A hybrid deep learning approach for winter wheat yield prediction: evidence from leveraging multi-source data

We acknowledge the contribution of Prof. Shan Balasubramaniam for the conceptual framework of the paper.

Authors and Affiliations

1. Department of Economics and Finance, BITS Pilani K K Birla Goa Campus, Goa, India

   Manogna R. L, Shaanil Punglia & Siddhant Tushar Joshi

Corresponding author

Correspondence to
Manogna R. L.

Competing interests

The authors declare no competing interests.

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Appendix A: List of Features

A.1 Meteorological variables

The following variables were collected from the NASA POWER API at daily temporal resolution and 0.5(^{circ }) (times) 0.625(^{circ }) spatial resolution:

1. 1.

   Precipitation (PRECTOTCORR)

2. 2.

   Maximum Temperature (T2M_MAX)

3. 3.

   Minimum Temperature (T2M_MIN)

4. 4.

   Average Temperature (T2M)

5. 5.

   Relative Humidity (RH2M)

6. 6.

   Solar Radiation (ALLSKY_SFC_SW_DWN)

7. 7.

   Wind Speed at 10 meters (WS10M)

8. 8.

   Specific Humidity (QV2M)

9. 9.

   Surface Pressure (PS)

Maximum and minimum vapor pressure deficit (max_vpd and min_vpd) were derived from the NASA POWER temperature and relative humidity variables as:

A.2 Soil properties

The following soil properties were obtained from the ISRIC SoilGrids250m Web Coverage Service at six standard depths (0-5 cm, 5-15 cm, 15-30 cm, 30-60 cm, 60-100 cm, and 100-200 cm) with 250 m spatial resolution:

1. 1.

   Soil Organic Carbon

2. 2.

   Soil pH

3. 3.

   Bulk Density

4. 4.

   Sand Content

5. 5.

   Silt Content

6. 6.

   Clay Content

7. 7.

   Cation Exchange Capacity

8. 8.

   Total Nitrogen

Appendix B: Hyperparameter search space and proposed-model configuration

B.1 Hyperparameter search space

Key hyperparameters and their search spaces for Bayesian optimization (Optuna with TPE sampler):

• Learning Rate: Log uniform from 1e-5 to 1e-2

• Number of BiLSTM Layers: Integer from 1 to 5

• BiLSTM Hidden Cells: Integer from 32 to 128

• CNN Kernel Size: Integer from 2 to 5

• CNN Output Channels: Integer from 8 to 64

• Number of MLP Layers: Integer from 3 to 7

• Width of MLP Layers: Integer from 16 to 256

• Dropout Rate: Float from 0.1 to 0.5

B.2 Best hyperparameters — proposed CNN-BiLSTM-attention model

The optimal hyperparameter configuration obtained from Bayesian optimization for the proposed CNN-BiLSTM with self-attention model is summarized in Table 8. The corresponding configuration files for each benchmarked baseline (1D-CNN, LSTM, BiLSTM, Transformer encoder, Parallel CNN-LSTM-Attn, XGBoost, and LightGBM) are catalogued separately in Appendix C.

Appendix C: Baseline architectures and best hyperparameters

This appendix catalogues the architectural specification and the best-hyperparameter values for every benchmarked baseline reported in Table 2. All baselines were optimised with Optuna using the TPE sampler and trained with the L2/MSE loss; the values reported below correspond to the configuration that minimised validation MSE.

C.1 Per-baseline diagnostic plots

The aggregate metrics in Table 2 are complemented by two per-baseline diagnostic panels that expose error structure the summary statistics alone obscure. Figure 12 plots predicted-versus-observed yields on the held-out 2022–2023 test set, revealing each model’s bias, dispersion, and tail behaviour against the 1:1 line, while Figure 13 maps district-level residuals for the 2023 sowing year to surface any regional patterns of over- or under-prediction. Both figures share the Table 2 ordering (best-to-worst on MAE) to allow direct cross-reference.

C.2 1D-CNN

A two-block 1D convolutional encoder along the temporal axis of the meteorological/RS sequence^14,15. Each block applies Conv1D(kernel=3, padding=same) (rightarrow) BatchNorm1d (rightarrow) ReLU; the second block is followed by an AdaptiveMaxPool1d(1) that collapses the time dimension. The pooled vector is concatenated with the flattened 48-D soil vector and the lagged yield scalar before entering the MLP head. Best-configuration values are reported in Table 9.

C.3 LSTM

A three-layer unidirectional LSTM following the winter-wheat yield-prediction formulation of Wang et al.²⁶ processes the 11-month temporal sequence; the final hidden state passes through layer normalisation and is concatenated with the flattened 48-D soil vector and the lagged yield scalar before entering the MLP head. Best-configuration values are reported in Table 10.

C.4 BiLSTM

A bidirectional variant of C.3 in which forward and backward LSTM streams are concatenated at each time step before fusion with the flattened soil vector and the lagged yield. Best-configuration values are reported in Table 11.

C.5 Transformer encoder

A vanilla nn.TransformerEncoder stack with a learnable additive positional embedding over the 11-month sequence, applied to a per-month projection of the 13-D temporal input vector. We adopt the simplified single-stream encoder formulation of Guo et al.²⁹ (the SLTF method’s transformer core, without the auxiliary LSTM/SSA components); the encoded sequence is mean-pooled across months and concatenated with the flattened 48-D soil vector and the lagged yield scalar before entering the MLP head. Best-configuration values are reported in Table 12.

C.6 Parallel CNN-LSTM-attention (TPCLA)

A two-branch parallel architecture re-implementing the temporal core of Song et al.¹⁷. The temporal stream is routed through both a 1D-CNN branch (two Conv1D blocks with adaptive max-pooling) and a stacked LSTM branch (whose hidden states are summarised by a Bahdanau additive attention module); the two branch outputs are concatenated with the flattened 48-D soil vector and the lagged yield scalar before entering the MLP head. The cross-regional transfer-learning component of TPCLA is not applicable in our single-domain setting and is therefore omitted. Best-configuration values are reported in Table 13.

C.7 Tree-based baselines: XGBoost, LightGBM, and random forest

The tree-based baselines were fitted on the flattened feature matrix, comprising 143 temporal columns (13 features (times) 11 months), 48 flattened soil columns, and the lagged yield scalar. Best-configuration values for XGBoost are reported in Table 14.

A leaf-wise LightGBM regressor was fitted on the same flattened feature matrix. Best-configuration values are reported in Table 15.

Finally, the best-configuration values for the Random Forest baseline are reported in Table 16.

Appendix D: Yield distribution and class imbalance

Because yield prediction is a regression task, conventional classification-style mitigations for class imbalance (e.g. SMOTE, inverse-frequency class weights) do not directly apply. We nonetheless characterise the empirical distribution of the training-set target here to verify that no district or year dominates and that the assumptions of the squared-error loss are not violated by extreme tails.

Figure 14 shows a histogram of the per-sample winter-wheat yield in the training split (4368 district-year observations spanning 2001–2018). The distribution is approximately unimodal with a mild right skew, peaks in the 2500–3500 kg/ha range, and exhibits a long tail of higher-yield observations from intensively managed Punjab and Haryana districts. The complementary breakdown into ordinal yield bins across the train, validation, and test splits is reported in Table 5 (Section Final Model Evaluation and Limitations); that table makes explicit that the test split is skewed toward high-yield observations, which underlies the regression-to-the-mean residual pattern discussed in Section Final Model Evaluation and Limitations.

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