Impedance-Driven Decoupling Water–Nitrogen Stress in Wheat: A Parallel Machine Learning Framework Leveraging Leaf Electrophysiology

Abstract

Accurately monitoring coupled water–nitrogen stress is critical for wheat (Triticum aestivum L.) productivity under climate change. This study developed a machine learning framework utilizing multimodal leaf electrophysiological signals––intrinsic resistance, impedance, capacitive reactance, inductive reactance, and capacitance––to decouple water and nitrogen stress signatures in wheat. A parallel modelling strategy was implemented employing Gradient Boosting, Random Forest, and Ridge Regression, selecting the optimal algorithm per feature based on predictive performance. Controlled pot experiments revealed IZ as the paramount biomarker across leaf positions, indicating its sensitivity to ion flux perturbations under abiotic stress. Crucially, algorithm-feature specificity was identified: Ridge Regression excelled in modeling linear responses due to its superior noise suppression, while GB effectively captured nonlinear dynamics. Flag leaves during reproductive stages provided significantly more stable predictions compared to vegetative third leaves, aligning with their physiological primacy as source organs. This framework offers a robust, non-invasive approach for real-time water and nitrogen stress diagnostics in precision agriculture.

1. Introduction

Optimizing crop management in the face of increasing abiotic stress requires precise monitoring of plant physiological status. Traditional smart agriculture primarily relies on environmental sensors to monitor factors such as temperature, humidity, and light. However, these indirect measurements often do not adequately capture the direct physiological responses of plants to changing stressors like water and nitrogen (N) limitations. Plant electrophysiology, which involves monitoring ion flux dynamics and changes in cellular membrane potential, provides a more reliable method for understanding plant stress physiology [1,2]. Reflecting the real-time adjustments to environmental perturbations, these signals give a possibility to a more physiologically relevant diagnostic tool than ambient measurements alone [3]. Specifically, water and N stress are paramount to wheat (Triticum aestivum L.) productivity globally. Nevertheless, their coupled effects and spatially/temporally dynamic impacts pose significant challenges for accurate monitoring and management. Plants mount integrated defense responses across molecular, physiological, and morphological levels under stress, often culminating in detectable alterations in electrophysiological activity [4]. In the study of stress resistance of Dendrobium officinale, it was shown that capacitance reflects the cell’s ion storage capacity, with high intrinsic physiological capacitance (ICP) indicating that its membrane structure is more stable. In contrast, lower intrinsic resistance (IR) and intrinsic inductive reactance (IXl) indicate that drought affects ion permeability less [5]. Consequently, decoding these electrophysiological signals holds significant potential for the rapid and non-invasive diagnosis of stress etiology [6].

Wheat is a vital staple crop crucial to global food security. However, it is particularly vulnerable to the combined challenges of water scarcity and nitrogen imbalances, which are exacerbated by climate change. Research has demonstrated that both nitrogen fertilizer and irrigation significantly impact wheat grain yield. When irrigation is inadequate, the beneficial effects of nitrogen fertilizer on yield are constrained. However, with sufficient irrigation, nitrogen fertilizer can greatly enhance yield potential. Applying higher levels of nitrogen fertilizer under medium irrigation conditions can help balance yield cost-effectively [7]. While hyperspectral remote sensing is widely used for nitrogen assessment, it faces significant limitations, notably spectral saturation during critical reproductive stages, hindering reliable field application. In the experiment of predicting the N and chlorophyll content of winter wheat using a support vector machine algorithm, the validation set R² of nitrogen content prediction can reach 0.62 [8], and chlorophyll prediction also performs well [9]. The algorithm further performs well in predicting water vapor pressure and estimating transpiration [10]; in particular, the test set R² of the random forest (RF) algorithm predicting water vapor pressure can reach 0.9694 [11], which proves the effectiveness of the machine learning algorithms in wheat production scenarios. Machine learning has enabled the development of an intelligent agricultural management system that collects real-time data on soil temperature, humidity, and light intensity. This data is gathered through satellite images, drone multispectral data, and ground sensor networks to inform zoned irrigation and dynamically adjust fertilization plans.

Electrophysiological signals function as sensitive, real-time indicators of environmental stressors, mirroring dynamic perturbations in ion channel conductance and cellular membrane potential [2]. The imposition of stress can drive plant electrical activity towards critical thresholds, eliciting complex nonlinear behaviors and burst in action potential [12]. In experiments on leaf water transport in three karst plant cells, the intracellular water holding capacity calculated by electrophysiological signals was also related to leaf photosynthesis, water potential, leaf tension, and chlorophyll fluorescence parameters [13]. Machine learning (ML) has emerged as a powerful tool for deciphering these complex signals. Techniques range from signal preprocessing (e.g., filtering, enhancement) and feature extraction (e.g., time domain, frequency domain, interval representation) [3,14] to advanced pattern recognition, including conversion to image representations for deep learning [15]. A study that used two types of machine learning models (classification and regression) associated with the electrophysiological signals of grapevines and classical water potential assessment methods showed that the regression model performed very well on the training set but also had the problem of insufficient generalization [16]. Some researchers have constructed a classification model based on the gradient boosting tree (GB) algorithm of electrophysiological signals and applied it to study tomato nutrient deficiency. The results showed that the model can effectively distinguish the stress state of the plant. The classification accuracy rates of nitrogen, manganese, iron, and calcium deficiency were 89.6%, 78.5%, 78.1%, and 78.1%, respectively. It can also predict nutrient deficiency several days or even two weeks before visual symptoms appear [17]. In the algorithm model research based on the electrophysiological frequency signals of tomatoes in greenhouse nitrogen stress experiments, the training set accuracy of the deep learning model was over 80% [18]. Successful applications include classifying diverse abiotic stresses (e.g., cold, osmotic, low-light) in soybean [3], and diagnosing multiple stresses (drought, salinity, light deficiency, mechanical damage, pathogens) in tomatoes under controlled conditions [19]. Crucially, water or N deficiency alters cellular osmolarity and ion homeostasis, perturbing transmembrane ion fluxes (e.g., K⁺, NO₃⁻) and generating distinct electrophysiological responses [4,20]. A study examining the effects of various N sources on energy distribution and N and phosphorus removal in iris plants found that different proportions of N sources significantly influenced cellular metabolic energy, which indicates a strong relationship between electrophysiological signals and nitrogen elements [21]. However, a critical limitation persists: electrophysiological signals are inherently multimodal and can be confounded by concurrent mechanical stimuli or biotic stresses [19]. This complexity necessitates sophisticated approaches, such as multimodal data fusion and robust ML algorithms, to isolate specific stress signatures, particularly for decoupling co-occurring stresses like water and N.

Electrophysiological monitoring presents a compelling, non-invasive, real-time alternative. However, two fundamental challenges impede its practical deployment for coupled stress diagnosis in wheat:

• Signal Entanglement: Disentangling the distinct electrophysiological signals contributed by co-occurring water and N stress within complex multimodal signals.
• Physiological Context Dependence: Ensuring model robustness and generalizability across various electrophysiological contexts, including different plant developmental stages and leaf positions, significantly influencing signal characteristics.

Despite numerous studies focusing on water and N stress, as well as the application of machine learning to assess plant growth, research on the non-destructive prediction of wheat’s water and N stress status through electrophysiological signals using machine learning is still in the developmental stage. To address these challenges, a novel ML framework was specifically designed to (i) decode multimodal leaf electrophysiological signals (intrinsic resistance, impedance, capacitive reactance, inductive reactance, and capacitance) for concurrent quantification of water and nitrogen stress intensity and (ii) explicitly incorporate physiological context (growth stage, leaf position) to enhance model robustness and generalizability. Contrary to approaches primarily focused on classifying stress states or studying electrophysiological mechanisms per state, the core objective is to establish a robust diagnostic tool for quantifying coupled environmental stress levels in field-deployable scenarios. We hypothesize that integrating multimodal electrophysiological profiling with a physiologically informed ML strategy can effectively decouple water and nitrogen stress signatures in wheat.

Previous research underscores the potential of ML for plant stress diagnosis using electrophysiology. Research has addressed highly imbalanced data using strategies such as transforming multiclass problems into binary tasks and conducting comprehensive benchmarking, thereby achieving effective multiclass classification of chemical stressors in tomatoes and cabbages [22]. Ensemble methods like RF and GB often demonstrate superior performance for stress state classification [20,22]. Some literature has employed approximate entropy to investigate the relationship between electrophysiological signals and the maturity of Solanum lycopersicum var. cerasiforme fruit, particularly concerning ethylene [23]. Comparing the accuracy of different machine learning algorithms, RF performed best in two-stage classification based on the maturity stage divided into mature green, broken color, and light red; Support Vector Classifier (SVC) had the highest accuracy in three-stage classification [24]. It was observed that the approximate entropy initially decreases and then increases during the ripening stage, providing a viable approach for predicting maturity. Building upon this foundation, this work extends beyond categorical classification towards continuous quantification of stress intensity. Furthermore, the critical issue of electrophysiological context dependence was explicitly addressed by rigorously evaluating the model’s performance at different leaf positions and developmental stages. Parallel modeling and multiple comparisons were used to enhance the robustness of the overall model, while GB, RF, and Ridge Regression were integrated to exploit their complementary strengths fully. Therefore, the specific objectives of this study were to:

• Decouple the electrophysiological signals of concurrent water and nitrogen stress in wheat using multimodal profiling (intrinsic resistance (IR), intrinsic impedance (IZ), intrinsic capacitive reactance (IXc), intrinsic inductive reactance (IXl), and intrinsic physiological capacitance (ICP))
• Develop and validate a stage- and position-aware prediction model for quantifying stress intensity.

We hypothesize that multimodal leaf electrophysiological profiling, analyzed within a physiologically contextualized ML framework, enables effective decoupling of water and nitrogen stress signatures.

2. Materials and Methods

A controlled pot experiment was conducted in the greenhouse at Jiangsu University, Zhenjiang, China (32.20° N, 119.45° E) from 1 March to 25 April 2025, encompassing key growth stages from regreening to grain filling. The entire planting experiment was conducted under natural light, temperature, and humidity without any human control. The region experiences a humid subtropical monsoon climate (mean annual temperature: 15.5 °C; mean annual precipitation: 1058.8 mm yr⁻¹) [25]. The overall climate during the experiment was mild, with less extreme weather, which could effectively reduce the impact of climatic conditions on the growth of experimental wheat and the collection of electrophysiological signals.

Uniform seedlings of Wheat (cv. Y34), sourced from Yangzhou Academy of Agricultural Sciences, Jiangsu Province, were transplanted on 1 March 2025 into 30 cm diameter pots filled with a 3:1 (v/v) peat: vermiculite mixture.

2.1. Plant Material and Stress Treatments

The experiment adopted a completely randomized block design with seven experimental treatments, including four moisture and three nitrogen gradients. Each treatment had nine pots as biological replicates, with four wheat plants planted in each pot, for a total of 252 plants. All pots received their respective nutrient solutions daily for 10 days prior to transplanting to equilibrate the substrate environment. Stress treatments commenced immediately after transplanting. Substrate water content was verified twice daily (morning and evening) using a calibrated moisture meter (SK-100, Sanko Electronic Laboratory Co., Ltd., Kawasaki, Japan). When the water content was lower than the set range of the treatment, the corresponding Hoagland solution was added, ensuring it did not exceed the upper limit of the treatment group.

• Control (CK): 100% N content Hoagland solution and relative water content was maintained at 75–80% (100% is defined as: after the substrate in the pot is thoroughly irrigated, it is drained until no water drips out, which is approximately equal to 100% field capacity).
• N-deficit groups: Hoagland solution with N-deficit (75%, 50%, or 25% of total nitrogen, other components unchanged) and relative water content was maintained at 75–80%.
• Water-deficient groups: 100% N content Hoagland solution and relative water content was maintained at 60–65% (LD), 45–50% (MD), and 30–35% (HD).

2.2. Electrophysiological Monitoring

Following a 10-day acclimatization period, electrophysiological signals were recorded daily between 09:00 and 11:00 a.m. local time using a Plant Life Analyzer (Jiangsu Zhongtian Smart Sense Life Data Co., Ltd., Zhenjiang China). Measurements were performed on the adaxial surface of intact leaves, avoiding the midrib, using copper electrodes (8 mm diameter) (Figure 1). For each treatment, three measured samples were completely randomly selected from individual plants per session each day.

The raw parameters measured were:

• Resistance (R, MΩ): the resistance that a conductor creates to the passage of electric current.
• Impedance (Z, MΩ): the total resistance to electric current in an AC circuit, which comprehensively reflects the resistance of resistance, inductance, and capacitance to AC current, and is a complex vector.
• Capacitive Reactance (X_C, MΩ): the resistance of capacitance to AC current, which is inversely proportional to frequency and capacitance.
• Inductive Reactance (X_L, MΩ): the resistance of inductance to AC current, which is directly proportional to frequency and inductance.
• Physiological Capacitance (Cp, pF): the capacitance characteristic exhibited by biological tissues or cells, which is produced by the capacitance structure formed by the cell membrane (lipid bilayer) and the internal and external electrolyte solutions.

When subjected to abiotic stresses, plant cells undergo changes in their anatomical structure, function, and metabolic activities, which are inevitably reflected in the electrical properties of plant tissues and organs [4]. The derived intrinsic electrophysiological parameters––intrinsic resistance (IR), intrinsic impedance (IZ), intrinsic capacitive reactance (IXc), intrinsic inductive reactance (IXl), and intrinsic physiological capacitance (ICP)––were calculated from the raw measurements following established protocols accounting for leaf thickness and electrode contact area [4,25].

Monitoring Protocol: During the vegetative growth stage (until heading), measurements were conducted solely on the third leaf (counted from the base). Upon heading, measurements were expanded to include the flag leaf (F), the penultimate leaf (F-1), and the third leaf.

2.3. Parallel Multi-Model Comparison Framework

A feature-specific model selection strategy was implemented:

2.3.1. Parallel ML Framework for Feature-Specific Modeling Rationale

A feature-specific modeling strategy was employed due to the unique biophysical origins of each electrophysiological feature (IR, IZ, IXc, IXl, ICP) and their potential relationships with water and nutrient stress. This approach suggests that the best predictive performance for each feature may be achieved by using different algorithms rather than relying on a single and unified model.

2.3.2. Parallel Model Training

The five electrophysiological features (IR, IZ, IXc, IXl, ICP) were independently used to train models with three different algorithms: Gradient Boosting (GB), Random Forest (RF), and Ridge Regression. The training process was expedited through parallel computing, which significantly decreased computational time and allowed a more efficient exploration of the model space.

2.3.3. Hyperparameter Optimization

Hyperparameters for each algorithm were optimized via stratified five-fold cross-validation (stratified by treatment and growth stage to maintain distribution) coupled with an exhaustive grid search over predefined ranges:

• GB: three key hyperparameters were considered for the GB algorithm: n_estimators: [50, 100], learning_rate: [0.05, 0.1], and max_depth: [3, 5] [26,27]. The n_estimators parameter controls the number of boosting stages. Increasing n_estimators typically improves model accuracy, but at a higher computational cost. The learning rate determines each tree’s contribution: a lower rate often builds a more robust model but requires more estimators. Finally, max_depth restricts individual tree depth to avoid overfitting.
• RF: In the case of the RF algorithm, three hyperparameters were introduced: n_estimators: [50, 100, 200], max_depth: [5, 10], and min_samples_split: [2, 5] [28,29]. The n_estimator specifies the number of trees in the forest. Generally, more trees improve model performance and stability. The max_depth parameter restricts the maximum depth of each tree. Finally, the min_samples_split determines the minimum number of samples to split an internal node.
• Ridge: For Ridge regression, the main hyperparameter is alpha: [0.1, 1, 10], which controls the amount of regularization applied to the model [30,31]. A larger alpha value increases the regularization strength, reducing the variance of the model but potentially increasing the bias.

Optimization aimed at maximizing the coefficient of determination (R²) on the cross-validation folds.

2.3.4. Optimal Model Selection

Following hyperparameter optimization, the single best-performing algorithm for predicting each specific electrophysiological feature was selected based solely on its R² score evaluated on a held-out independent test set (20% of replicates, stratified by treatment/growth stage). This strategy prioritizes generalization performance for each feature’s prediction task.

2.3.5. Biological Replicates

Nine pots (four plants per pot) were used for each treatment, generating 36 sample pools for each treatment measurement, with three plants of each treatment selected randomly for each daily measurement. To ensure representativeness and consider biological variability, the data split (training/validation/testing) was stratified by treatment and growth stage to avoid averaging and preserve the full range of variation within the model.

2.4. Evaluation Metrics

Given the regression nature of stress intensity prediction (continuous % levels), model performance was primarily assessed using:

2.4.1. Coefficient of Determination (R²)

Quantifies the proportion of variance in the target explained by the model.

2.4.2. Root Mean Squared Error (RMSE)

Measures the average magnitude of prediction errors (units same as target). Lower RMSE indicates higher precision.

2.4.3. SHapley Additive exPlanations (SHAP)

The relative contribution of each input feature (the electrophysiological parameters) to the predictions of the optimal model for each specific feature’s prediction task was evaluated using SHAP (SHapley Additive exPlanations) values [32]. SHAP provides a unified, game-theoretic measure of feature importance and directionality (positive/negative effect) [32]. This analysis identifies key electrophysiological indicators most responsive to water–N stress.

2.5. Model Validation and Overfitting Control

To ensure model generalizability and prevent overfitting:

2.5.1. Independent Test Set

To rigorously assess generalizability, 20% of the biological replicates (stratified by treatment and growth stage) were held out prior to any model training or hyperparameter optimization and used only for the final evaluation of the selected optimal models. This provides an unbiased estimate of out-of-sample performance.

2.5.2. Learning Curve Analysis

To diagnose overfitting and evaluate data efficiency, learning curves were generated for key models. Models were trained on incrementally larger subsets of the training data (10%, 20%, …, 100%), and both training and validation (using a fixed validation set from the training partition) R² scores were recorded at each step. The divergence between training and validation performance (especially increasing training R² with stagnant or decreasing validation R²) indicates overfitting. This analysis helps determine if model performance has saturated with the available data.

3. Results

After preliminary data cleaning, there were 252 sets of data for the flag leaf and the penultimate leaf, 246 sets for the third leaf, and a total of 750 data sets in the entire experimental period. After code division, 80% of the data was used as a training set and 20% as a test set. The random seed was set to 42 to ensure that the results of each division were the same, securing the repeatability of the model code. The five-fold cross-validation method was used to evaluate the model’s performance.

3.1. Feature Analysis

The SHAP values are based on the Shapley value concept in game theory. They calculate the marginal contribution of a feature to the final result in model prediction. Its value is the amplitude of change in the predicted value, representing the amount by which the feature increases/decreases the predicted result. In the same model, the larger the absolute value of the SHAP value, the stronger the influence of the feature on the predicted result (regardless of whether it is positive or negative; positive means promotion and negative means inhibition).

SHAP analysis (Figure 2) revealed that IZ was the most significant electrophysiological feature across all leaf positions and types of stress, demonstrating its reliability as a biomarker for water and nitrogen stress. In the flag leaf model (Figure 2a), IZ was particularly prominent, consistently ranking as the most important feature, regardless of stress type or algorithm.

In the penultimate leaf model (Figure 2b), IZ was the dominant factor in the Ridge model for both water and nitrogen stress, as well as in the RF model specifically for water stress. For the third leaf model (Figure 2c), IZ was again the key feature in the RF model for water and nitrogen stress, the GB model for water stress, and the Ridge model for water stress. This aligns with existing research that links IZ to the dynamics of water transport within leaf cells, as well as its role in photosynthesis and growth [16,19].

In the analysis of the penultimate leaf under nitrogen stress (Figure 2b), intrinsic reactance (IXl) was identified as the most significant factor in the GB model for both types of stress and in the RF-N model. Only in the Ridge-N model did ICP emerge as the main predictor for the third leaf (Figure 2c). A comprehensive analysis of all leaf positions (Figure 2d) further confirmed the overall importance of IZ.

Model stability, assessed via cross-validation R² variability (Figure 3), differed markedly between leaf positions. The horizontal axis represents the model’s coefficient of determination on the test set, which measures the model’s goodness of fit to the data. The closer it is to 1, the stronger the model’s ability to explain the test set data and the better the effect of fit. The vertical axis represents the standard deviation of the coefficient of determination in cross-validation. The standard deviation reflects the degree of dispersion of the data. Here, it reflects the fluctuation of the model’s coefficient of determination results under different cross-validation folds. The smaller the value, the more stable the model is during cross-validation and the more consistent the results are. The reference line is the red solid line (value 0.10) and the red dotted line (value about 0.05). The preset threshold line determines whether the model stability meets the standard quickly. If the vertical axis data exceeds these lines, the model stability is poor; the stability is relatively good below the threshold line. Flag leaf models demonstrated exceptional stability during the reproductive stage (mean CV of R²: 0.8%; mean R²: 0.992 ± 0.008; Interquartile Range, IQR: 0.983–0.998). Penultimate leaf models exhibited moderate dispersion (IQR: 0.942–0.978), with increased instability under N stress (e.g., 12.5% of GB predictions yielded R² < 0.94). In stark contrast, third leaf (vegetative) models showed significantly higher prediction volatility (CV: 4.7%; p < 0.001 vs. flag leaf CV), attributable to greater developmental noise from active cell division processes.

Both p-value and effect size (

Table 1. Model evaluation metrics (p-value and effect size) for water stress identification across leaf positions.

Feature	Model	Flag		Penultimate		Third		Overall
		p-Value	Effect Size	p-Value	Effect Size	p-Value	Effect Size	p-Value	Effect Size
IR	RF vs. Ridge	0.052	−1.439	<0.01 **	−2.128	<0.01 **	−2.617	<0.01 **	−2.484
	GB vs. Ridge	<0.05 *	−1.574	0.060	−1.381	0.091	−1.216	<0.05 *	−1.906
	RF vs. GB	0.840	−0.132	0.352	0.624	0.078	−1.278	0.061	−1.381
IZ	RF vs. Ridge	<0.01 **	−2.142	<0.01 **	−2.423	<0.05 *	−1.612	0.034	−1.619
	GB vs. Ridge	0.064	−1.361	0.100	−1.174	<0.05 *	−1.704	0.034	−1.613
	RF vs. GB	0.127	−1.075	0.968	−0.026	0.814	−0.154	0.158	−0.986
IXl	RF vs. Ridge	0.071	−1.314	<0.01 **	−2.469	0.168	−0.959	<0.05 *	−1.666
	GB vs. Ridge	<0.05 *	−1.552	0.260	−0.767	0.283	−0.728	<0.05 *	−2.095
	RF vs. GB	0.132	−1.062	0.733	0.223	0.734	−0.223	0.332	−0.653
IXc	RF vs. Ridge	<0.05 *	−1.852	<0.01 **	−2.178	<0.05 *	−1.540	<0.01 **	−3.730
	GB vs. Ridge	<0.05 *	−1.570	<0.05 *	−2.015	<0.05 *	−1.495	<0.05 *	−2.044
	RF vs. GB	0.609	−0.337	0.208	−0.865	0.462	−0.489	0.300	−0.701
ICP	RF vs. Ridge	0.201	−0.880	<0.05 *	−1.811	<0.01 **	−3.652	0.208	−0.867
	GB vs. Ridge	0.134	−1.054	<0.05 *	−1.992	0.125	−1.083	0.139	−1.040
	RF vs. GB	0.657	−0.292	0.427	−0.529	0.326	0.662	0.658	−0.291

* represents p < 0.05 (statistically significant), and ** represents p < 0.01 (highly statistically significant)

and

Table 2. Model evaluation metrics (p-value and effect size) for nitrogen stress identification across leaf positions.

Feature	Model	Flag		Penultimate		Third		Overall
		p-Value	Effect Size	p-Value	Effect Size	p-Value	Effect Size	p-Value	Effect Size
IR	RF vs. Ridge	<0.01 **	−3.178	0.091	−1.215	0.174	−0.944	0.054	−1.430
	GB vs. Ridge	<0.05 *	−1.750	0.053	−1.438	0.114	−1.121	<0.01 **	−2.146
	RF vs. GB	0.374	−0.596	0.646	−0.302	0.996	0.004	0.193	−0.899
IZ	RF vs. Ridge	0.181	−0.928	0.084	−1.248	0.113	−1.124	0.139	−1.041
	GB vs. Ridge	0.114	−1.122	0.184	−0.919	0.213	−0.856	0.082	−1.256
	RF vs. GB	0.813	−0.155	0.550	−0.395	0.639	−0.308	0.428	−0.528
IXl	RF vs. Ridge	<0.05 *	−1.527	0.196	−0.893	<0.05 *	−2.073	<0.05 *	−1.644
	GB vs. Ridge	0.073	−1.305	0.063	−1.366	<0.05 *	−1.599	0.063	−1.366
	RF vs. GB	0.425	−0.532	0.981	0.016	0.313	−0.681	0.886	−0.094
IXc	RF vs. Ridge	0.124	−1.086	0.051	−1.452	0.143	−1.026	<0.01 **	−2.277
	GB vs. Ridge	0.194	−0.897	0.088	−1.230	0.066	−1.343	<0.01 **	−2.373
	RF vs. GB	0.610	−0.336	0.471	−0.479	0.312	−0.682	0.659	−0.290
ICP	RF vs. Ridge	0.060	−1.383	0.257	−0.772	0.263	−0.761	0.105	−1.157
	GB vs. Ridge	<0.05 *	−2.035	0.329	−0.658	0.165	−0.966	<0.05 *	−1.894
	RF vs. GB	0.191	−0.904	0.861	−0.114	0.975	0.020	0.170	−0.954

* represents p < 0.05 (statistically significant), and ** represents p < 0.01 (highly statistically significant)

) are important metrics for comparing the performance of different models. The p-value is a measure of statistical significance. In this data set, the p-value is used to measure the significance of the performance difference between different models. On average, the p-value of RF–GB vs. Ridge is relatively small, which may suggest significant differences in more cases when compared with the Ridge model. In contrast, the p-value of RF vs. GB is relatively large, indicating that there may not be significant differences when compared with the two models in most cases. The effect size measures the actual size of the difference between two data sets or the effect’s strength. If the absolute value of the effect size is large, then the performance of the two models in actual use may be very different. The mean is negative, which may suggest that, in most cases, the performance of the compared model is worse than that of the control model. For example, the absolute value of the effect size of RF–GB vs. Ridge is larger than that of the other two, which may indicate that the performance gap between the other two models and the Ridge model is obviously at a disadvantage.

3.2. Model Performance

All models exhibited high predictive accuracy on the training set (

Table 3. Training model performance metrics (R² and RMSE) and training and independent test discrepancy in R² (ΔR²) on the training set for flag leaf.

Stress		Moisture			Nitrogen
Feature	Model	R2	RMSE	ΔR2	R2	RMSE	ΔR2
IR	RF	0.98039	0.017	0.001	0.99302	0.002	0.001
	GB	0.9828	0.023	0.002	0.99519	0.003	0.003
	Ridge	0.99998	<0.001	<0.001	0.99998	<0.001	<0.001
IZ	RF	0.97579	0.012	−0.001	0.98089	0.025	0.002
	GB	0.99109	0.006	0.001	0.98523	0.017	0.001
	Ridge	0.99995	<0.001	<0.001	0.99995	<0.001	<0.001
IXc	RF	0.99076	0.007	0.003	0.98465	0.018	0.002
	GB	0.99403	0.004	<0.001	0.99	0.012	0.003
	Ridge	0.99998	<0.001	<0.001	0.99998	<0.001	<0.001
IXl	RF	0.98796	0.015	0.006	0.97243	0.023	0.006
	GB	0.99764	0.002	0.003	0.98708	0.012	0.002
	Ridge	1	<0.001	<0.001	1	<0.001	<0.001
ICP	RF	0.9927	0.009	0.024	0.98179	0.019	0.001
	GB	0.9959	0.005	0.016	0.99697	0.002	0.045
	Ridge	0.99999	<0.001	<0.001	1	<0.001	<0.001

,

Table 4. Training model performance metrics (R² and RMSE) and training and independent test discrepancy in R² (ΔR²) on the training set for penultimate leaf.

Stress		Moisture			Nitrogen
Feature	Model	R2	RMSE	ΔR2	R2	RMSE	ΔR2
IR	RF	0.98146	0.009	0.003	0.96569	0.037	0.02
	GB	0.97008	0.024	0.002	0.97399	0.031	0.029
	Ridge	0.99999	<0.001	<0.001	0.99998	<0.001	<0.001
IZ	RF	0.97844	0.012	0.021	0.9746	0.027	0.027
	GB	0.98438	0.016	0.014	0.98376	0.025	0.01
	Ridge	0.99997	<0.001	<0.001	0.99998	<0.001	<0.001
IXc	RF	0.98812	0.008	0.006	0.97928	0.018	0.001
	GB	0.99186	0.003	0.014	0.9865	0.017	<0.001
	Ridge	0.99998	<0.001	<0.001	0.99999	<0.001	<0.001
IXl	RF	0.99469	0.003	0.004	0.96405	0.044	0.038
	GB	0.9919	0.014	0.009	0.96516	0.029	0.011
	Ridge	0.99999	<0.001	<0.001	1	<0.001	<0.001
ICP	RF	0.9782	0.016	0.002	0.96697	0.052	0.003
	GB	0.98351	0.011	0.026	0.97511	0.048	0.004
	Ridge	1	<0.001	<0.001	0.99999	<0.001	<0.001

,

Table 5. Training model performance metrics (R² and RMSE) and training and independent test discrepancy in R² (ΔR²) on the training set for third leaf.

Stress		Moisture			Nitrogen
Feature	Model	R2	RMSE	ΔR2	R2	RMSE	ΔR2
IR	RF	0.96916	0.014	0.002	0.98628	0.019	0.012
	GB	0.98504	0.019	<0.001	0.98816	0.014	0.005
	Ridge	0.99999	<0.001	<0.001	0.99999	<0.001	<0.001
IZ	RF	0.96693	0.024	<0.001	0.9863	0.016	0.006
	GB	0.97272	0.021	0.008	0.99189	0.012	0.001
	Ridge	0.99998	<0.001	<0.001	0.99999	<0.001	<0.001
IXc	RF	0.96728	0.029	−0.004	0.99066	0.01	0.005
	GB	0.98154	0.015	0.001	0.99708	0.003	<0.001
	Ridge	0.99999	<0.001	<0.001	0.99999	<0.001	<0.001
IXl	RF	0.93858	0.081	−0.001	0.97876	0.012	0.003
	GB	0.96155	0.063	0.008	0.99035	0.008	0.004
	Ridge	1	<0.001	<0.001	1	<0.001	<0.001
ICP	RF	0.98534	0.007	0.089	0.9822	0.03	−0.001
	GB	0.9603	0.066	0.11	0.98115	0.026	0.001
	Ridge	1	<0.001	<0.001	0.99999	<0.001	<0.001

and

Table 6. Training model performance metrics (R² and RMSE) and training and independent test discrepancy in R² (ΔR²) on the training set for integrated leaf.

Stress		Moisture			Nitrogen
Feature	Model	R2	RMSE	ΔR2	R2	RMSE	ΔR2
IR	RF	0.99833	0.001	0.001	0.99883	0.001	<0.001
	GB	0.99932	<0.001	<0.001	0.99957	<0.001	<0.001
	Ridge	1	<0.001	<0.001	1	<0.001	<0.001
IZ	RF	0.99754	0.002	<0.001	0.99884	0.001	<0.001
	GB	0.99945	<0.001	<0.001	0.9994	0.001	<0.001
	Ridge	1	<0.001	<0.001	1	<0.001	<0.001
IXc	RF	0.99928	<0.001	<0.001	0.99946	<0.001	<0.001
	GB	0.99949	<0.001	<0.001	0.99958	<0.001	<0.001
	Ridge	1	<0.001	<0.001	1	<0.001	<0.001
IXl	RF	0.99834	0.001	<0.001	0.99905	0.001	0.001
	GB	0.9991	0.001	0.001	0.99917	0.001	<0.001
	Ridge	1	<0.001	<0.001	1	<0.001	<0.001
ICP	RF	0.99658	0.005	0.002	0.99877	0.001	<0.001
	GB	0.99784	0.003	<0.001	0.99977	<0.001	<0.001
	Ridge	1	<0.001	<0.001	1	<0.001	<0.001

). Ridge Regression frequently achieved near-perfect training performance, attributable to the effectiveness of its L₂ regularization in suppressing multicollinearity among features.

Critically, performance on the independent test set revealed substantial insights:

Leaf Position Dependence: Predictive accuracy varied significantly with leaf position. Third leaf models consistently yielded the lowest test R² (e.g., min R² = 0.93858 for RF-water predicting IXl, Table 5). Conversely, flag leaf models maintained robust performance across features and stress types (min test R² = 0.97243 Table 3).

IZ Consistency: Predictions based on IZ demonstrated consistently high test accuracy (mean test R² = 0.991 ± 0.012 Table 3, Table 4, Table 5 and Table 6), irrespective of the modelling algorithm (GB, RF, Ridge) or stress type (water or N).

Ridge Generalization: Despite the risk of overfitting suggested by perfect training fits, Ridge models exhibited excellent generalization, evidenced by minimal discrepancies (ΔR² < 10⁻⁵) between training and test R² (Table 3, Table 4, Table 5 and Table 6), confirming the efficacy of L₂ regularization.

3.3. Overfitting Diagnostics

The generalization gap, quantified as ΔR² = R²_train-R²_test, revealed distinct patterns (Table 3, Table 4, Table 5 and Table 6):

Tree-Based Model Sensitivity: GB and RF models, particularly for ICP prediction in third leaves, exhibited significant overfitting (max ΔR² = 0.112, Table 5). This likely stems from the inherent developmental noise (e.g., active cell division) in vegetative-stage third leaves, which is confounded with stress signatures. The high flexibility of tree-based models allowed them to overfit this noise and spurious correlations within the training set.

Ridge Robustness: In contrast, Ridge models consistently maintained minimal generalization gaps (ΔR² < 10⁻⁵), attributable to the noise-suppressing effect of L₂ regularization, even when training R² reached 1.000. This confirms effective control of overfitting despite potential noise fitting.

Leaf Position Effect: Penultimate leaves under N stress showed the largest ΔR² among non-third-leaf positions (e.g., ΔR² = 0.038 for IXl–RF, Table 4), indicating relatively lower stability.

Learning curve analysis (Figure 4, Figure 5, Figure 6 and Figure 7) for key feature–algorithm combinations (e.g., Ridge predicting IZ–IXl in flag leaves) further validated model behavior. The horizontal axis is the number of training samples, representing how many data sets are used to train the model. The vertical axis is the model’s “fitting–prediction effect” evaluation index. The closer it is to 1, the higher the model’s ability to explain the data/prediction accuracy. The red line is the model’s score on the training set, and the green line is the model’s score on the cross-validation set (new data that did not participate in training). Key observations:

Training R² rapidly approached 1.0 as sample size increased, stabilizing beyond around 100 samples.

The minimal gap between training and validation R² curves across increasing sample sizes indicates strong generalization capability and efficient learning of the underlying physiological patterns for these key features (e.g., IZ, IXl).

This convergence confirms that approximately 100 samples sufficed for stable model performance, informing resource-efficient future studies.

The score on the training set is close to 1 at the beginning, indicating that the model fits the training data very well; it remains stable as the number of samples increases because the model has fully learned the training data patterns. The model’s score on the cross-validation set is low when the initial sample size is small because the model cannot learn enough patterns with little data and has poor generalization ability; as the number of samples increases, the score rises rapidly and approaches 1, indicating that more data allows the model to learn more stable patterns and improve its ability to generalize to new data; as the sample size continues to increase, the score stabilizes near 1, almost coinciding with the training score, indicating that the model has strong predictive ability on new data and good generalization.

The correlation coefficient is a statistic used to measure the degree of linear correlation between two variables, reflecting the strength and direction of the linear relationship between variables. When the absolute value of the correlation coefficient is high, it is believed that strong collinearity may lead to unstable estimation of regression model parameters. However, the correlation coefficient heat map of the five electrophysiological parameters in Figure 8 shows no strong collinearity and their absolute values are all less than 0.6. The largest is 0.597 for IR and IZ in the penultimate leaf, which belongs to moderate collinearity. However, Ridge regression has a mitigating effect on collinearity through L₂ regularization constraints, and even if there are moderately collinear parameters, it will not significantly impact the stability of the model.

4. Discussion

This study successfully developed a machine learning framework that can differentiate between water and N stress signatures in wheat by utilizing multimodal leaf electrophysiology, thereby validating the central hypothesis. The key findings include (i) the significant importance of IZ as a strong biomarker, (ii) the critical role of algorithm-feature specificity, with Ridge regression being effective for linear responses and Gradient Boosting for nonlinear dynamics, and (iii) the enhanced stability of signals from the flag leaf during the reproductive stage. These findings provide a novel and physiologically grounded approach to diagnosing abiotic stress. The results demonstrate high predictive accuracy (R² > 0.938, with a minimum test R² of 0.972 for flag leaves) and generalizability, evidenced by low ΔR² and stable learning curves achieved through this methodology under controlled conditions.

The consistent dominance of the IZ across different models and leaf positions (Figure 2) strongly supports its role as a key integrator of cellular ionic status under combined water–N stress. The IZ represents the opposition of the alternating current flow within leaf tissues, a property significantly influenced by ion concentration and mobility [4]. In experimental environments experiencing drought stress, the IZ and the leaf water dissipation rate derived from the IZ are more reliable indicators of water recharge timing than water potential [25]. Water deficit primarily compromises membrane integrity and electrolytic conductivity, leading to increased electrolyte leakage, elevated leaf temperature, and reduced relative water content in the leaves [33], while N deficiency directly disrupts the activity of key ion transporters (e.g., for K⁺, NO₃⁻, NH₄⁺) and alters cellular osmolyte composition [20,34]. Therefore, the IZ serves as a sensitive indicator of the combined disturbances in ionic balance, particularly the fluxes of potassium (K⁺) and nitrate (NO₃⁻) resulting from these two types of stress [2,34]. This interpretation aligns with studies across various species that have connected IZ dynamics to intracellular water transport, adaptation to salt stress in mangroves [35], and the regulation of diurnal ion flux [36]. Although the direction and magnitude of changes in specific electrophysiological parameters vary according to the type of stress, species, and measurement environments [25], these collective changes consistently indicate crucial physiological adjustments that impact growth.

A central insight of this study is the critical importance of algorithm-feature specificity for optimal performance. The parallel framework revealed that:

Ridge Regression achieves nearly perfect generalization for linear relationships due to its ability to suppress noise through L₂ regularization. On the other hand, GB excels at capturing nonlinear dynamics, as evidenced by its performance in the IXl response under N stress (see Figure 2b). The significant limitations of relying on a single “best” algorithm are underscored here. Single-method approaches can lead to suboptimal performance because they may not align the algorithm’s inductive biases with the specific biophysical relationships represented by each electrophysiological feature.

To address this limitation, feature-specific selection strategies prove to be effective. Learning curve analysis (Figure 4, Figure 5, Figure 6 and Figure 7) further validates this approach’s robustness and data efficiency for key features such as IZ and IXl, with performance reaching a plateau as sample size increases. While overfitting was noticed for certain feature position combinations, such as GB–RF modeling using ICP in the third leaf, the framework successfully identified these instances through generalization gap analysis (Table 3, Table 4, Table 5 and Table 6), pinpointing areas for future improvement.

These results clearly demonstrate the profound impact of leaf position and developmental stage on electrophysiological signal stability and model performance. Flag leaves, as the main photosynthetic source organ during the grain filling period, exhibit mature, stable physiological structure and vasculature [36]. This inherent physiological stability directly translates into significantly lower electrophysiological signal fluctuations and consistently superior model robustness (highest test R², lowest CV value, smallest ΔR²). Although the third leaf is a key signal source during vegetative growth, its physiological relevance decreases after heading, while signal variability increases significantly. This increase in noise may be due to the ongoing cell division and metabolism in maturing leaves, which are asynchronous with development processes and not directly related to specific water or N stress responses. Therefore, the flag leaf is the best physiologically plausible target for electrophysiological stress monitoring during the critical reproductive stage of wheat. This finding provides an important simplification for field deployment, allowing sensing to be focused on the most informative organ.

Compared to established techniques like hyperspectral imaging for N assessment, which suffers from saturation issues during reproduction (RMSE: 0.05–0.12 [37]), the electrophysiological framework achieved superior quantitative accuracy (RMSE < 0.02 for key features/stages) under controlled conditions, potentially at lower hardware cost and complexity (ground-based vs. UAV-mounted sensors). Although this experiment does not have clear data that demonstrates water and fertilizer saving, by monitoring the electrophysiological signals of tomato leaves and using the CNN model to analyze the generated scalogram images, the single irrigation time can be reduced from 4.85 min to 3.88 min (saving 20% water), and the overall system can reduce water consumption by at least 10% [38].

However, translating this laboratory-grade accuracy (test R² > 0.99 for flag leaves) to field environments presents challenges. Key limitations of this study include:

Controlled conditions: Since the experiment was conducted in a greenhouse, some field confounding factors such as wind, rain, extreme temperature fluctuations, and biological stress were isolated. At the same time, temperature and humidity were not included as independent variables in the model, so this experiment was conducted under relatively ideal controlled conditions.

Background noise: Wind can cause the wheat leaves to move. Although the wheat leaves were well fixed between the copper electrodes in the experiment, they may still cause data fluctuations. This experiment did not include background noise as an influencing factor in the model, which may lead to some defects.

To enable field deployment, future research must:

Include denoising: Regarding background noise, some studies introduce different environmental parameters such as light, heat, and humidity, and use the KNN algorithm to classify data under different environmental stimuli, providing a feasible and low-complexity supervised machine learning implementation method [39]. In further experiments, it is considered feasible to plan to record more electrophysiological signals of leaves within controllable soil water–N conditions in the natural environment, set environmental variables such as temperature, humidity and wind speed as influencing factors, analyze the fluctuation law of their influence on electrophysiological signals, and establish a background noise removal model to minimize the impact of intrinsic physiological fluctuations in the future.

Conduct rigorous field validation: Once a comprehensive background denoising model is established, the experiment will be expanded to the field scale, and the framework will be tested in different environments under actual agronomic conditions.

Study the interaction of biological stresses: After verification by field experiments, introducing more stress environments and exploring the ability to extend this model framework to other stress identification models should be considered.

Optimize dynamic modeling: Given that the water–N stress in the current experimental design is a continuous effect, introducing a stress recovery environment to restore the control state after stress and exploring the recognition ability and temporal dynamics of electrophysiological parameters under stress recovery conditions is considered in the later stage.

Hardware improvements: Hardware changes can also be used to reduce noise. In experiments on Arabidopsis thaliana and Venus flytrap, organic electrochemical transistor materials can record plant electrophysiological signals without distortion, and the signal-to-noise ratio is significantly better than traditional electrodes [40]. Flexible multi-electrode arrays (MEAs) based on organic electronics can fit tightly to the curved surface of insect traps to avoid interference from mechanical stimulation and distinguish between active propagation and volume conduction of action potentials with a resolution far exceeding that of traditional electrodes [41]. In subsequent experiments, different electrode materials can be considered as sensors. The most suitable electrode material can be determined by comparing the electrophysiological signal data collected by different materials to obtain more stable electrophysiological data.

5. Conclusions

This study achieved high-precision decoupled wheat water and N stress quantification through a multimodal electrophysiology + parallel machine learning framework, breaking through the monitoring bottleneck of traditional methods. Its algorithm-feature adaptation strategy and physiological background integration provide a new paradigm for crop stress diagnosis. It is expected to promote precision agriculture from “environmental monitoring” to “plant physiological intelligence” and provide key technical support for efficient resource utilization and climate change response. The key conclusions are:

Intrinsic impedance (IZ) emerged as the paramount, robust biomarker across growth stages and leaf positions, reflecting integrated perturbations in ion homeostasis (particularly K⁺/NO₃⁻ fluxes) under abiotic stress.

Algorithm-feature specificity is critical: Ridge Regression delivered optimal performance for features with linear stress responses (e.g., IXc) due to its superior noise suppression, while Gradient Boosting excelled in capturing nonlinear dynamics (e.g., IXl under N stress).

Flag leaves during reproductive stages provided significantly more stable and reliable signals (CV = 0.8%) compared to vegetative third leaves (CV = 4.7%, p < 0.001), establishing them as the optimal monitoring target post-anthesis due to their physiological primacy as source organs.

This framework achieved high diagnostic accuracy (test R² > 0.99 for flag leaves) under controlled conditions, offering a promising non-invasive tool for real-time stress monitoring. While validation under field conditions is essential, the approach holds significant potential for enabling precision irrigation and N management. This contributes to resource savings (water and fertilizer when needed) and enhanced climate resilience in wheat production through the timely detection of abnormal conditions. Future work will focus on field deployment, incorporating background denoising, and integrating electrophysiological diagnostics with growth models to predict yield outcomes, moving beyond environmental status assessment towards predictive crop management.