A Hybrid Modeling Framework for Crop Prediction Tasks via Dynamic Parameter Calibration and Multi-Task Learning

William Solow; Paola Pesantez-Cabrera; Markus Keller; Lav Khot; Sandhya Saisubramanian; Alan Fern

cs.AIMar 16, 2026

A Hybrid Modeling Framework for Crop Prediction Tasks via Dynamic Parameter Calibration and Multi-Task Learning

Authors: William Solow, Paola Pesantez-Cabrera, Markus Keller, Lav Khot, Sandhya Saisubramanian, Alan Fern

Organizations: Oregon State University · Washington State University

Abstract

Accurate prediction of crop states (e.g., phenology stages and cold hardiness) is essential for timely farm management decisions such as irrigation, fertilization, and canopy management to optimize crop yield and quality. While traditional biophysical models can be used for season-long predictions, they lack the precision required for site-specific management. Deep learning methods are a compelling alternative, but can produce biologically unrealistic predictions and require large-scale data. We propose a hybrid modeling approach that uses a neural network to parameterize a differentiable biophysical model and leverages multi-task learning for efficient data sharing across crop cultivars in data limited settings. By predicting the parameters of the biophysical model, our approach improves the prediction accuracy while preserving biological realism. Empirical evaluation using real-world and synthetic datasets demonstrates that our method improves prediction accuracy by 60% for phenology and 40% for cold hardiness compared to deployed biophysical models.

Figures & tables

Figure 1: Overview of our proposed method using phenology prediction as an example. In this case, seasonal phenological stages guide vineyard management operations. Our Dynamic Model Calibration via Multi-Task Learning (DMC-MTL) approach uses a pretrained neural network and biophsyical model to produce high fidelity and biologically realistic phenology state forecasts. The pretrained RNN produces daily parameter predictions (Base Temperature, Temperature Sum for Bud Break, etc.) of the Growing Degree Day (GDD) phenology model which handles the daily stage prediction.

Modeling Approach	Biologically Realistic	Exogenous Features	Temporal Info.
Biophysical Model	✓	✗	✗
Deep Learning	✗	✓	✓
PINN	Sometimes	✓	✓
Residual	Sometimes	✓	✓
Process Replacement	✓	✗	✗
DMC-MTL (Ours)	✓	✓	✓

Table 1: Modeling approaches for crop state forecasting tasks evaluated along different desiderata. PINN, Residual, Process Replacement, and DMC-MTL are all hybrid models. Biologically realistic means the model predictions reflect biological laws. Exogenous features means that the model output can be conditioned on additional weather features. Temporal info. indicates that the model can leverage historical input in addition to what the biophysical model uses.

Figure 2: The network architecture of our approach DMC-MTL. The multi-task RNN (

\mathcal{F}_{\theta}

) sequentially embeds cultivar i.d.

i

and concatenates it with the daily weather features

W_{t}

to predict a parameterization

\omega_{t}

of the biophysical model

\mathcal{M}

. Using the weather input to the biophysical model

W_{t}^{\prime}

and the daily parameterization

\omega_{t}

, crop state forecasts

Y_{t}^{\prime}\ldots Y_{t+k}^{\prime}

can be generated.

Figure 3: In-Season Adaptation with DMC-MTL. Cultivar i.d. $i$ and error between observed and DMC-MTL predicted crop states are passed to the EEN. The parameters predicted by the EEN are combined additively to the prediction made by DMC-MTL’s pretrained RNN before parameterizing the biophysical model.

	Solution Approaches	Grape Phenology	Grape Cold Hardiness
Q1a:	DMC-MTL (Ours)	7.63 $\pm$ 3.56	1.21 $\pm$ 0.39
	Bio. Model (Deployed)	18.58 $\pm$ 5.03 ∗	2.03 $\pm$ 0.39 ∗
	Bio. Model (Gradient Descent)	12.21 $\pm$ 5.13 ∗	1.88 $\pm$ 0.42 ∗
	Deep-MTL	8.16 $\pm$ 4.20 ∗	1.30 $\pm$ 0.46
	TempHybrid	9.84 $\pm$ 4.35 ∗	3.45 $\pm$ 0.98 ∗
	PINN	8.61 $\pm$ 4.32 ∗	1.30 $\pm$ 0.43

Table 2: The average seasonal error (RMSE in days for phenology and

{}^{\circ}C

for cold hardiness) over all cultivars and five seeds in the testing set for grape phenology and cold hardiness. DMC-MTL is compared against two optimization procedures for the biophysical model, a deep learning approach, three hybrid models, and two DMC variants. Best-in-class results are reported in bold. A ∗ indicates that DMC-MTL yields a statistically significant improvement (

p<0.05

) using the paired t-test relative to the corresponding baseline.

Figure 4: DMC-MTL, Classification, and Regression model predictions for (a) grape phenology and (b) grape cold hardiness. DMC-MTL makes biologically realistic predictions while deep learning model predictions do not always respect biologicaly laws.

Figure 5: The performance of DMC-MTL models compared to deep learning and biophysical models under limited per-cultivar training data for grape phenology (Pheno) and cold hardiness (CH). Results are averaged over five seeds using the same two-seasons-per-cultivar evaluation sets.

Figure 6: Performance of the base DMC-MTL with increasing per-cultivar data compared to the performance of the DMC-MTL with the additional in-season adaptation training for grape phenology (Pheno) and cold hardiness (CH). Results averaged over five seeds.

	Phenology				cold hardiness
Approach	WA (Train Loc.)	VT	CA	OR	WA (Train Loc.)	VT	CA	OR
DMC-MTL	5.9 $\pm$ 2.7	8.8 $\pm$ 5.6	30.4 $\pm$ 9.3	17.7 $\pm$ 0.5	0.42 $\pm$ 0.28	0.76 $\pm$ 0.31	1.37 $\pm$ 0.16	3.59 $\pm$ 0.24
Deep-MTL	6.1 $\pm$ 3.0	96.2 $\pm$ 10.8	120. $\pm$ 1.4	78.0 $\pm$ 1.9	0.34 $\pm$ 0.22	5.98 $\pm$ 1.57	6.01 $\pm$ 0.07	3.73 $\pm$ 0.46
PINN	5.3 $\pm$ 2.9	60.5 $\pm$ 14.2	59.8 $\pm$ 1.3	58.4 $\pm$ 3.9	0.39 $\pm$ 0.23	4.86 $\pm$ 1.41	8.38 $\pm$ 0.25	4.02 $\pm$ 0.40
TempHybrid	6.4 $\pm$ 5.2	97.3 $\pm$ 16.2	118. $\pm$ 20.	83.0 $\pm$ 18.	4.25 $\pm$ 0.98	5.60 $\pm$ 0.98	8.57 $\pm$ 1.14	6.43 $\pm$ 1.33

Table 3: RMSE (days and

{}^{\circ}C

) for grape phenology and cold hardiness respectively, evaluated on unseen data sampled from the training location (WA) and from locations with a moderately similar weather (Vermont, California, and Oregon). Results averaged over five seeds.

Figure 7: Percentage of all cultivars with cumulative error below a given RMSE threshold modeling a grape grower’s tolerance for model prediction error. Results are reported over five seeds for (a) phenology and (b) cold hardiness.

Figure 8: Screenshot of the publicly accessible user interface on AgWeatherNet. The weather station-specific phenology forecasts during the 2025 season for the Cabernet Sauvignon cultivar of the Zapata (GDD-based biophysical model) are compared with the hybrid (DMC-MTL) model.

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

	Parameter Name	Parameter Description	Unit	Min Value	Max Value
GDD Model	TBASEM	Base Temperature ( $T_{b}$ )	${}^{\circ}C$	0	15
	TEFFMX	Maximum Effective Temperature ( $T_{m}$ )	${}^{\circ}C$	15	45
	TSUMEM	Temperature Sum for Bud Break	${}^{\circ}C$	10	100
	TSUM1	Temperature Sum for Bud Break	${}^{\circ}C$	100	1000
	TSUM2	Temperature Sum for Bloom	${}^{\circ}C$	100	1000
	TSUM3	Temperature Sum for Veraison	${}^{\circ}C$	100	1000

Appendix

Table 4: The parameters of the GDD Model, Ferguson Model, and WOFOST model used in the DMC-MTL approach. The ranges correspond to the minimum and maximum values that the parameter can be after

\tanh

activation normalizing from the range

[-1,1]

Figure 9: Daily crop state observations for five cultivars of (a) grape phenology and (b) grape cold-hardiness during a single growing season. Modeling approaches must predict these curves with biologically consistency. Despite experiencing the same weather, cultivars exhibit different behaviors, making naive data aggregation inadequate and motivating the use of a multi-task approach.

Cultivar	Years of Pheno. Data	Years of LTE Data	Total LTE Samples
Aligote	9	2	20
Alvarinho	9	10	120
Auxerrois	9	8	101
Barbera	8	11	130
Cabernet Franc	17	3	28
Cabernet Sauvignon	18	27	629

Appendix

Table 5: Summary of real-world grapevine cultivar phenology and cold-hardiness observations collected from Washington State University in Prosser, WA.

Models	Hidden Size	Learning Rate	Batch Size	Learning Rate Anneal
DMC-MTL	1024	0.0001	12	0.9
DMC-STL	1024	0.005	4	0.9
RNN	2048	0.0001	12	0.9
PINN	2048	0.0001	12	0.9
TempHybrid	64	0.02	4	0.9
Gradient Descent	N/A	0.1	4	0.9

Appendix

Table 6: Best hyperparameters found for each model type after five-fold cross validation on the entire grape phenology dataset.

	Solution Approaches	Synthetic Wheat Yield
Q1a:	DMC-MTL (Ours)	10.63 $\pm$ 7.39
	Gradient Descent	12.69 $\pm$ 10.7 ∗
	Deep-MTL	31.63 $\pm$ 16.8 ∗
	PINN	36.56 $\pm$ 18.8 ∗
	Residual Hybrid	14.11 $\pm$ 10.9 ∗
Q1b:	DMC-STL	15.46 $\pm$ 17.1 ∗

Appendix

Table 7: The average seasonal error (RMSE in

kg/ha

for wheat yield) over all ten cultivars and five seeds in the testing set. DMC-MTL is compared against gradient descent on the biophysical model, a deep learning approach, two hybrid models, and five DMC variants. Best-in-class results are reported in bold. A ∗ indicates that DMC-MTL yields a statistically significant improvement (

p<0.05

) using the paired t-test relative to the corresponding baseline.

	Phenology	Cold-Hardiness
% Improve	84%	100%
Avg. Increase	2.41 $\pm$ 1.88	0.37 $\pm$ 0.15
Avg. Decrease	0.51 $\pm$ 0.28	0.00 $\pm$ 0.00

Appendix

Table 8: Comparison of DMC-MTL vs DMC-STL on a per-cultivar basis with the percentage of cultivars that saw a reduction in error from DMC-STL to DMC-MTL along with the average reduction in error (RMSE in days for phenology,

{}^{\circ}C

for cold-hardiness) and the average increase in error for cultivars where accuracy worsened.

Figure 10: The distribution of per-stage prediction error (RMSE in days) of the DMC-MTL model and GDD model. Additionally, DMC-MTL-SS models were trained to minimize per-stage error (as opposed to cumulative stage error).

Figure 11: The performance of DMC-MTL with decreased parameter smoothing. Results are averaged over five seeds

Figure 12: The performance of DMC-MTL with a sliding weather window. Results are averaged over five seeds.

Figure 13: The integrated gradients values of the Base Temperature Sum parameter prediction for the 2024 growing season of the Chardonnay cultivar. Red values indicate positive attribution and blue values indicate negative attribution.

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Calibrating Biophysical Models for Grape Phenology Prediction via Multi-Task Learning

William Solow, Sandhya Saisubramanian

Oregon State University

Multi-Task Learning Model Calibration

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Accurate prediction of grape phenology is essential for timely vineyard management decisions, such as scheduling irrigation and fertilization, to maximize crop yield and quality. While traditional biophysical models calibrated on historical field data can be used for season-long predictions, they lack the precision required for fine-grained vineyard management. Deep learning methods are a compelling alternative but their performance is hindered by sparse phenology datasets, particularly at the cultivar level. We propose a hybrid modeling approach that combines multi-task learning with a recurrent neural network to parameterize a differentiable biophysical model. By using multi-task learning to predict the parameters of the biophysical model, our approach enables shared learning across cultivars while preserving biological structure, thereby improving the robustness and accuracy of predictions. Empirical evaluation using real-world and synthetic datasets demonstrates that our method significantly outperforms both conventional biophysical models and baseline deep learning approaches in predicting phenological stages, as well as other crop state variables such as cold-hardiness and wheat yield.

Abstract

Precision Agriculture

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