R ) / ( NIR + R This is then used as an input feature for subsequent steps.

[0034] Secondly, the remote sensing data processing equipment generates a simulated sample set containing simulated spectral feature data and corresponding true values ​​of leaf area index based on the radiative transfer model.

[0035] Remote sensing data processing equipment operates radiative transfer models (such as the PROSAIL model). A radiative transfer model is a mathematical model used to simulate the physical processes of light interaction with the vegetation canopy. The equipment uses various vegetation biophysical parameters, including leaf area index, chlorophyll content, and leaf tilt angle distribution, as well as soil background parameters, as input variables to the radiative transfer model. The equipment then uses the radiative transfer model to generate simulated spectral data corresponding to the input variables.

[0036] If the target spectral feature data is set as reflectance in the aforementioned steps, the remote sensing data processing device directly uses the simulated reflectance output by the radiative transfer model as the simulated spectral feature data. If the target spectral feature data is set as a vegetation index in the aforementioned steps, the remote sensing data processing device further calculates the corresponding vegetation index (such as NDVI, MNDVI, SR, or PVI) using the simulated reflectance output by the radiative transfer model, and uses the calculated simulated vegetation index as the simulated spectral feature data. Finally, the remote sensing data processing device constructs a simulated sample set containing a large number of data pairs. Each data point in the simulated sample set includes the true value of the leaf area index as input and the corresponding simulated spectral feature data.

[0037] Next, the remote sensing data processing equipment calculates the sensitivity of the spectral response of the radiative transfer model to the input parameters, and, in conjunction with the prior uncertainty of the input parameters, calculates the first uncertainty arising from the transmission of physical model parameters.

[0038] Remote sensing data processing equipment utilizes the uncertainty propagation law to quantify how errors in input parameters are transmitted to the output of a radiative transfer model. The equipment calculates the sensitivity of the radiative transfer model's output to each input parameter and obtains prior uncertainty information for each input parameter (e.g., standard uncertainty and error covariance). Based on the sensitivity and prior uncertainty information, the equipment calculates the first uncertainty characterizing the error propagation effect of the physical parameters.

[0039] Subsequently, the remote sensing data processing equipment constructs a machine learning inversion model, and uses a simulated sample set to repeatedly train the machine learning inversion model to obtain a model set consisting of multiple trained sub-models.

[0040] In this application embodiment, the machine learning inversion model constructed by the remote sensing data processing equipment is not limited to a specific type. As a preferred implementation, a neural network model can be used. As other optional implementations, the machine learning inversion model can also be constructed using algorithms such as Random Forest (RF), eXtreme Gradient Boosting (XGBoost), or Support Vector Regression (SVR). As long as the model can learn the nonlinear mapping relationship in the simulated sample set and supports obtaining the statistical dispersion of the model prediction through repeated training or ensemble learning, it is within the protection scope of this application.

[0041] In a preferred embodiment of this application, a neural network model is used as the machine learning inversion model for explanation. The remote sensing data processing device trains the machine learning inversion model using a simulated sample set, and repeatedly executes the training process by adjusting the initial parameters of the machine learning inversion model or the training set sampling method. R Each training iteration (e.g., 100 iterations) is performed. After each training cycle, the remote sensing data processing device saves the parameters of the model generated during the current training, treating the currently generated model as a trained sub-model. The remote sensing data processing device then combines all trained sub-models to form a model set.

[0042] Then, the remote sensing data processing equipment inputs the target spectral feature data into each sub-model in the model set to obtain the leaf area index prediction value output by each sub-model, and calculates the second uncertainty arising from the randomness of the machine learning training process based on the statistical dispersion of multiple leaf area index prediction values.

[0043] The remote sensing data processing equipment simultaneously inputs the target spectral feature data (reflectance or vegetation index) of the same pixel in the remote sensing image of the area to be measured into all sub-models contained in the model set. Each sub-model outputs a corresponding leaf area index prediction value. The remote sensing data processing equipment statistically analyzes the dispersion of the leaf area index prediction values ​​output by all sub-models (e.g., the relationship between the standard deviation and the mean) to quantify the randomness of the machine learning algorithm itself, thus obtaining the second uncertainty.

[0044] Finally, the remote sensing data processing equipment obtains the total uncertainty of the leaf area index inversion of the area to be measured based on the first uncertainty and the second uncertainty.

[0045] The remote sensing data processing equipment considers the first uncertainty to represent the error at the physical mechanism level, and the second uncertainty to represent the error at the data-driven algorithm level. The remote sensing data processing equipment combines the first uncertainty and the second uncertainty to obtain the total uncertainty of leaf area index inversion at the pixel location in the area to be measured, and generates a spatial distribution map containing the predicted leaf area index value and its corresponding total uncertainty of leaf area index inversion.

[0046] The leaf area index (LAI) inversion uncertainty quantification method provided in this application ensures data quality through a comprehensive remote sensing image preprocessing workflow and offers multiple feature extraction schemes based on reflectance or vegetation indices, enhancing the method's applicability and flexibility. By separately calculating the first uncertainty originating from the transmission of physical model parameters and the second uncertainty originating from the randomness of the machine learning training process, and then combining the first and second uncertainties, the method achieves decoupling and comprehensive quantification of physical modeling errors and algorithmic randomness errors in the LAI inversion process, thereby providing high-precision LAI inversion results.

[0047] Furthermore, in the process of calculating the sensitivity of the spectral response of the radiative transfer model to the input parameters, given that the radiative transfer model usually has a complex nonlinear structure, it is often difficult to directly obtain an accurate mathematical analytical solution. Therefore, the remote sensing data processing equipment uses numerical calculation methods to obtain the sensitivity.

[0048] In one specific implementation, calculating the sensitivity of the spectral response of the radiative transfer model to the input parameters includes the following steps: Step 201: Use the central difference method to approximate the partial derivatives of the radiative transfer model; Step 202: For each target parameter in the input parameters, set a small perturbation step size; Step 203: Calculate the change in spectral reflectance output by the radiative transfer model when the target parameter increases and decreases the perturbation step size, respectively; Step 204: Determine the sensitivity of the spectral response to the target parameter based on the ratio of the change to twice the perturbation step size.

[0049] Specifically, the remote sensing data processing equipment uses the central difference method to approximate the partial derivatives of the radiative transfer model.

[0050] The central difference method is a numerical differentiation method that uses the value of a function in the neighborhood of a point to approximate the derivative. It can effectively evaluate the sensitivity of the model output to the input when there is no explicit analytical expression.

[0051] For each target parameter in the input parameters, the remote sensing data processing equipment sets a small perturbation step size. The remote sensing data processing equipment then determines the target parameters. The current value is set, and a small change relative to that value is set as the perturbation step size. To ensure the accuracy of approximate calculations, remote sensing data processing equipment typically adjusts the perturbation step size. Set as target parameter A very small percentage of the input interval length, for example, set to 0.1% of the input interval length.

[0052] Subsequently, the remote sensing data processing equipment calculated the changes in spectral reflectance output by the radiative transfer model as the perturbation step size of the target parameters increased and decreased. The remote sensing data processing equipment maintained the values ​​excluding the target parameters... All other input parameters remain unchanged, only the target parameter is changed. The value is adjusted to The spectral reflectance under positive perturbation is obtained by running the radiative transfer model. Similarly, remote sensing data processing equipment will process target parameters. The value is adjusted to The spectral reflectance under negative perturbation is obtained by running the radiative transfer model. .

[0053] Finally, the remote sensing data processing equipment determines the sensitivity of the spectral response to the target parameters based on the ratio of the change to twice the perturbation step size. The equipment then calculates approximate values ​​of the partial derivatives using the central difference formula, as follows: ; in, That is, the spectral response to the target parameter Sensitivity, That is, the change in spectral reflectance. This is the total change step size. When the perturbation step size... When sufficiently small, this ratio can approximate the true partial derivative with high accuracy. The remote sensing data processing equipment repeats the above process for all input parameters to obtain the sensitivity vector of the radiative transfer model output for each input parameter.

[0054] This application's embodiments overcome the technical challenge of directly differentiating complex physical models (such as PROSAIL) by employing the central difference method to calculate sensitivity. This method utilizes small perturbation step sizes. Numerical approximation (e.g., using an interval length of 0.1%) allows for precise quantification of the specific impact of minute fluctuations in each physical parameter (such as chlorophyll and leaf tilt angle) on the final spectral reflectance, even without analytical expressions. This not only provides crucial gradient information for subsequent uncertainty calculations based on the law of error propagation but also significantly improves the applicability and accuracy of the uncertainty quantification process when dealing with complex nonlinear physical models.

[0055] Furthermore, in calculating the first uncertainty arising from the transfer of physical model parameters, remote sensing data processing equipment needs to comprehensively consider the random errors of the input parameters themselves as well as the interdependencies between the parameters in order to achieve accurate error transfer calculation.

[0056] In one specific implementation, the first uncertainty arising from the propagation of physical model parameters is calculated by considering the prior uncertainty of the input parameters, specifically including the following steps: Step 301: Determine the standard uncertainty of each input parameter; Step 302: Calculate the error covariance between correlated input parameters; Step 303: Based on the sensitivity, the standard uncertainty, and the error covariance, calculate the simulated uncertainty of each band using the uncertainty propagation law; Step 304: Calculate the weighted sum of squares of the simulation uncertainty of each band based on the bandwidth of each band, and take the square root of the calculation result to obtain the first uncertainty.

[0057] Specifically, the remote sensing data processing equipment first determines the standard uncertainty of each input parameter. The remote sensing data processing equipment then applies this to the PROSAIL model function. Set the input parameters other than LAI to a truncated normal distribution with the midpoint of the interval as the mean and 1 / 6 of the interval length as the standard deviation.

[0058] Based on the parameter independence assumption, remote sensing data processing equipment targets parameters. conduct m The input sample set is obtained by sampling once, while fixing other parameters at their expected values. Where i = 1, 2, ..., n, j = 1, 2, ..., m. For each set of samples, the remote sensing data processing equipment calculates the inversion output. Based on the output sample set Remote sensing data processing equipment directly calculates parameters using the following formula. Simulated mean reflectance under different sampling conditions With uncertainty measurement index : ; in, Indicates the first j The reflectance output value corresponding to the next sample. This is the standard uncertainty required for subsequent calculations.

[0059] Secondly, the remote sensing data processing equipment calculates the error covariance between correlated input parameters. To accurately assess the uncertainty caused by the coordinated changes in correlated parameters, the equipment further calculates the error correlation between reflectance changes caused by these parameters. The remote sensing data processing equipment calculates the parameters... and The output sample sets obtained after inputting them into the PROSAIL model and And use the following formula to calculate the error correlation. : in, and . Indicates all The average value, Indicates all The average value. Correlation coefficient value. The closer the value is to 1, the stronger the correlation between the two variables. Subsequently, the remote sensing data processing equipment uses the following formula to calculate the error covariance. : .

[0060] in, and Parameters and The standard uncertainty is determined by introducing error covariance. Remote sensing data processing equipment can effectively capture the impact of coordinated parameter variations on model output.

[0061] Next, the remote sensing data processing equipment calculates the simulated uncertainty for each spectral band based on sensitivity, standard uncertainty, and error covariance, using the uncertainty propagation law. The remote sensing data processing equipment addresses each spectral band... b The uncertainty propagation law (LPU) is used to propagate the error from the input to the output, and the reflectivity of this band is calculated. simulation uncertainty The specific calculation formula is as follows: ; In the formula, the first term The second term represents the variance contribution caused by the independent action of each parameter. This represents the covariance contribution caused by the correlation between parameters. By including the covariance term, this calculation process corrects for the error estimation bias under the traditional independence assumption.

[0062] Finally, the remote sensing data processing equipment calculates the weighted sum of squares of the simulation uncertainties for each band based on the bandwidth of each band, and then takes the square root of the calculation result to obtain the first uncertainty. Since different bands have different bandwidths in the spectral response function, their information content and contribution to the total error also differ. The remote sensing data processing equipment acquires the first... b Bandwidth of each band And synthesize all of them using the following formula. k The uncertainty of each band is used to obtain the final first uncertainty. : .

[0063] This application's embodiments overcome the limitations of traditional methods that assume independent input parameters by introducing error covariance calculation, realistically revealing the impact of complex biophysical relationships among vegetation parameters on the inversion results. Simultaneously, weighted synthesis using bandwidth ensures a reasonable weight allocation between wide and narrow bands in the total uncertainty. This process, starting from the source of the physical mechanism, achieves precise analysis of the propagation process of model input errors to the output, providing a rigorously physical quality evaluation index for the final LAI inversion product.

[0064] To construct a high-precision leaf area index inversion model with strong generalization ability, the remote sensing data processing equipment adopts a strategy of optimizing the neural network using a genetic algorithm to generate a model set containing multiple sub-models.

[0065] In one specific implementation, a machine learning inversion model is constructed, and the machine learning inversion model is repeatedly trained using the simulated sample set to obtain a model set consisting of multiple trained sub-models. The specific steps include: Step 401: Construct a machine learning inversion model of the neural network structure; Step 402: Encode the weight parameters and bias parameters of the neural network as chromosomes using real values ​​to generate an initial population; Step 403: Using the training and validation data in the simulated sample set, calculate the fitness function value of individuals in the initial population; Step 404: Based on the fitness function value, perform selection, crossover, and mutation operations on the initial population, iteratively update the population until the stopping condition is met, and obtain the trained sub-model; Step 405: Repeat the above process until a preset number of trained sub-models are obtained, and generate the model set.

[0066] Specifically, the remote sensing data processing equipment first constructs a machine learning inversion model with a neural network structure. The equipment designs a Multi-Layer Perceptron (MLP) as the basic inversion network. This neural network consists of an input layer, several hidden layers, and an output layer. The number of nodes in the input layer corresponds to the dimension of the simulated spectral feature data (e.g., the number of bands or vegetation indices), and the output layer has one node, corresponding to the predicted value of the leaf area index (LAI).

[0067] Secondly, the remote sensing data processing equipment encodes the weight and bias parameters of the neural network as chromosomes using real values, generating an initial population. Instead of using traditional random initialization or gradient descent to directly update parameters, the equipment concatenates the weights of all connections and the biases of all nodes in the neural network to form a long vector. This long vector is defined as a chromosome in the genetic algorithm. The equipment randomly generates multiple such chromosomes, forming the initial population for the genetic algorithm. Each chromosome in the population represents a neural network instance with a specific weight and bias configuration.

[0068] Next, the remote sensing data processing equipment uses training and validation data from the simulated sample set to calculate the fitness function values ​​of individuals in the initial population. The equipment divides the simulated sample set into training and validation sets. For each individual in the population (i.e., each set of specific network parameters), the equipment decodes and assigns the values ​​to the neural network. The equipment then uses this neural network to make predictions on both the training and validation sets and calculates the error between the predictions and the actual LAI values. Based on this error, the equipment calculates the fitness function value, which reflects the quality of the current neural network parameter configuration.

[0069] Subsequently, the remote sensing data processing equipment performs selection, crossover, and mutation operations on the initial population based on the fitness function value, iteratively updating the population until a stopping condition is met, resulting in a trained sub-model. The equipment uses roulette wheel or tournament selection to select superior individuals based on the fitness function value. Crossover is performed on the selected individuals, exchanging chromosome segments to generate new offspring. Simultaneously, mutation is performed on the offspring with a certain probability, randomly changing some gene values ​​in the chromosomes to increase population diversity and prevent getting trapped in local optima. This selection, crossover, and mutation process is repeated for multiple generations until a preset number of iterations is reached or the fitness no longer significantly improves (stopping condition). At this point, the equipment decodes the individual with the highest fitness in the population into the final weights and biases, thus obtaining a trained sub-model.

[0070] Finally, the remote sensing data processing equipment repeats the above process until a predetermined number of trained sub-models are obtained, generating a model set. To quantify the randomness of the algorithm itself, the remote sensing data processing equipment repeatedly executes the entire process of training a neural network based on a genetic algorithm. R Next (for example) R =100). During each repeated training iteration, the remote sensing data processing device reinitializes the population, resulting in multiple sub-models with slightly different parameter configurations but all achieving optimal performance. The remote sensing data processing device will then... R The trained sub-models are encapsulated to form the final model set.

[0071] This application's embodiments effectively overcome the problems of traditional gradient descent algorithms, such as getting trapped in local optima and sensitivity to initial values, by introducing a genetic algorithm to globally search and optimize the weights and biases of the neural network. Real-valued encoding transforms complex network parameters into evolutionary chromosomes, enabling the model to explore more broadly in the solution space. Furthermore, by repeatedly performing this evolutionary training process to build a model set, not only is a high-performance inversion generator obtained, but also the necessary statistical sample basis is provided for subsequent calculations of the second uncertainty arising from the randomness of the algorithm's training process. This significantly improves the stability and generalization ability of the inversion model when facing complex remote sensing data.

[0072] Furthermore, in the process of calculating the fitness function value of individuals in the initial population using training and validation data from the simulated sample set, in order to prevent the neural network from overfitting the training data and losing its ability to generalize to unknown data, the remote sensing data processing equipment adopts a strategy of weighted fusion of training error and validation error.

[0073] In one specific implementation, the fitness function value of individuals in the initial population is calculated using the training and validation data in the simulated sample set, specifically including the following steps: Step 501: Calculate the first root mean square error of the current individual on the training data and the second root mean square error on the validation data, respectively; Step 502: Perform a weighted summation of the first root mean square error and the second root mean square error to obtain the fitness function value.

[0074] Specifically, the remote sensing data processing equipment first calculates the first root mean square error (RMSE) of the current individual on the training data and the second RMSE on the validation data. The equipment then decodes the individual's chromosome into weights and bias parameters for a neural network. Using this neural network, the equipment predicts the LAI value for all samples in the training set and calculates the first RMSE between the predicted and actual LAI values. The calculation formula is as follows: ; in, The total number of samples in the training set. T For the training set sample index set, For the first i The true LAI value of each sample This is the current neural network's prediction for this sample.

[0075] Similarly, the remote sensing data processing equipment uses this neural network to predict all samples in the validation set and calculates the second root mean square error between the predicted LAI value and the true LAI value. The calculation formula is as follows: ; in, The total number of samples in the validation set, V This is the set of sample indexes for the validation set.

[0076] Subsequently, the remote sensing data processing equipment performs a weighted summation of the first root mean square error and the second root mean square error to obtain the fitness function value. The remote sensing data processing equipment then constructs the comprehensive fitness function based on the following formula. Fit : ;in, α The weighting coefficients are used to verify the error.

[0077] In this embodiment, to emphasize the model's generalization performance and avoid situations where it performs well only on the training set but fails on the validation set, the remote sensing data processing device adjusts the weighting coefficients. α Set to a value greater than 1 (e.g., 2). Calculated by the remote sensing data processing equipment. Fit The smaller the value, the better the overall performance of the current individual, and the higher the probability that it will be retained in the subsequent genetic selection process.

[0078] This application's embodiments construct an optimization objective that balances training fit and generalization ability by explicitly introducing validation error into the fitness function and assigning it a high weight (e.g., twice the weight). This design forces the genetic algorithm to focus not only on the learning effect on known samples but also on the prediction stability of unseen samples when searching for the optimal parameter space, thereby fundamentally improving the applicability and robustness of the final generated inversion model in real remote sensing scenarios.

[0079] Furthermore, in calculating the second uncertainty arising from the randomness of the machine learning training process, the remote sensing data processing equipment utilizes the statistical characteristics of the prediction results of multiple sub-models in the model set to quantify the inversion fluctuations caused by training randomness (such as the initial population differences and mutation randomness of the genetic algorithm).

[0080] In one specific implementation, a second uncertainty arising from the randomness of the machine learning training process is calculated based on the statistical dispersion of the multiple leaf area index predictions, specifically including the following steps: Step 601: Calculate the predicted mean and predicted standard deviation based on the leaf area index predictions output by all the sub-models. Step 602: Calculate the ratio of the predicted standard deviation to the predicted mean to obtain the second uncertainty.

[0081] Specifically, the remote sensing data processing equipment first calculates the predicted mean and standard deviation based on the leaf area index predictions output by all sub-models. The remote sensing data processing equipment collects all... M Each sub-model outputs a predicted leaf area index value for the same pixel's target spectral feature data. Remote sensing data processing equipment calculates this M The average of the predicted values μ The calculation formula is: ; At the same time, the remote sensing data processing equipment calculates this M Standard deviation of each predicted value σ The calculation formula is: ; The standard deviation σ It intuitively reflects the degree of dispersion of the output results of different sub-models when faced with the same input.

[0082] Subsequently, the remote sensing data processing equipment calculates the ratio of the predicted standard deviation to the predicted mean, obtaining the second uncertainty. To obtain a relative, dimensionless measure of uncertainty, the remote sensing data processing equipment uses the standard deviation... σ Divide by the mean μ This yields the relative error in the form of the coefficient of variation. The remote sensing data processing equipment defines this ratio as the second uncertainty arising from the randomness of the machine learning training process. The calculation formula is as follows: .

[0083] Alternatively, to maintain consistency with the variance form, remote sensing data processing equipment can also use the square form for intermediate calculations, as shown in the following formula: ; Finally, the second uncertainty It quantifies the proportion of prediction uncertainty introduced solely by the randomness of the algorithm itself.

[0084] Furthermore, in the process of obtaining the total uncertainty of the leaf area index inversion of the area to be measured, the remote sensing data processing equipment uses the error synthesis method to integrate the uncertainty at the physical mechanism level and the uncertainty at the data-driven level.

[0085] In one specific implementation, the total uncertainty of the leaf area index inversion of the region to be measured is obtained based on the first uncertainty and the second uncertainty, specifically including the following steps: Step 701: Calculate the sum of the square of the first uncertainty and the square of the second uncertainty; Step 702: Calculate the square root of the sum of the squares to obtain the total uncertainty of the leaf area index inversion of the region to be measured.

[0086] Specifically, the remote sensing data processing equipment first calculates the sum of the squares of the first uncertainty and the second uncertainty. The remote sensing data processing equipment then obtains the first uncertainty derived from the physical model parameter transfer, calculated in the aforementioned steps. (Usually in relative value form or normalized to the mean) (same units) and the second uncertainty arising from the randomness of the machine learning training process. Remote sensing data processing equipment assumes that these two sources of error are statistically independent. Therefore, based on the principle of independence of error propagation, the squares of both are calculated separately. and Then add the two squared values ​​together.

[0087] Subsequently, the remote sensing data processing equipment calculates the square root of the sum of squares to obtain the total uncertainty in leaf area index retrieval for the measured area. The equipment then performs a square root operation on the sum of squares to obtain the final total uncertainty in leaf area index retrieval. The specific synthesis formula is as follows: ; The remote sensing data processing equipment will calculate the results. For each pixel associated with the remote sensing image, an uncertainty distribution map with the same spatial resolution as the original image is generated. Each pixel value in this distribution map represents the confidence interval range of the LAI inversion result at the corresponding location (e.g., if the inversion result is...). ).

[0088] In another possible implementation, refer to Figure 2 , Figure 2 This is the second flowchart illustrating the uncertainty quantification method for leaf area index inversion provided by this invention. Figure 2 As shown, the specific process of the remote sensing data processing equipment executing this method is as follows: First, the remote sensing data processing equipment executes the data preparation process. The equipment acquires remote sensing images of the area to be measured. Then, it performs data preprocessing on the remote sensing images. This preprocessing includes radiometric calibration, atmospheric correction, and geometric correction, aiming to convert the raw images into high-quality reflectance data, providing an input basis for subsequent inversion.

[0089] Simultaneously, the remote sensing data processing equipment constructs training samples based on physical mechanisms. The equipment runs the PROSAIL physical model. Using the PROSAIL model, the equipment simulates the interaction between light and the canopy, generating a physical simulation sample set containing a large number of simulated spectra and corresponding ground truth values. This physical simulation sample set serves as the foundational data source for subsequent machine learning training.

[0090] Next, the remote sensing data processing equipment executes... Figure 2 The machine learning training process is shown in the dashed box. This process employs a strategy combining genetic algorithms and neural networks. Specifically, the remote sensing data processing equipment runs the genetic algorithm (GA). The GA searches for the optimal solution in the solution space through selection, crossover, and mutation operations, generating an optimal chromosome. The remote sensing data processing equipment decodes the optimal chromosome and transforms it into specific neural network (NN) parameters (including weights and biases). Subsequently, the remote sensing data processing equipment uses a physically simulated sample set to calculate the fitness function under the current parameter configuration. The remote sensing data processing equipment determines whether the fitness function value meets the preset convergence conditions. If the result is not met, the process returns to the genetic algorithm (GA) stage to continue population iteration and parameter optimization; if the result is met, the determined NN-GA network mapping relationship is output, i.e., the trained single-step inversion model.

[0091] The remote sensing data processing equipment constructs multiple sets of trained models by repeatedly performing the aforementioned machine learning training process. The equipment then inputs pre-processed remote sensing imagery into these sets. Each sub-model in the model set outputs a prediction result, which the equipment then statistically analyzes to generate an LAI inversion result map (expected value and standard deviation). This result map includes not only the best estimate of the leaf area index (expected value) but also a statistical indicator (standard deviation) characterizing the dispersion of the model's predictions.

[0092] Subsequently, the remote sensing data processing equipment enters the uncertainty quantification stage, which is divided into two branches: physical-driven and machine learning.

[0093] In the physics-driven branch, the remote sensing data processing equipment, based on the PROSAIL physical model, performs a pixel-by-pixel Monte Carlo simulation for each pixel location in the image (Note: This corresponds to the text in the attached figure; in actual calculations, it can be combined with the sensitivity method or sampling statistics method in the aforementioned embodiments). By simulating the perturbation and propagation of input parameters, the remote sensing data processing equipment performs physics-driven uncertainty calculations to obtain the first uncertainty originating from the propagation of physical model parameters.

[0094] In the machine learning branch, remote sensing data processing equipment performs machine learning uncertainty calculations based on statistical indicators (such as the ratio of standard deviation to expected value) in the aforementioned generated LAI inversion result map, and obtains the second uncertainty arising from the randomness of the machine learning training process.

[0095] Finally, the remote sensing data processing equipment performs uncertainty synthesis. It comprehensively calculates the physical driving uncertainty and machine learning uncertainty (e.g., sum of squares and square roots) to generate a LAI inversion uncertainty map. This map provides end-to-end quality identification of the leaf area index inversion results, offering a reliable confidence level for subsequent applications of remote sensing products.

[0096] Reference Figure 3 , Figure 3 This is a schematic diagram of the uncertainty quantification system for leaf area index inversion provided by the present invention. The system includes: The first processing module is used to extract target spectral feature data based on remote sensing images of the area to be measured; The second processing module is used to generate a simulated sample set containing simulated spectral feature data and corresponding true values ​​of leaf area index based on the radiative transfer model. The third processing module is used to calculate the sensitivity of the spectral response of the radiative transfer model to the input parameters, and, in combination with the prior uncertainty of the input parameters, calculate the first uncertainty arising from the parameter propagation of the physical model. The fourth processing module is used to construct a machine learning inversion model, and to repeatedly train the machine learning inversion model using the simulated sample set to obtain a model set consisting of multiple trained sub-models. The fifth processing module is used to input the target spectral feature data into each sub-model in the model set to obtain the leaf area index prediction value output by each sub-model, and to calculate the second uncertainty caused by the randomness of the machine learning training process based on the statistical dispersion of the multiple leaf area index prediction values. The sixth processing module is used to obtain the total uncertainty of leaf area index inversion of the region to be measured based on the first uncertainty and the second uncertainty.

[0097] It should be noted that the leaf area index inversion uncertainty quantification system provided by the present invention can execute the leaf area index inversion uncertainty quantification method of any of the above embodiments during specific operation, which will not be elaborated in this embodiment.

[0098] Figure 4 This is a schematic diagram of the structure of the electronic device provided by the present invention, such as... Figure 4 As shown, the electronic device may include a processor 410, a communication interface 420, a memory 430, and a communication bus 440, wherein the processor 410, the communication interface 420, and the memory 430 communicate with each other through the communication bus 440. The processor 410 can call logical instructions in the memory 430 to execute the leaf area index inversion uncertainty quantification method provided in the above embodiments.

[0099] Furthermore, the logical instructions in the aforementioned memory 430 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0100] On the other hand, the present invention also provides a computer program product, which includes a computer program stored on a non-transitory computer-readable storage medium. The computer program includes program instructions, and when the program instructions are executed by a computer, the computer is able to execute the leaf area index inversion uncertainty quantification method provided in the above embodiments.

[0101] In another aspect, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to perform the leaf area index inversion uncertainty quantification method provided in the above embodiments.

[0102] The system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0103] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of various embodiments or some parts of embodiments.

[0104] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for quantifying the uncertainty of leaf area index inversion, characterized in that, include: Extract target spectral feature data from remote sensing images of the area to be measured; Based on the radiative transfer model, a simulated sample set containing simulated spectral feature data and corresponding true values ​​of leaf area index is generated. Calculate the sensitivity of the spectral response of the radiative transfer model to the input parameters, and, in conjunction with the prior uncertainty of the input parameters, calculate the first uncertainty arising from the propagation of the physical model parameters; A machine learning inversion model is constructed, and the machine learning inversion model is repeatedly trained using the simulated sample set to obtain a model set consisting of multiple trained sub-models. The target spectral feature data is input into each sub-model in the model set to obtain the leaf area index prediction value output by each sub-model. Based on the statistical dispersion of the multiple leaf area index prediction values, the second uncertainty arising from the randomness of the machine learning training process is calculated. Based on the first uncertainty and the second uncertainty, the total uncertainty of the leaf area index inversion of the region to be measured is obtained.

2. The method for quantifying the uncertainty of leaf area index inversion according to claim 1, characterized in that, The process of constructing a machine learning inversion model involves repeatedly training the model using the simulated sample set to obtain a model set consisting of multiple trained sub-models, including: Constructing a machine learning inversion model with a neural network structure; The weight parameters and bias parameters of the neural network are encoded as chromosomes using real values ​​to generate an initial population. Using the training and validation data in the simulated sample set, the fitness function value of individuals in the initial population is calculated; Based on the fitness function value, the initial population is subjected to selection, crossover, and mutation operations, and the population is iteratively updated until the stopping condition is met to obtain the trained sub-model; Repeat the above process until a preset number of trained sub-models are obtained, thus generating the model set.

3. The method for quantifying the uncertainty of leaf area index inversion according to claim 2, characterized in that, The step of calculating the fitness function value of individuals in the initial population using the training and validation data in the simulated sample set includes: Calculate the first root mean square error of the current individual on the training data and the second root mean square error on the validation data, respectively; The fitness function value is obtained by weighted summation of the first root mean square error and the second root mean square error.

4. The method for quantifying the uncertainty of leaf area index inversion according to claim 1, characterized in that, The calculation of the sensitivity of the spectral response of the radiative transfer model to the input parameters includes: The partial derivatives of the radiative transfer model are approximated using the central difference method; For each target parameter in the input parameters, a small perturbation step size is set; Calculate the change in spectral reflectance output by the radiative transfer model when the target parameter is increased and the perturbation step size is decreased, respectively; The sensitivity of the spectral response to the target parameter is determined based on the ratio of the change to twice the perturbation step size.

5. The method for quantifying the uncertainty of leaf area index inversion according to claim 1, characterized in that, The calculation of the first uncertainty stemming from the propagation of physical model parameters, incorporating the prior uncertainty of the input parameters, includes: Determine the standard uncertainty of each input parameter; Calculate the error covariance between correlated input parameters; Based on the sensitivity, the standard uncertainty, and the error covariance, the simulated uncertainty of each band is calculated using the uncertainty propagation law. The simulated uncertainty of each band is calculated by weighted sum of squares based on the bandwidth of each band, and the square root of the calculation result is obtained to obtain the first uncertainty.

6. The method for quantifying uncertainty in leaf area index inversion according to claim 1, characterized in that, The calculation of the second uncertainty arising from the randomness of the machine learning training process based on the statistical dispersion of multiple leaf area index predictions includes: Based on the leaf area index predictions output by all the sub-models, the prediction mean and prediction standard deviation are calculated. The second uncertainty is obtained by calculating the ratio of the predicted standard deviation to the predicted mean.

7. The method for quantifying the uncertainty of leaf area index inversion according to claim 1, characterized in that, The step of obtaining the total uncertainty of leaf area index inversion for the region to be measured based on the first uncertainty and the second uncertainty includes: Calculate the sum of the square of the first uncertainty and the square of the second uncertainty; The total uncertainty of the leaf area index inversion for the region to be measured is obtained by calculating the square root of the sum of the squares.

8. A system for quantifying uncertainty in leaf area index inversion, characterized in that, include: The first processing module is used to extract target spectral feature data based on remote sensing images of the area to be measured; The second processing module is used to generate a simulated sample set containing simulated spectral feature data and corresponding true values ​​of leaf area index based on the radiative transfer model. The third processing module is used to calculate the sensitivity of the spectral response of the radiative transfer model to the input parameters, and, in combination with the prior uncertainty of the input parameters, calculate the first uncertainty arising from the parameter propagation of the physical model. The fourth processing module is used to construct a machine learning inversion model, and to repeatedly train the machine learning inversion model using the simulated sample set to obtain a model set consisting of multiple trained sub-models. The fifth processing module is used to input the target spectral feature data into each sub-model in the model set to obtain the leaf area index prediction value output by each sub-model, and to calculate the second uncertainty caused by the randomness of the machine learning training process based on the statistical dispersion of the multiple leaf area index prediction values. The sixth processing module is used to obtain the total uncertainty of leaf area index inversion of the region to be measured based on the first uncertainty and the second uncertainty.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the leaf area index inversion uncertainty quantification method as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the leaf area index inversion uncertainty quantification method as described in any one of claims 1 to 7.

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