Crop height and yield prediction method across regions based on meta-learning and adversarial domain adaptation

Abstract

A cross-region crop height and yield prediction method based on meta-learning and adversarial domain adaptation, acquires a crop dataset containing genotype, environmental type and phenotype data; based on the meta-learning method, a source domain meta-training task set is constructed, different regional prediction tasks are defined as subtasks, a GEfused module extracts genotype and environmental type features from the corresponding support set through a multi-branch structure and fuses them to obtain fused features; a Reptile meta-learning strategy is used for double cycle training to learn global meta initial parameters with cross-domain generalization ability; through a feature distribution alignment strategy, explicit statistical distribution constraints are applied to the fused features obtained from the source domain and the target domain to reduce the statistical difference of the features; through a domain adversarial training mechanism, the GEfused module is guided to learn cross-domain general features, phenotype prediction is realized while completing domain adaptation, and a gradient attribution method is used for explainability analysis of the model. The patent effectively improves the accuracy of cross-region crop phenotype prediction and provides technical support for crop breeding.

Description

Technical Field

[0001] This invention belongs to the field of crop breeding technology, and specifically relates to a method for predicting crop plant height and yield across regions based on meta-learning and adversarial domain adaptation. Background Technology

[0002] Accelerating the breeding of superior crop varieties and improving breeding efficiency are of great significance. Crop phenotype is the result of the combined effects of genotype and environmental type, directly reflecting the crop's growth status and yield potential. Phenotype is a core indicator for screening superior varieties and a carrier for analyzing crop genetic regulation mechanisms and environmental response patterns. However, traditional field observation of phenotypes is inefficient and time-consuming, severely hindering the breeding process. Genomics, as a modern breeding technology, utilizes genetic marker information to accurately predict unobserved phenotypes, providing strong support for accelerating the breeding process.

[0003] With the development of big data and artificial intelligence technologies, data-driven phenotypic prediction has become a mainstream research direction. Early phenotypic prediction mainly relied on statistical models such as mixed linear models and best linear unbiased prediction. Although these models can quantify genetic and environmental effects, they struggle to handle high-dimensional sparse genotype data and complex environmental time-series data. Machine learning models such as random forests and support vector machines have improved prediction accuracy through nonlinear fitting, but they suffer from limited feature extraction capabilities. In recent years, deep learning technology has been widely used in phenotypic prediction due to its powerful feature mining capabilities. Existing deep learning models, such as DNNGP and GEFormer, have achieved efficient mining of genotype and environmental features using structures such as convolutional neural networks and Transformers. However, these models are highly dependent on large-scale labeled samples. Furthermore, the limited availability of crop breeding data restricts the generalization performance of these models.

[0004] To address the issue of poor model performance in small-sample scenarios, transfer learning has been applied to phenotypic prediction. By transferring knowledge from the source domain to the target domain, the problem of insufficient samples can be effectively alleviated. Transfer learning models such as Transfer RR and TrG2P have been initially applied in crop phenotypic prediction. However, these methods rely heavily on fine-tuning of model parameters and have limited ability to quickly adapt to unknown new environments. In contrast, meta-learning, by learning a general learning strategy across tasks, can quickly adapt to new target tasks, providing a better solution for small-sample prediction. Model-independent meta-learning (MAML) proposed by Finn et al. learns general initial parameters through two-layer optimization, enabling rapid adaptation to new tasks with a small number of samples. These methods have been widely applied in computer vision, reinforcement learning, and other fields. Furthermore, even within the same genetic population, phenotypic performance varies significantly under different environmental conditions. This leads to a severe shift in the feature distribution between the source and target domains, making it difficult for traditional transfer learning models to effectively align the distributions of the two domains, thus affecting transfer performance and failing to meet the practical needs of cross-environment phenotypic prediction. Summary of the Invention

[0005] In order to overcome the shortcomings of the prior art, the present invention aims to provide a cross-regional crop plant height and yield prediction method based on meta-learning and adversarial domain adaptation (MAGEP) to solve the problems of low phenotypic prediction accuracy and poor generalization ability in cross-environment small sample domain offset scenarios.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for predicting cross-regional crop plant height and yield based on meta-learning and adversarial domain adaptation includes the following main steps: crop dataset acquisition, meta-training task construction, gene-environment fusion (GEfused) module construction, global meta-parameter learning, cross-domain feature distribution alignment, domain-invariant feature mining, and phenotypic data prediction. The specific implementation is as follows: Step 1: Obtain the crop dataset.

[0007] The acquired crop dataset contains genotype, environmental, and phenotypic data; and is divided into source and target domains according to planting regions; the source domain data is used for meta-learning training and cross-domain general feature learning; the target domain data is cross-regional data for phenotypic prediction.

[0008] Step 2, Meta-training task construction.

[0009] Based on source domain data, a meta-learning method is used to define prediction tasks for different regions as subtasks; each subtask takes genotype data and corresponding environmental data as input and phenotypic data as output; the datasets corresponding to each subtask are divided into non-overlapping support sets and query sets.

[0010] Step 3, construct the GEfused module.

[0011] The GEfused module extracts genotype and environmental features from the corresponding support set through a multi-branch structure and fuses them to obtain the fused features of the target domain task and the sub-task.

[0012] Step 4, global meta-parameter learning.

[0013] Based on the obtained fusion features, the Reptile meta-learning strategy is adopted, and global meta-parameters with cross-domain generalization ability are learned through double loop training.

[0014] Step 5: Cross-domain feature distribution alignment and domain-invariant feature mining.

[0015] By applying explicit statistical distribution constraints to the fused features obtained from the source and target domains, the feature distribution distance between the two domains is calculated and minimized to initially reduce the statistical difference between cross-domain features. The features constrained by statistical distribution are then input into the gradient inversion layer. By introducing a domain adversarial training mechanism, the GEfused module is guided to learn cross-domain universal domain-invariant features and connected to the domain classifier to complete the classification task.

[0016] Step 6, Phenotypic Data Prediction.

[0017] Using a fully connected network, phenotypic data prediction is achieved by extracting genotype and environmental data fusion features based on the trained GEfused module, and the prognostic interpretability of the model is analyzed using the gradient attribution method.

[0018] In one embodiment, the crop dataset is further preprocessed, specifically: The genotype data is gene SNP data. Samples with an individual-level genotype deletion rate greater than 10% and SNP sites with a site-level deletion rate greater than 10% are filtered out. The filtered genotype data undergoes linkage disequilibrium pruning to retain independent SNP sites, and the pruned genotype data is binarized and encoded as follows: 0 represents the homozygous genotype 0 / 0, and 1 represents the homozygous genotype 1 / 1; The environmental data includes four environmental factors: temperature, relative humidity, solar radiation, and precipitation. After cleaning up missing data, the time-series statistical characteristics related to crop growth and development and biomass accumulation are calculated, including basic statistical characteristics, growth days, water vapor pressure deficit, cumulative effective sunshine duration, cumulative effective radiation intensity (solar radiation), and cumulative precipitation. The phenotypic data includes plant height and yield, which are normalized after missing data cleaning.

[0019] In one embodiment, the basic statistical characteristics are the statistical indicators of the four environmental factors and the four-quartile characteristics. The statistical indicators include the mean, standard deviation, minimum, maximum and median, and the four-quartile characteristics are the lower quartile, median, upper quartile and maximum. The growth period days are calculated using the following formula: ,in, Let be the average daily temperature on day i, and n be the total number of days in the growth cycle. The minimum effective temperature for crop growth; The formula for calculating the water vapor pressure deficit is as follows: , The saturated vapor pressure is calculated using the following formula: , The actual water vapor pressure is calculated using the following formula: ,in, The representative temperature used to calculate the day's highest and lowest temperatures. It refers to relative humidity; The cumulative effective illumination duration is calculated using the following formula: ,in, Let I be the instantaneous solar radiation at hour j on day i. Let I() be an indicator function that takes the value 1 if the condition is met, and 0 otherwise. The effective illumination threshold; The cumulative effective radiation intensity of solar radiation is calculated using the following formula: ; The cumulative precipitation is calculated using the following formula: ,in, Rainfall on day i; Calculate the three features: mean (VPD) value, cumulative VPD value (∑VPD), and diurnal humidity difference (VPD). ), where day_rh_mean is the daytime average relative humidity and the diurnal humidity difference: in, The average relative humidity during the day. This represents the average relative humidity at night.

[0020] Compared with existing technologies, this invention proposes a deep learning framework (MDGEP) that integrates meta-learning and adversarial domain adaptation to achieve efficient genotype and environmental phenotypic prediction in small-sample cross-environment scenarios. Specifically, firstly, a dual-channel GEfused module design is constructed to extract and model the interaction between genotype and environmental traits. Secondly, a Reptile meta-learning strategy is introduced to learn source domain features, improving the model's rapid adaptation capability in small-sample target domains and alleviating the constraint of insufficient samples. Then, combined with adversarial domain adaptation technology, a domain classifier and gradient inversion mechanism are constructed to effectively align the feature distributions of the source and target domains, solving the domain shift problem in cross-environment scenarios. Finally, based on gradient attribution methods, the contribution of genotype and environmental features to phenotypic prediction is quantified, improving the model's interpretability. Comparative experimental results show that this invention helps improve the accuracy and robustness of crop phenotypic prediction in small-sample cross-environment scenarios, providing an efficient technical solution for precision crop breeding.

[0021] This invention, based on the publicly available maize GXE dataset, designed four cross-domain prediction scenarios and compared MAGEP with eight baseline models. The results show that the MAGEP model significantly outperforms the comparison models in terms of prediction accuracy and robustness. Among them, MAGEP(CORAL) performed best, with average PCCs of 0.75 and 0.45 for plant height and grain yield predictions, respectively, representing improvements of 44.20% and 55.20% compared to MAGEP(MMD). Gradient experiments with target domain data volume show that MAGEP(CORAL) maintains a more stable advantage under different data volumes, confirming that the CORAL domain adaptation strategy has stronger adaptability. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the MAGEP meta-learning framework that integrates adversarial domain adaptation, as described in this invention.

[0023] Figure 2 This is a schematic diagram of the GEfused module of the present invention.

[0024] Figure 3 These are the phenotypic distribution characteristics in the embodiments of the present invention.

[0025] Figure 4 This is a distribution of prediction errors for maize plant height and yield by nine models under four cross-domain scenarios in an embodiment of the present invention. Detailed Implementation

[0026] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings and examples.

[0027] In the technical solution of this invention, a method for predicting crop plant height and yield across regions based on meta-learning and adversarial domain adaptation is provided. This method achieves precision breeding through crop phenotypic prediction that is coordinated by genes and environment. This invention integrates meta-learning and domain adversarial strategies to construct a prediction model that is adapted to small samples and can achieve cross-environmental distribution alignment, thereby improving the generalization ability of phenotypic prediction.

[0028] Specifically, firstly, a GEfused module is designed as a feature extractor, extracting genotype and environment-based fusion features through a multi-branch structure. These features are then used for Reptile meta-learning to learn cross-environment general feature representations. Simultaneously, a gradient inversion layer is introduced to construct an adversarial training mechanism, guiding the feature extractor to learn domain-invariant features. Combined with MMD and CORAL domain adaptation strategies, the feature distribution differences between the source and target domains are quantified and reduced. Finally, a gradient attribution method is used to perform prognostic interpretability analysis of the model.

[0029] In a specific embodiment of this invention, maize was used as the research object. A GXE study was conducted using maize genotype, environmental type, and phenotype datasets from 10 different environmental environments. The results showed that maize plant height and grain yield are synergistically regulated by multiple gene loci, and the model can accurately identify key environmental factors in different environmental domains. This not only verifies the biological rationality of the model's predictions but also provides quantitative evidence for elucidating the genetic and environmental synergistic regulatory mechanisms of crop phenotypes.

[0030] The following is a detailed description of the implementation process of this invention.

[0031] Step 1: Obtain a crop dataset containing genotype, environmental type, and phenotypic data; wherein, the phenotypic data includes plant height and yield, that is, the plant height and yield prediction of this invention is achieved through phenotypic data prediction.

[0032] The maize (Zea mays) dataset used in this invention comes from the publicly available Genomes to Fields (G2F) initiative (https: / / www.genomes2fields.org). This embodiment uses the 2018 G2F dataset, which integrates comprehensive maize genotypic, environmental, and phenotypic data. The maize hybrid populations include PHW65×PHN11, PHW65, Mo44, and PHW65. Two key agronomic traits are analyzed: plant height (PH, cm) and grain yield (GY, bu / A). Four core meteorological parameters (air temperature, relative humidity, solar radiation, and precipitation) are recorded at 30-minute intervals throughout the growing season and until harvest, providing a continuous environmental context for phenotypic variation analysis. Samples of genotypic and phenotypic data are matched through data preprocessing; detailed samples are shown in Table 1.

[0033] Table 1. The experimental dataset includes sample size and environmental data from different locations. For the obtained crop dataset, this invention divides it into a source domain and a target domain according to the planting area; the source domain data is used for meta-learning training and cross-domain general feature learning; the target domain data is cross-regional data to be used for phenotypic prediction.

[0034] Step 2: Preprocess the crop dataset.

[0035] Genotype data preprocessing: The original maize genotype data contained 312 individuals, each with 1,352,275 single nucleotide polymorphism (SNP) sites. To ensure the reliability of the genotype data and reduce the interference of low-quality data on subsequent analysis results, data preprocessing was required. First, high-quality SNP sites were screened through data quality control, filtering out maize samples with an individual-level genotype deletion rate greater than 10%, and SNP sites with a site-level deletion rate greater than 10%. Linkage disequilibrium pruning was then performed on the quality-controlled genotype data to retain independent SNP sites. Parameter settings: sliding window of 50, step size of 10, and linkage disequilibrium coefficient R² of 0.1. The input VCF file contained homozygous genotypes 0 / 0 and 1 / 1, which were binarized and encoded as follows: .

[0036] Environmental data preprocessing: The raw environmental data consisted of time-series data collected under ten experimental settings, including four environmental factors: temperature (T), relative humidity (RH), solar radiation (SAR), and precipitation (RN). Due to errors in field monitoring equipment and interference from extreme weather, some values ​​were missing, requiring data cleaning. Based on the high-quality time-series data, time-series statistical characteristics closely related to maize growth and development and biomass accumulation were calculated, including: Basic statistical characteristics were used to comprehensively characterize the overall distribution characteristics, dispersion and central tendency of each environmental factor. The statistical indicators of the four environmental factors were calculated, including: mean, standard deviation, minimum, maximum and median. The four quantile characteristics were: lower quartile (25th quantile), median (50th quantile), upper quartile (75th quantile) and maximum (100th quantile).

[0037] Growing days (GDD) are a core indicator reflecting the accumulation of effective accumulated temperature in maize. 10℃ is considered the minimum effective temperature for maize growth; below this temperature, growth essentially ceases. The calculation formula is as follows: in, Let be the average daily temperature on day i, and n be the total number of days in the growth cycle.

[0038] Vapor pressure deficit (VPD) directly reflects the degree of air dryness and has a significant impact on the transpiration efficiency and water use efficiency of maize. The saturated vapor pressure is calculated based on the Tetens formula: in, The representative temperature used to calculate the day's highest and lowest temperatures. .

[0039] Derive the actual water vapor pressure based on relative humidity: Calculate the three features: mean (VPD) value, cumulative VPD value (∑VPD), and diurnal humidity difference (VPD). ), where day_rh_mean is the daytime average relative humidity and the diurnal humidity difference: in, The average relative humidity during the day. This represents the average relative humidity at night.

[0040] Cumulative effective sunshine duration and cumulative effective radiation intensity: Solar radiation is the energy source for maize photosynthesis, and its cumulative effect directly determines the synthesis rate and total amount of photosynthetic products. Using a solar radiation intensity of 100 W / m² as the effective sunshine threshold, the cumulative effective sunshine duration and cumulative effective radiation intensity are calculated as follows: in, Let I be the instantaneous SAR of the j-th hour of the i-th day, and let I() be the indicator function (it takes the value 1 when the condition is met, and 0 otherwise).

[0041] Cumulative precipitation reflects the total amount of water supplied in the field during the maize growth cycle, directly affecting maize root development, nutrient absorption, and physiological metabolic activities. The calculation formula is as follows: in, Rainfall on day i.

[0042] Phenotypic data preprocessing: The maize phenotypic dataset was obtained through field experiments, covering agronomic phenotypic traits under ten experimental settings, including plant height (PH) and grain yield (GY). Each phenotypic index was observed twice. To ensure data accuracy and reliability, the raw data underwent preprocessing. Missing values ​​due to omissions in field observations were removed. The arithmetic mean of the two observations was calculated as the final phenotypic value for each sample, thereby reducing random measurement error. Furthermore, to eliminate the interference of units on model training, the cleaned phenotypic data underwent Z-score normalization.

[0043] Step 3, build the model.

[0044] To improve the robustness of crop phenotypic prediction in different regional environments, this invention proposes a meta-learning framework, MAGEP, which integrates adversarial domain adaptation and can accurately predict crop phenotypic data based on genotype and environmental data. The overall process of the MAGEP framework is shown in Figure 1.

[0045] Step 3.1: Based on the meta-learning method, a meta-training task set is constructed for the source domain data. Prediction tasks in different regions are defined as sub-tasks. Global meta-initial parameters with cross-domain generalization ability are learned through the meta-learning paradigm. In each sub-task, genotype data and corresponding environmental data are used as inputs, and phenotypic data are used as outputs. The dataset corresponding to each sub-task is divided into a non-overlapping support set and a query set.

[0046] The core bottleneck in cross-environment crop phenotypic prediction is the insufficient adaptability to small samples under environmental domain distribution shifts. Existing transfer learning methods rely on large amounts of target domain data, but high-throughput phenotypic acquisition is costly and time-consuming. While the mainstream meta-learning algorithm MAML can achieve fast adaptation, its second-order gradient optimization computational complexity is high. (where p is the SNP locus dimension), which cannot handle high-dimensional sparse genotype data. Reptile (Nichol et al., 2018), as a first-order metamorphic learning algorithm, replaces sample-level gradient backtracking with distribution-level parameter evolution, achieving a computational complexity of only [missing information]. (k is the number of inner loop steps). It can learn a cross-domain common initial parameter space and adapt to the small sample transfer needs of crop environment domains in different locations.

[0047] This invention defines different environmental domain phenotypes as subtasks, and for the obtained source domain task set Each It corresponds to an independent source environment domain, containing a support set. and query set .

[0048] This invention defines the data that did not participate in the meta-training as the target domain, and randomly divides the target domain samples into training set and test set in an 8:2 ratio. Among them, 80% of the training set is used for domain adaptation distribution alignment; and 20% of the test set is used to evaluate the model's cross-regional crop phenotypic prediction performance.

[0049] Step 3.2: For the target domain task and each of the subtasks, features are extracted using the GEfused module. Specifically, genotype and environmental features are extracted from the corresponding support set through its multi-branch structure and then deeply fused to obtain fused features.

[0050] Specifically, such as Figure 2 As shown, the GEfused module is the core feature extraction and fusion unit of the MDGEP framework, responsible for efficiently encoding genotype (G) and environment (E) information into a unified representation to capture G×E interaction effects. This module is divided into a genotype feature extraction branch, an environment feature extraction branch, and a final fusion layer.

[0051] The genotype feature extraction branch takes a high-dimensional SNP genotype matrix as input. To capture SNP site interaction effects at different scales, it employs multi-scale dilated convolution as the core extraction unit. The two sub-branches sequentially extract sequence associations through dilated convolution (with different dilation rates of 1 and 2), zero-padding, and 1×1 convolution. The outputs of the two sub-branches are then fused element-wise to achieve multi-scale feature fusion, thereby uncovering local association patterns in high-dimensional sparse gene data. Finally, the fused feature vector is the output representation of the genotype branch. .

[0052] Environmental heterogeneity is one of the core challenges in crop phenotypic prediction, encompassing both statistical distribution differences across environments and dynamic temporal dependencies within the same environment. The environmental feature extraction branch employs two sub-branches to model these two types of information respectively. The first sub-branch calculates a feature vector composed of temporal statistical features from multivariate environmental data such as temperature, relative humidity, solar radiation, and precipitation. Static features are obtained through linear transformation and regularization. : Where FC is regularization, LN is used to normalize the feature distribution, and GELU is a non-linear activation function; Statistical features only reflect the overall distribution of the environment and cannot capture the periodic fluctuations of time-series data. Therefore, the second sub-branch uses a Transformer encoder to extract environmental time-series data. The trend characteristics. Compared to RNN / LSTM, the Transformer's self-attention mechanism can directly capture the dependencies at any time step, as follows: First, the low-dimensional temporal features are mapped to the Transformer model dimension. : Then, sine and cosine positional coding is introduced to distinguish features at different time steps. The positional coding is as follows: in, , This refers to the position in the sequence. pos The dimensions are 2 respectively. i (Even-numbered dimension index of the positional encoding vector) and 2 i +1 (odd-dimensional index of the position encoding vector) is the position encoding value; pos The position index of the element in the sequence (starting from 0, in the range [0, T)). [1], where T is the sequence length); This is the hidden dimension of the Transformer model, namely the dimension of the word embedding vector and the position encoding vector.

[0053] Therefore, the position-encoded input is: It is a positional encoding vector. ; This is then encoded using a multi-head attention encoder to capture long-range dependencies in the temporal context. The attention weights for each head are calculated as follows: in, , , These are query, key, and value matrices, respectively. For each head's feature dimension, These are learnable linear projection matrices, namely the query projection matrix, key projection matrix, and value projection matrix.

[0054] Finally, the multi-head outputs are concatenated and then processed through a feedforward network and normalized to enhance the feature representation, resulting in dynamic features. Static features With dynamic characteristics After dimensional alignment and weighted fusion, the output is a unified dimensional environmental feature. In the fusion layer, to effectively model G×E interactions, genotype features are incorporated. Environmental characteristics The final fused feature is obtained by linear projection after channel stitching. (Source domain is denoted as) The target domain is denoted as ).

[0055] Step 3.3: Based on the obtained fusion features, the Reptile meta-learning strategy is adopted to learn global meta-parameters with cross-domain generalization ability through double-loop training.

[0056] The core of Reptile's dual-loop training mechanism is to learn general initial parameters that can quickly adapt to new environments, including an inner loop and an outer loop. The specific method is as follows: Inner Loop (In-Task Adaptation): For each randomly sampled source domain task to support its set Input the GEfused module to extract source domain fusion features Used for meta-training, in the meta-training phase, for the first... Sub-tasks Starting from global meta-initial parameters Starting from this point, perform k-step SGD updates using the support set of the current subtask to obtain task-specific parameters adapted to this environment, as shown in the following formula: in, For the inner loop learning rate, The mean squared error loss for phenotypic prediction. for Support set, For the first j The gradient update term of the step, This represents the number of iterations in the inner loop. For the first Sub-tasks Task-specific parameters after the inner loop; Refer to The gradient of the variable.

[0057] Outer Loop (Meta-update): Using querysets Evaluate the performance after task adaptation and update the global meta-initial parameters. : in, The meta-learning rate. Through repeated iterations of the inner and outer loops, the model learns initialization parameters that allow for rapid adaptation to new environmental domains. Figure 1Universal global meta-initial parameters in This enables few-sample generalization from the source domain to the target domain.

[0058] Step 3.4 introduces a feature distribution alignment strategy to constrain the distribution differences between the source and target domains, and adopts a domain adversarial training mechanism to learn cross-domain universal domain-invariant features.

[0059] The feature distribution offset between the source and target domains affects the robustness of crop phenotypic prediction across regions. To address this, this invention introduces a distribution alignment and domain adversarial mechanism. By applying explicit statistical distribution constraints to the fused features obtained from the source and target domains, the feature distribution distance between the two domains is calculated and minimized to initially reduce the statistical differences in cross-domain features. Subsequently, the statistically constrained features are input into a gradient inversion layer (GRL). Through the gradient inversion effect of GRL during backpropagation, an adversarial game is constructed between the GEfused module and the domain classifier. This domain adversarial training mechanism guides the GEfused module to learn cross-domain universal domain-invariant features and integrates with the domain classifier to complete the classification task. Ultimately, this achieves deep alignment of the fused features between the source and target domains, improving the model's generalization ability across environments with small samples. Specifically: This invention employs the Maximum Mean Discrepancy (MMD) or Correlation Alignment (CORAL) methods to impose statistical distribution constraints on the fusion features of the source and target domains, as follows: Based on the maximum mean difference method, the source domain fusion features of GEfused output are analyzed. Features fused with the target domain Calculate the distribution distance loss. MMD calculates the mean difference between the two domains in the reproducing kernel Hilbert space (RKHS): in, , The feature distributions of the source domain and the target domain are respectively. For the characteristic mapping of the regenerating kernel Hilbert space, It is the RKHS space norm; It is a feature vector of a single sample in the source or target domain.

[0060] For a finite sample, the standard empirical estimate is: in, , The number of samples in the source domain and the target domain. For the kernel function, this invention uses the Gaussian kernel function. , , These are sample sets from the source domain and the target domain, respectively. , Samples in the source domain i and j Feature vector; , The sample feature vector in the target domain; Therefore, the formula for calculating MMD loss is: Alternatively, based on relevant alignment methods, aligning the second-order statistics (covariance matrix) reduces the overall discrepancy, resulting in Coral loss. for: in, , Let be the covariance matrices of the features of the source domain and the target domain, respectively. d For feature dimensions.

[0061] Then, the aligned features are input into the GRL, which is then used by the domain classifier for domain classification. Domain adversarial analysis is achieved by reversing the gradient in the GRL. The domain classifier attempts to accurately distinguish the domain to which a sample belongs, while the feature extractor attempts to generate domain-invariant features that the domain classifier cannot distinguish. Ultimately, this forces the feature extractor to learn general features that do not depend on a specific domain, thus improving the model's cross-domain prediction ability.

[0062] GRL forward propagation uses an identity mapping, and backward propagation reverses the gradient sign as follows: in, The resistance coefficient; It is the identity matrix; This refers to the fusion feature, specifically the source domain fusion feature. or target domain fusion features .

[0063] For domain classifiers, the cross-entropy loss is used to measure the classification accuracy of the domain classifier head: in, This represents the batch sample size. For domain tags, This is the output of the classifier.

[0064] Loss prediction based on source domain phenotype in the MDGEP framework Target domain phenotypic prediction loss Distribution alignment loss Domain confrontation losses Its composition, and its mathematical expression are as follows: in, For distribution alignment loss and , The number of samples in the source domain. , Let be the predicted phenotypic value and the actual phenotypic value for the i-th sample, respectively. , , These are the corresponding weight coefficients, used to balance the contributions of different loss terms. The source domain phenotype prediction loss and the target domain phenotype prediction loss are used to supervise the phenotype prediction capability of the genotype-environment fusion feature extraction module; the distribution alignment loss is used to constrain the statistical distribution differences between the fused features of the source and target domains; and the domain adversarial loss is used to guide the model to learn domain-invariant features, achieving adversarial domain adaptation.

[0065] The above framework design can alleviate the problem of distribution offset in different regional environments, realize rapid knowledge transfer from known to unknown environments, effectively enhance the robustness of crop phenotypic prediction in cross-regional scenarios, and ultimately achieve accurate prediction of crop phenotypic characteristics across regions.

[0066] Finally, using a fully connected network, the genotype and environmental data fusion features were extracted based on the trained GEfused module to predict phenotypic data, and the gradient attribution method was used to analyze the prognostic interpretability of the model.

[0067] To evaluate the performance of MDGEP in cross-environmental phenotypic prediction, this invention uses commonly used evaluation metrics such as root mean square error (RMSE), mean absolute error (MAE), and Pearson correlation coefficient (PCC): Figure 3 This study presents the phenotypic distribution characteristics of maize in plant height and grain yield traits under 10 environmental conditions. Figure 3 (a) and Figure 3As shown in Figure (b), significant phenotypic differentiation exists among populations in regions such as IAH, ARH, GAH, and TXH. Different environments within the same region (e.g., IAH1 vs. IAH3, ARH1 vs. ARH2) also exhibit marked phenotypic heterogeneity. In the IAH region, IAH3 shows the highest peak values ​​and more concentrated curves for plant height and grain yield, while IAH1 and IAH2 have wider distribution ranges and slightly lower peak values. In the ARH region, ARH2 shows significantly higher plant height and yield distributions than ARH1. GAH1 vs. GAH2 and TXH1 vs. TXH2 also show phenotypic distribution shifts, with TXH1 showing significantly lower plant height and yield than TXH2, placing it at a lower level overall across all environments. These differences directly reflect the influence of the interaction between regional environment and population genetic background on crop phenotypic plasticity. Furthermore, due to the heterogeneity of phenotypic distributions across regions, predictive models trained solely on phenotypic data from a single region or environment are prone to domain shift when applied to other environments due to differences in data distribution, resulting in insufficient generalization ability. Therefore, adapting and optimizing phenotypic data for different environments is crucial to improving the reliability of cross-environment phenotypic predictions.

[0068] To explore the impact of the model on maize phenotypic prediction performance in a cross-regional environment, four cross-regional prediction scenarios I-IV were set up with different combinations of regions as the source and target domains, as shown in Table 2.

[0069] Table 2. Four Cross-Domain Scenario Settings In each cross-domain scenario, the source domain dataset was used as the training set, and the target domain dataset was used as the test set. Tables 3 and 4 compare the performance of the baseline model and the proposed MDGEP model in predicting maize plant height and grain yield across the four scenarios. The baseline models include traditional breeding models (rrBLUP, BayesB), machine learning models (RF, SVR, XGBoost, LightGBM), deep learning models (GEFormer), and transfer learning models (TrG2P).

[0070] The root mean square error (RMSE), mean absolute error (MAE), and Pearson correlation coefficient (PCC) were used as core evaluation metrics to assess the model's predictive accuracy and generalization ability. Tables 3 and 4 compare the performance of the baseline model and our proposed MAGEP model in predicting maize plant height and grain yield across four scenarios. Specifically, the baseline models include statistical models (rrBLUP, BayesB), machine learning models (RF, SVR, XGBoost, LightGBM), deep learning models (GEFormer), and transfer learning models (TrG2P). RMSE, MAE, and PCC were used as evaluation metrics to assess the model's predictive accuracy and generalization ability. As shown in Tables 3 and 4, the traditional rrBLUP and BayesB models exhibited poor predictive performance across all cross-domain scenarios. For grain yield and plant height prediction, their RMSE and MAE remained at high levels, while their PCC values ​​were typically low. Notably, in Scenario 4, rrBLUP had an RMSE of 132.58 cm for plant height prediction (Table 3), while BayesB had an RMSE of 117.74 bu / A for grain yield prediction (Table 4). This indicates that traditional models trained on single genetic and environmental data struggle to adapt to the phenotypic distribution characteristics of the target domain. Machine learning models (RF, SVR, XGBoost, LightGBM) showed slightly better performance than traditional models in some cases. In Scenario II (Table 4), XGBoost reduced the RMSE for grain yield prediction to 32.97 bu / A, while in Scenario I (Table 3), LightGBM's MAE for plant height prediction was as low as 49.55 cm. The performance stability of these models remains insufficient. The deep learning model GEFormer exhibited particularly unstable performance, with its RMSE soaring to 133.78 cm in Scenario 4, and an RMSE of 75.43 bu / A for both plant height and yield prediction. The transfer learning model TrG2P maintains a low PCC in most scenarios, indicating that it can learn specific features within the source domain but cannot effectively capture generalizable features across domains. In contrast, the MAGEP model, which combines a domain adaptation strategy with two distribution alignment methods (MMD and CORAL), demonstrates superior predictive performance in four cross-domain scenarios. This suggests that the MAGEP model, by combining MMD or CORAL strategies, can effectively mitigate the domain shift caused by environmental heterogeneity. In the maize plant height prediction task, MAGEP (CORAL) achieved an average PCC of 0.75, significantly higher than MAGEP (MMD)'s 0.52.In the grain yield prediction task, MAGEP(CORAL) achieved an average PCC of 0.45, which is higher than MAGEP(MMD)'s 0.29. The advantages were most pronounced in scenarios II and III, with PCC improvements of 0.34 and 0.17 respectively. Overall, MAGEP(CORAL) outperforms MAGEP(MMD), indicating that the distribution alignment strategy based on CORAL can more effectively reduce inter-domain differences.

[0071] Table 3. Comparison of the predictive performance of different models for maize plant height under four cross-domain scenarios. The best results are highlighted in bold, and the second-best results are highlighted with an underline. Table 4. Comparison of the predictive performance of different models for maize yield under four cross-domain scenarios. The best results are highlighted in bold, and the second-best results are highlighted with an underline. To further verify the performance stability and robustness of each model in cross-domain phenotypic prediction, box plots were used to visualize the prediction error distribution of different models for plant height and grain yield in four cross-domain scenarios, such as... Figure 4From the error distribution of plant height prediction, BayesB, RF, SVR, XGBoost, and LightGBM all exhibited significant prediction errors in scenarios 1-4. In scenario 1, the median error of these models generally remained in the 30–60 cm range, with a high box height and a large number of high-value outliers. Although the deep models GEFormer and TrG2P reduced their errors in some scenarios, their stability remained insufficient. GEFormer performed the worst in scenario 4, possibly due to the small number of training samples in this scenario. The errors of other models also increased significantly in this scenario. In contrast, the median error of the MDGEP model was controlled below 20 cm in all scenarios, with the lowest box height and fewer outliers. In particular, MDGEP (CORAL) maintained an extremely low error level in scenario 4, demonstrating the improvement in accuracy and stability of plant height prediction by the domain adaptation strategy. Regarding the error distribution of grain yield prediction... The median error of traditional breeding models and classic machine learning models reaches 40–80 bu / A in most scenarios, and even exceeds 120 bu / A in some scenarios, with high bin size and many outliers. The deep model GEFormer and the transfer learning model TrG2P exhibit drastic error fluctuations, showing significant performance degradation in scenarios 3 and 4. In contrast, the two MDGEP models consistently maintain excellent performance: their median error remains stable in the 20–40 bu / A range, with compact bin size and very few outliers. These results demonstrate that the MDGEP model, by incorporating a domain adaptation strategy, not only effectively reduces the error level of cross-domain prediction but also significantly enhances the stability and robustness of the prediction results.

[0072] In summary, to address the issues of low prediction accuracy and poor generalization performance of crop phenotypic prediction in small sample sizes across environments, this invention proposes a deep learning framework (MDGEP) that integrates Reptile meta-learning and adversarial domain adaptation. To verify the effectiveness of the MDGEP model, cross-domain prediction scenarios 1-4 were designed. Using RMSE, MAE, and PCC as core evaluation metrics, the prediction performance of MDGEP was systematically compared with rrBLUP, BayesB, RF, SVR, XGBoost, LightGBM, GEFormer, and TrG2P. Experimental results show that the MDGEP model significantly outperforms all the compared models in terms of prediction accuracy and robustness. Specifically, in the scenario IV grain yield prediction where domain shift is most significant, MDGEP (CORAL) performs best, with an RMSE of only 25.22 and a PCC of 0.803, which is 86.9% lower than the traditional rrBLUP model (RMSE 193.58) and 136.2% higher than the BayesB model (PCC 0.34). In the scenario III grain yield prediction, its MAE decreases to 20.09 and its PCC increases to 0.555, significantly outperforming XGBoost (RMSE 29.45), LightGBM (MAE 25.01), and GEFormer (scenario III plant height RMSE 106.89). The MDGEP proposed in this invention achieves accurate prediction of maize phenotypes in small samples across environments, effectively alleviating the performance degradation caused by insufficient samples and domain shift, and providing a feasible reference and methodological support for cross-environment small sample phenotype prediction research. In the future, multi-omics data such as transcriptomics and metabolomics can be integrated to design improved feature fusion methods to explore the patterns of recessive genetic-environment interactions, providing technical support for precision crop breeding.

Claims

1. A method for predicting cross-regional crop plant height and yield based on meta-learning and adversarial domain adaptation, characterized in that, Includes the following steps: Step 1: Obtain the crop dataset, which includes genotype, environmental type, and phenotypic data; divide the crop dataset into source domain and target domain according to the planting area; the source domain data is used for meta-learning training and cross-domain general feature learning. The target domain data consists of cross-regional data for which phenotypic prediction is to be performed; Step 2: Based on the source domain data, use meta-learning methods to define the prediction tasks for different regions as sub-tasks; The subtask takes genotype data and corresponding environmental data as input and phenotypic data as output; the dataset corresponding to the subtask is divided into a non-overlapping support set and a query set. Step 3: Construct the GEfused module. The GEfused module extracts genotype and environmental features from the corresponding support set through a multi-branch structure and fuses them to obtain the fused features of the target domain task and the sub-task. Step 4: Based on the obtained fusion features, the Reptile meta-learning strategy is adopted to learn global meta-parameters with cross-domain generalization ability through double loop training. Step 5: By applying explicit statistical distribution constraints to the fused features obtained from the source and target domains, the feature distribution distance between the two domains is calculated and minimized to initially reduce the statistical difference between cross-domain features. The features after statistical distribution constraints are then input into the gradient reversal layer. By introducing a domain adversarial training mechanism, the GEfused module is guided to learn cross-domain universal domain-invariant features and connected to the domain classifier to complete the classification task. Step 6: Using a fully connected network, extract genotype and environmental data fusion features based on the trained GEfused module to predict phenotypic data, and use the gradient attribution method to analyze the prognostic interpretability of the model.

2. The method for predicting cross-regional crop plant height and yield based on meta-learning and adversarial domain adaptation according to claim 1, characterized in that, Preprocessing of the crop dataset includes: The genotype data is gene SNP data. Samples with an individual-level genotype deletion rate greater than 10% and SNP sites with a site-level deletion rate greater than 10% are filtered out. The filtered genotype data undergoes linkage disequilibrium pruning to retain independent SNP sites, and the pruned genotype data is binarized and encoded as follows: 0 represents the homozygous genotype 0 / 0, and 1 represents the homozygous genotype 1 / 1; The environmental data includes four environmental factors: temperature, relative humidity, solar radiation, and precipitation. After cleaning up missing data, the time-series statistical characteristics related to crop growth and development and biomass accumulation are calculated, including basic statistical characteristics, growth days, water vapor pressure deficit, cumulative effective sunshine duration, cumulative effective radiation intensity (solar radiation), and cumulative precipitation. The phenotypic data includes plant height and yield, which are normalized after missing data cleaning.

3. The method for predicting cross-regional crop plant height and yield based on meta-learning and adversarial domain adaptation according to claim 2, characterized in that, The basic statistical characteristics are the statistical indicators of the four environmental factors and the four-quartile characteristics. The statistical indicators include the mean, standard deviation, minimum, maximum and median. The four-quartile characteristics are the lower quartile, median, upper quartile and maximum. The growth period days are calculated using the following formula: ,in, Let be the average daily temperature on day i, and n be the total number of days in the growth cycle. The minimum effective temperature for crop growth; The formula for calculating the water vapor pressure deficit is as follows: , The saturated vapor pressure is calculated using the following formula: , The actual water vapor pressure is calculated using the following formula: ,in, The representative temperature used to calculate the day's highest and lowest temperatures. It refers to relative humidity; The cumulative effective illumination duration is calculated using the following formula: ,in, For the instantaneous solar radiation in the j-th hour of day i, I ( x The function is an indicator function that takes the value 1 if the condition is met, and 0 otherwise. The effective illumination threshold; The cumulative effective radiation intensity of solar radiation is calculated using the following formula: ; The cumulative precipitation is calculated using the following formula: ,in, Rainfall on day i; Calculate the three features: mean (VPD) value, cumulative VPD value (∑VPD), and diurnal humidity difference (VPD). ), where day_rh_mean is the daytime average relative humidity and the diurnal humidity difference: in, The average relative humidity during the day. This represents the average relative humidity at night.

4. The method for predicting cross-regional crop plant height and yield based on meta-learning and adversarial domain adaptation according to claim 1 or 2, characterized in that, The GEfused module includes a genotype feature extraction branch, an environmental feature extraction branch, and a fusion layer; The genotype feature extraction branch uses multi-scale dilated convolution as the core extraction unit. The two sub-branches sequentially extract sequence associations through dilated convolution, zero-padding, and 1×1 convolution. The dilation rates of the dilated convolutions in the two sub-branches differ. The outputs of the two sub-branches are fused using element-wise addition to achieve multi-scale feature fusion, which constitutes the output representation of the genotype branch. ; The environment-based feature extraction branch employs two sub-branches to model the statistical distribution differences across environments and the dynamic temporal dependencies within the same environment, respectively; the first sub-branch focuses on the feature vector composed of temporal statistical features. Static features are obtained through linear transformation and regularization. : Where FC is regularization, LN is used to normalize the feature distribution, and GELU is a non-linear activation function; The second sub-branch uses a Transformer encoder to extract environmental timing data. The trend characteristics are identified using the following methods: First, the low-dimensional temporal features are mapped to the Transformer model dimension. : Then, sine and cosine positional coding is introduced to distinguish features at different time steps. The positional coding is as follows: in, , This refers to the position in the sequence. pos The dimensions are 2 respectively. i and 2 i +1 is the position code value; pos The position index of an element in the sequence; This refers to the hidden dimensions of the Transformer model, namely the dimensions of the word embedding vector and the positional encoding vector. The position-encoded input is: It is a positional encoding vector. ; This is then encoded using a multi-head attention encoder to capture long-range dependencies in the temporal context. The attention weights for each head are calculated as follows: in, , , These are query, key, and value matrices, respectively. For each head's feature dimension, These are learnable linear projection matrices, namely the query projection matrix, the key projection matrix, and the value projection matrix; Finally, the multi-head outputs are concatenated and then processed through a feedforward network and normalized to enhance the feature representation, resulting in dynamic features. static features With dynamic characteristics After dimensional alignment and weighted fusion, the output is a unified dimensional environmental feature. ; The fusion layer will incorporate genotype characteristics. Environmental characteristics The final fused feature is obtained by linear projection after channel stitching. .

5. The method for predicting cross-regional crop plant height and yield based on meta-learning and adversarial domain adaptation according to claim 1 or 2, characterized in that, Step 4, the dual-loop training, includes an inner loop and an outer loop, and the training method is as follows: The inner loop, for each randomly sampled source domain subtask, inputs its support set into the GEfused module to extract source domain fusion features. Used for meta-training; during the meta-training phase, for the first... Sub-tasks Starting from global meta-initial parameters Starting from this point, perform k-step SGD updates using the support set of the current subtask to obtain task-specific parameters adapted to this environment, as shown in the following formula. in, For the inner loop learning rate, The mean squared error loss for phenotypic prediction. for Support set, For the first j The gradient update term of the step, This represents the number of iterations in the inner loop. For the first Sub-tasks Task-specific parameters after the inner loop; Refer to The gradient of the variable; The outer loop uses a query set. Evaluate the performance after task adaptation and update the global meta-initial parameters. : in, The meta-learning rate; By iterating through the inner and outer loops, a universal global initial parameter is eventually obtained. .

6. The method for predicting cross-regional crop plant height and yield based on meta-learning and adversarial domain adaptation according to claim 1 or 2, characterized in that, Step 5 involves applying statistical distribution constraints to the fusion features of the source and target domains using either the Maximum Mean Discrepancy (MMD) or Correlation Alignment (CORAL) method, as follows: Based on the maximum mean difference method, the source domain fusion features obtained using the GEfused module are analyzed. Features fused with the target domain Calculate the distribution distance loss; Alternatively, based on relevant alignment methods, the alignment of second-order statistics can reduce overall differences, where the second-order statistics are covariance matrices.

7. The method for predicting cross-regional crop plant height and yield based on meta-learning and adversarial domain adaptation according to claim 6, characterized in that, The maximum mean difference method calculates the mean difference between the source domain and the target domain in the reproducing kernel Hilbert space: in, , The feature distributions of the source domain and the target domain are respectively. For the characteristic mapping of the regenerating kernel Hilbert space, It is the RKHS space norm; It is a feature vector of a single sample in the source or target domain; For a finite sample, the standard empirical estimate is: in, , The number of samples in the source domain and the target domain. For kernel function, , These are sample sets from the source domain and the target domain, respectively. , Samples in the source domain i and j Feature vector; , The sample feature vector in the target domain; The formula for calculating MMD loss is: CORAL loss for: in, , Let be the covariance matrices of the features of the source domain and the target domain, respectively. d For feature dimensions.

8. The method for predicting cross-regional crop plant height and yield based on meta-learning and adversarial domain adaptation according to claim 6, characterized in that, The forward propagation of the gradient inversion layer is an identity mapping, and the gradient sign is inverted during backward propagation: in, The resistance coefficient; It is the identity matrix; This refers to the fusion feature, specifically the source domain fusion feature. or target domain fusion features .

9. The method for predicting cross-regional crop plant height and yield based on meta-learning and adversarial domain adaptation according to claim 6, characterized in that, The domain classifier uses cross-entropy loss to measure the classification accuracy of the domain classifier head. in, This represents the batch sample size. For domain tags, This is the output of the classifier.

10. The method for predicting cross-regional crop plant height and yield based on meta-learning and adversarial domain adaptation according to claim 6, characterized in that, The model's total loss function is composed of the source domain phenotype prediction loss. Target domain phenotypic prediction loss Distribution alignment loss Domain confrontation losses Its composition, and its mathematical expression are as follows: in, For distribution alignment loss and , The number of samples in the source domain. , Let be the predicted phenotypic value and the actual phenotypic value for the i-th sample, respectively. , , These are the corresponding weighting coefficients, used to balance the contributions of different loss terms.

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