SEAGAN: Graph Analysis of A–Ci Curves

• SEAGAN is a domain-specific graph attention network that treats leaf-level A–Ci curves as small graphs with nodes as measurement points and edges encoding local plant physiology.
• It leverages physiology-inspired auxiliary signals (sAc and sAj) as node features and computes edge attributes from their differences, enhancing classification near regime transitions.
• The model employs a multi-head attention mechanism with weighted cross-entropy loss, achieving superior F1 scores and accuracy compared to traditional fitting and baseline methods.

SEAGAN denotes the domain-Specific and Edge-Aware Graph Attention Network for Dynamic Plant Processes, introduced for node-wise classification of biochemical limitation states along leaf-level photosynthetic $A$–$C_i$ curves in C$_3$ plants (Srivastava et al., 17 Jun 2026). In this formulation, each curve is treated as a small graph whose nodes are measurement points and whose edges encode local relational structure in the $(C_i, A_\text{net})$ response space. The method addresses a specific bottleneck in $A$–$C_i$ analysis: assigning each measured point to the active limitation regime—Rubisco limitation, electron-transport limitation, or triose-phosphate utilization limitation—before downstream parameter estimation under the Farquhar–von Caemmerer–Berry (FvCB) framework (Srivastava et al., 17 Jun 2026).

1. Biochemical setting and problem formulation

The target object is the A–Ci curve, which relates net CO$_2$ assimilation rate $A_\text{net}$ to intercellular CO$_2$ concentration $C_i$. Under the FvCB model for C$C_i$0 photosynthesis, assimilation at a point is governed by the minimum of three candidate biochemical rates,

$C_i$1

where $C_i$2 is the Rubisco-limited rate, $C_i$3 is the RuBP-regeneration or electron-transport-limited rate, and $C_i$4 is the triose-phosphate utilization-limited rate (Srivastava et al., 17 Jun 2026).

For a typical A–Ci curve, low $C_i$5 is associated with $C_i$6 limitation, intermediate $C_i$7 with $C_i$8 limitation, and high $C_i$9, under certain parameter regimes, with $_3$0 limitation (Srivastava et al., 17 Jun 2026). The classification of each point into one of these limitation states is operationally important because FvCB parameter estimation for $_3$1, $_3$2, TPU, $_3$3, and $_3$4 depends on fitting the correct portion of the curve under the correct regime. The paper states that mislabeling points near regime transitions causes biased or non-identifiable parameter estimates (Srivastava et al., 17 Jun 2026).

The difficulty of this labeling problem arises from several factors explicitly identified in the study: regime transitions are blurred in noisy data, gas-exchange measurements are noisy and subject to experimental artifacts, the FvCB model is switch-like because it uses a $_3$5 operator, and some curves weakly express one limitation state—especially TPU—so the data may contain little direct evidence for that regime (Srivastava et al., 17 Jun 2026). Historically, practitioners have relied on heuristics or manual assignment, while automated fitting tools such as plantecophys, msuRACiFit, PhoTorch, and PhotoGEA attempt to infer limitation states and parameters jointly by numerical optimization. The paper’s motivation is that these approaches remain sensitive to regime misidentification and identifiability issues, and therefore a separate supervised learning formulation of limitation-state identification is warranted (Srivastava et al., 17 Jun 2026).

2. Graph representation of A–Ci curves

SEAGAN recasts each individual A–Ci curve as a graph $_3$6, with each measurement point represented as a node. Curve lengths are small and variable, with $_3$7–15 nodes per curve after subsampling (Srivastava et al., 17 Jun 2026). This graph construction is central rather than incidental: the paper’s stated key idea is to formulate limitation-state identification as a graph-based node classification problem so that local relational structure along the response curve can be exploited (Srivastava et al., 17 Jun 2026).

Each node $_3$8 is assigned a four-dimensional feature vector

$_3$9

where $(C_i, A_\text{net})$0 and $(C_i, A_\text{net})$1 are the raw gas-exchange observations and $(C_i, A_\text{net})$2, $(C_i, A_\text{net})$3 are physiology-inspired auxiliary signals derived from FvCB structure using $(C_i, A_\text{net})$4 in place of $(C_i, A_\text{net})$5 (Srivastava et al., 17 Jun 2026). The paper interprets these auxiliary quantities as effective capacities under Rubisco-like and electron-transport-like response factors. It further states that $(C_i, A_\text{net})$6 tends to increase mainly within the Rubisco-limited region, whereas $(C_i, A_\text{net})$7 increases through the $(C_i, A_\text{net})$8 and $(C_i, A_\text{net})$9 regions and then often flattens or declines as TPU limitation emerges (Srivastava et al., 17 Jun 2026). Because noise prevents their use as hard thresholds, they are treated as informative features rather than deterministic indicators.

Two graph connectivity schemes are defined. The first is a distance-based k-nearest-neighbor graph, which is the configuration used by SEAGAN. For each node, Euclidean distance is computed in the observed response space $A$0, the $A$1 nearest neighbors are selected, directed edges are created to these neighbors, and reverse edges are added to make the graph bidirectional (Srivastava et al., 17 Jun 2026). This produces a locally dense graph in which each node exchanges information with at least four neighbors close in the A–Ci plane; importantly, the points are deliberately shuffled so that node order does not trivially encode the curve trajectory (Srivastava et al., 17 Jun 2026).

The second scheme is the auxiliary-signal-guided (ASG) graph, used for comparison. In this construction, points are sorted by increasing $A$2, peaks are detected in the sorted auxiliary sequences, the curve is partitioned into three contiguous groups, nodes are fully connected within groups, and boundary edges are added between adjacent groups (Srivastava et al., 17 Jun 2026). The study reports that SEAGAN ultimately uses the simpler kNN connectivity because it is performance-superior in the attention-based setting (Srivastava et al., 17 Jun 2026).

For every directed edge $A$3, the edge attribute vector is defined as

$A$4

These attributes encode pairwise changes in the auxiliary signals and therefore provide information about local slopes and relative positions in limitation space (Srivastava et al., 17 Jun 2026). The reverse edge carries the negated attribute vector. This edge design is one of the paper’s principal domain-specific elements.

Ground-truth node labels are assigned directly from the synthetic FvCB generative model: class 0 corresponds to $A$5-limited, class 1 to $A$6-limited, and class 2 to $A$7-limited, with the label at each point determined by the index of the minimum among $A$8, $A$9, and $C_i$0 (Srivastava et al., 17 Jun 2026).

3. Architecture and domain-specific design

SEAGAN is identified in the paper as the best-performing configuration among the compared models. Architecturally, it is a Graph Attention Network (GAT) operating on the kNN graph with edge attributes and trained using weighted cross-entropy loss; in the code naming reported by the paper, it corresponds to GAT-kNN-$C_i$1 (Srivastava et al., 17 Jun 2026).

The base message-passing mechanism follows the standard multi-head GAT formulation. Let $C_i$2 denote the hidden representation of node $C_i$3 at layer $C_i$4, and let $C_i$5 be the number of attention heads. For intermediate layers,

$C_i$6

while in the final GAT layer the heads are averaged rather than concatenated (Srivastava et al., 17 Jun 2026). The nonlinear activation is tanh, batch normalization is applied after graph layers, and dropout with $C_i$7 is used for regularization (Srivastava et al., 17 Jun 2026). The number of layers $C_i$8 is not explicitly stated, but the paper notes that at least two layers are used because it distinguishes intermediate and final layers (Srivastava et al., 17 Jun 2026).

The attention mechanism is edge-aware. Although the paper does not provide an explicit symbolic expression for the attention coefficients $C_i$9, it states that the attention kernel receives the transformed target-node representation, the transformed neighbor representation, and the edge attribute $_2$0 (Srivastava et al., 17 Jun 2026). In consequence, the model can modulate neighborhood aggregation using both node states and pairwise physiological differences. The study interprets this as allowing the network to emphasize edges whose auxiliary-signal differences support a particular limitation regime, especially around ambiguous transition points (Srivastava et al., 17 Jun 2026).

After the final GAT layer, node embeddings are mapped to class logits through a linear classifier,

$_2$1

and prediction for node $_2$2 is obtained by

$_2$3

Softmax over $_2$4 yields class probabilities used for losses and interpretability analyses (Srivastava et al., 17 Jun 2026).

The paper explicitly locates the distinctiveness of SEAGAN not in a novel generic GAT backbone, but in its domain-specific representation design. Three elements are emphasized: physiology-aware node features through inclusion of $_2$5 and $_2$6, physiology-aware edge attributes defined from differences in those auxiliary signals, and physiology-aware connectivity built in the $_2$7 plane (Srivastava et al., 17 Jun 2026). The authors describe these design choices as what makes the GNN process-aware.

4. Training protocol and synthetic benchmark construction

The training objective used by SEAGAN is a weighted cross-entropy loss to compensate for imbalance among the three classes. The standard multi-class cross-entropy is modified by class weights $_2$8, computed from training class frequencies and inversely related to class prevalence, yielding

$_2$9

with $A_\text{net}$0 classes (Srivastava et al., 17 Jun 2026). The study also evaluates a weighted focal loss, but SEAGAN specifically uses $A_\text{net}$1 (Srivastava et al., 17 Jun 2026).

The dataset consists of 10,000 synthetic curves, each generated on a dense grid of 100 $A_\text{net}$2 points spanning 20 to 1000 ppm and then subsampled to 8–15 points to mimic real experiments (Srivastava et al., 17 Jun 2026). The subsampled points are shuffled so that increasing $A_\text{net}$3 order is not preserved (Srivastava et al., 17 Jun 2026). Parameter values at $A_\text{net}$4C are sampled by Latin Hypercube Sampling over the ranges stated in the paper: $A_\text{net}$5 from 20 to 150 $A_\text{net}$6mol m$A_\text{net}$7 s$A_\text{net}$8, $A_\text{net}$9 from 4 to 25 $_2$0mol m$_2$1 s$_2$2, $_2$3 from 0.5 to 5 $_2$4mol m$_2$5 s$_2$6, $_2$7 from 0.05 to 0.8 mol m$_2$8 s$_2$9, $C_i$0 from 1.5 to 2.5, and leaf temperature $C_i$1 from 25 to 35$C_i$2C (Srivastava et al., 17 Jun 2026). Environmental conditions are fixed at $C_i$3 kPa and O$C_i$4 $C_i$5 mbar (Srivastava et al., 17 Jun 2026). Temperature response functions for $C_i$6 are taken from Sharkey et al. and Bernacchi et al. (Srivastava et al., 17 Jun 2026).

To mimic measurement error, Gaussian noise is added to $C_i$7. The paper reports a mean curve-wise standard deviation of added noise of approximately 1.5 $C_i$8mol m$C_i$9 s$C_i$00, corresponding to a normalized noise magnitude of $C_i$01, or 10% of each curve’s original $C_i$02 variability (Srivastava et al., 17 Jun 2026). The authors characterize this level as introducing noticeable variability without dominating the signal.

Training, validation, and test splits are made at the curve level as 60%, 20%, and 20%, respectively, preventing leakage across splits (Srivastava et al., 17 Jun 2026). Node features and edge attributes are z-score standardized using the training-set mean and standard deviation. Optimization uses Adam with learning rate 0.001 and weight decay 0.0001; batches contain 128 curves; non-U-Net models are trained for 800–1000 epochs; and the best checkpoint is selected by validation macro-F1 rather than by classical early stopping (Srivastava et al., 17 Jun 2026). Each configuration is trained with 30 random initializations, and the resulting performance distributions are compared statistically using ANOVA and Tukey–HSD (Srivastava et al., 17 Jun 2026).

A methodological consequence of this setup is that SEAGAN is evaluated under conditions where ground-truth limitation states are fully known from the generative model. This suggests that the reported results isolate the regime-classification problem itself rather than confounding it with manual labeling inconsistencies.

5. Comparative evaluation and empirical performance

The study compares SEAGAN against feature-based baselines, graph baselines, and an automated fitting-based benchmark (Srivastava et al., 17 Jun 2026). The feature-based models are Random Forest, Support Vector Machine with polynomial or RBF kernels, XGBoost, and a feed-forward neural network. These models take flattened vectors of length $C_i$03 as inputs and produce $C_i$04 outputs, with a separate model trained for each curve length $C_i$05 (Srivastava et al., 17 Jun 2026). The graph baselines include GCN-kNN and Graph U-Net variants based on GCN or GAT with kNN or ASG connectivity and several loss functions (Srivastava et al., 17 Jun 2026). The fitting-based benchmark is PhoTorch, which is run on each noisy synthetic curve to fit FvCB parameters and then derive limitation-state labels from the fitted $C_i$06, $C_i$07, and $C_i$08 values (Srivastava et al., 17 Jun 2026).

The held-out test-set metrics reported in the paper are summarized below (Srivastava et al., 17 Jun 2026).

Model	F1	Accuracy
PhoTorch benchmark	0.735	0.751
Best feature-based NN baseline	0.713	0.766
Baseline GCN-kNN $C_i$09	0.722	0.778
Best GCN-U-Net-ASG $C_i$10	0.817	0.851
SEAGAN: GAT-kNN-$C_i$11	0.857	0.882

For SEAGAN specifically, the paper reports F1 = 0.857, recall = 0.861, precision = 0.853, and accuracy = 0.882 (Srivastava et al., 17 Jun 2026). Closely related GAT-kNN variants using unweighted cross-entropy or weighted focal loss perform similarly, with F1 values of 0.854 and 0.855, respectively (Srivastava et al., 17 Jun 2026). The Tukey–HSD analysis over 12 GNN models and 30 runs places the GAT-kNN variants in the top statistical groups, and the paper characterizes GAT-kNN-$C_i$12 as the best compromise between highest mean F1 and recall and robustness, with fewer low-performing outliers (Srivastava et al., 17 Jun 2026).

The paper also reports qualitative behavior near transition regions. Feature-based baselines often place the $C_i$13 transition too late and the $C_i$14 transition too early, and they can produce isolated mislabels inside otherwise homogeneous regions (Srivastava et al., 17 Jun 2026). GCN-kNN improves transition handling but still misclassifies some boundary points. In a representative example, PhoTorch shifts the $C_i$15 transition earlier than ground truth, whereas SEAGAN correctly recovers the transition node and assigns $C_i$16 versus $C_i$17 for that node (Srivastava et al., 17 Jun 2026). Even so, the paper notes that some $C_i$18 transitions remain difficult for all models, including SEAGAN and PhoTorch, especially when TPU limitation is weakly expressed (Srivastava et al., 17 Jun 2026).

Several comparative conclusions are drawn directly from the reported experiments. First, graph structure itself adds value, because GCN-kNN exceeds the SVM, XGBoost, and feed-forward NN baselines in F1 (Srivastava et al., 17 Jun 2026). Second, attention outperforms fixed graph convolution, as GAT variants substantially exceed GCN and GCN-U-Net variants (Srivastava et al., 17 Jun 2026). Third, kNN connectivity outperforms ASG connectivity in GAT models by several points in F1 and accuracy, with statistically significant differences (Srivastava et al., 17 Jun 2026). Fourth, hierarchical pooling improves GCN but does not improve plain GAT-kNN, which the paper plausibly attributes to the small size of the graphs and the local nature of the discriminative information (Srivastava et al., 17 Jun 2026).

6. Interpretability, physiological significance, and limitations

Interpretability analysis is performed with GNNExplainer, which is used to identify influential edges for a given node prediction and to perform edge ablation by perturbing those edges and measuring probability changes, particularly $C_i$19 around transition nodes (Srivastava et al., 17 Jun 2026). For the GCN baseline, the important edges associated with a transition node tend to support the wrong class and are less focused on physiologically relevant neighbors (Srivastava et al., 17 Jun 2026). For GAT-kNN, the important edges connect the ambiguous node to neighbors on both sides of the $C_i$20 boundary, and ablating those edges reduces the probability of the correct class, indicating that they positively support correct classification (Srivastava et al., 17 Jun 2026). GAT-ASG also improves over GCN but relies more on self or within-group connections and provides less robust cross-regime information than GAT-kNN (Srivastava et al., 17 Jun 2026).

The paper interprets these findings physiologically. SEAGAN appears to learn that transitions are best resolved by comparing ambiguous points with nearby points across regimes, and the kNN graph supplies those cross-boundary neighbors while the edge attributes describe differences in the auxiliary signals $C_i$21 and $C_i$22 (Srivastava et al., 17 Jun 2026). The resulting predictions better preserve contiguous regions corresponding to each limitation state, which the authors connect to the physical expectation that biochemical regimes change smoothly along the response trajectory rather than through isolated jumps (Srivastava et al., 17 Jun 2026).

An important misconception addressed by the study is that SEAGAN is not a replacement for biochemical parameter estimation. The authors explicitly frame it as a regime-classification model rather than a direct estimator of $C_i$23, $C_i$24, TPU, $C_i$25, or $C_i$26 (Srivastava et al., 17 Jun 2026). A plausible implication is that its main value lies in decoupling classification from fitting, thereby providing a cleaner upstream signal for downstream parameter inference.

The paper also enumerates several limitations. Validation is conducted only on synthetic curves, so generalization to real experimental A–Ci data, with different noise patterns, species, measurement protocols, or systematic biases, remains untested (Srivastava et al., 17 Jun 2026). The graphs are small, and no scalability experiments are reported beyond the 8–15 node regime (Srivastava et al., 17 Jun 2026). Transition ambiguity persists, especially for weakly expressed TPU limitation (Srivastava et al., 17 Jun 2026). Graph construction assumptions may also matter: kNN in $C_i$27 space may not be optimal under heavy noise or unusual sampling, and ASG connectivity depends on peak detection in auxiliary signals, which may be noise-sensitive (Srivastava et al., 17 Jun 2026).

Within those bounds, the authors position SEAGAN as a pre-fitting component for automated photosynthesis analysis pipelines. They suggest that fitting tools such as PhoTorch, PhotoGEA, and plantecophys could use SEAGAN predictions to restrict fitting to regime-appropriate points, constrain transition locations, or initialize or regularize change-point models (Srivastava et al., 17 Jun 2026). The paper further proposes that the general methodology—graph representation of response trajectories with process-aware features and edge attributes—may extend to other dynamic plant processes, including stomatal responses to VPD, light-response curves, and chlorophyll fluorescence kinetics (Srivastava et al., 17 Jun 2026). This suggests a broader research program in which small graphs encode local structure in physiological trajectories and edge-aware attention is used to resolve latent process states.