光合响应模型与理论指导的神经网络融合的多因素光合速率预测模型

doi:10.17521/cjpe.2024.0288

植物生态学报 ›› 2026, Vol. 50 ›› Issue (1): 173-187.DOI: 10.17521/cjpe.2024.0288

光合响应模型与理论指导的神经网络融合的多因素光合速率预测模型

苏晨飞¹^,^*, 田慰²^,¹^,^*, 张楠³^,¹, 唐龙¹^,^**(), 赵宇玮⁴, 王耀¹

¹ 西安交通大学人居环境与建筑工程学院, 西安 710049
² 西安交通大学能源与动力工程学院, 西安 710049
³ 西安交通大学电气工程学院, 西安 710049
⁴ 西北大学生命科学学院, 西安 710069

收稿日期:2024-08-23 接受日期:2025-01-09 出版日期:2026-01-20 发布日期:2026-02-13
通讯作者: **唐龙(tanglong@mail.xjtu.edu.cn)
作者简介:第一联系人：
*同等贡献
基金资助:
国家自然科学基金(31872032);国家自然科学基金(31670548)

Multi-factor photosynthetic rate prediction model by fusion of photosynthetic response model and theory-guided neural network

SU Chen-Fei¹^,^*, TIAN Wei²^,¹^,^*, ZHANG Nan³^,¹, TANG Long¹^,^**(), ZHAO Yu-Wei⁴, WANG Yao¹

¹ School of Human Settlements and Civil Engineering, Xi’an Jiaotong University, Xi’an 710049, China
² School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an 710049, China
³ School of Electrical Engineering, Xi’an Jiaotong University, Xi’an 710049, China
⁴ College of Life Sciences, Northwest University, Xi’an 710069, China

Received:2024-08-23 Accepted:2025-01-09 Online:2026-01-20 Published:2026-02-13
Contact: **TANG Long (tanglong@mail.xjtu.edu.cn)
About author:First author contact:
*Contributed equally to this work
Supported by:
National Natural Science Foundation of China(31872032);National Natural Science Foundation of China(31670548)

摘要/Abstract

摘要：

近年来, 由于温室气体的大量排放, 极端天气事件的频发已对植物光合作用产生显著影响。光合作用不仅直接关系到植物的生长发育, 其光合速率更是评估植物健康状况与预测未来全球碳循环动态的关键指标。此外, 净光合速率还是设施农业环境调控中的重要参数。因此, 准确预测植物光合速率对农业、林业和草业的科学发展具有重要意义。该研究首先使用光合测量仪获取不同环境下芦苇(Phragmites australis)和互花米草(Spartina alterniflora)的光合数据, 随后拟合了7种单因素光合响应模型, 并基于理论指导的神经网络(TgNN)建立了多因素光合速率预测模型。研究结果表明, 现有的单因素光合响应模型虽取得不错的拟合效果, 但其理论研究的价值有限; 而基于TgNN建立的多因素光合速率预测模型展现了较好的预测能力和泛化能力。该研究为构建准确、可靠的植物光合速率预测模型提供了一种新的方法和思路。

关键词: 光合预测模型, 神经网络, 光合响应模型, 灰箱模型

Abstract:

Aims In recent years, the ever increasing greenhouse gas (GHG) emissions and extreme weather events had significantly impacted plant photosynthesis. Photosynthesis is closely related to plant growth and development, with photosynthetic rate is a key indicator of plant health, which has been widely used in predicting global carbon cycle dynamics. The net photosynthesis rate is also an important parameter in calibrating agriculture facility. Therefore, accurate prediction of plant photosynthesis rate is important to agriculture, forestry and grassland research.

Methods We used photosynthesis meter to obtain photosynthetic data of common reed (Phragmites australis) and smooth cordgrass (Spartina alterniflora) under different environmental conditions, we then fitted seven single-factor photosynthetic response models, and developed multifactorial photosynthetic rate prediction model using theory-guided neural network (TgNN).

Important findings All existing single-factor photosynthetic response models show good performances in fitting photosynthetic data but lack theoretical research value; whereas the multifactor photosynthetic model based on TgNN shows good predictability and generality. Our contribution provides a new avenue for calibrating more accurate and reliable models for predicting plant photosynthetic rate.

Key words: photosynthetic prediction model, neural network, photosynthetic response model, grey box model

苏晨飞, 田慰, 张楠, 唐龙, 赵宇玮, 王耀. 光合响应模型与理论指导的神经网络融合的多因素光合速率预测模型. 植物生态学报, 2026, 50(1): 173-187. DOI: 10.17521/cjpe.2024.0288

SU Chen-Fei, TIAN Wei, ZHANG Nan, TANG Long, ZHAO Yu-Wei, WANG Yao. Multi-factor photosynthetic rate prediction model by fusion of photosynthetic response model and theory-guided neural network. Chinese Journal of Plant Ecology, 2026, 50(1): 173-187. DOI: 10.17521/cjpe.2024.0288

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链接本文: https://www.plant-ecology.com/CN/10.17521/cjpe.2024.0288

https://www.plant-ecology.com/CN/Y2026/V50/I1/173

图/表 18

图1 多因素光合速率预测模型建模流程。A, 净光合速率; Amin, 最小净光合速率; Amax, 最大净光合速率; E, 蒸腾速率; WUE, 水分利用效率; X, 芦苇和互花米草的光合数据; Ŷ, 神经网络的输出。

Fig. 1 Modeling process for multifactorial photosynthetic rate prediction model. A, net photosynthetic rate; Amin, minimum net photosynthetic rate; Amax, maximum net photosynthetic rate; E, transpiration rate; WUE, water use efficiency; X, photosynthesis data for Phragmites australis and Spartina alterniflora; Ŷ, the output of the neural network.

表1 芦苇光响应曲线模型参数平均值

Table 1 Mean values of model parameters for Phragmites australis light response curve

模型 Model	叶片温度 T_leaf (℃)	初始斜率 α	最大净光合速率 A_max (µmol·m^-2·s^-1)	光补偿点 I_c (µmol·m^-2·s^-1)	暗呼吸速率 R_d (µmol·m^-2·s^-1)	模型拟合的决定系数 R²
直角双曲线模型 Rectangular hyperbola model	20	0.055 4	76.109 1	108.260 3	5.561 6	0.983 7
	25	0.049 4	81.143 2	62.736 8	2.985 4	0.989 0
	30	0.059 2	78.160 6	97.101 2	5.355 6	0.975 6
	35	0.059 5	77.629 1	100.994 0	5.574 3	0.976 0
	40	0.054 0	76.456 4	98.070 3	4.952 9	0.983 6
非直角双曲线模型 Non-rectangular hyperbolic model	20	0.033 0	43.819 3	70.154 9	2.314 6	0.989 6
	25	0.035 7	52.939 4	29.800 2	1.060 3	0.990 2
	30	0.031 0	39.988 4	33.141 6	1.028 4	0.992 7
	35	0.031 9	41.794 3	45.647 5	1.460 1	0.990 5
	40	0.036 4	53.005 1	59.875 5	2.174 3	0.985 1
直角双曲线修正模型 Modified model of rectangular hyperbola	20	0.040 2	37.973 3	91.036 5	3.584 2	0.988 6
	25	0.040 5	42.891 8	43.780 7	1.747 9	0.989 8
	30	0.043 6	39.648 7	86.064 3	3.670 5	0.986 9
	35	0.043 5	39.269 2	88.745 7	3.775 4	0.985 7
	40	0.039 5	38.420 6	77.286 2	2.992 2	0.987 6
指数模型 Exponential Model	20	0.044 2	47.011 6	25.302 6	1.103 9	0.985 8
	25	0.042 2	51.911 4	25.027 3	1.045 1	0.989 6
	30	0.047 7	48.645 4	23.276 0	1.098 4	0.979 4
	35	0.047 5	48.226 8	23.476 4	1.102 8	0.979 6
	40	0.043 6	47.714 3	25.250 0	1.089 4	0.985 4

表2 互花米草光响应曲线模型参数平均值

Table 2 Mean values of model parameters for Spartina alterniflora light response curve

模型 Model	叶片温度 T_leaf (℃)	初始斜率 α	最大净光合速率 A_max (µmol·m^-2·s^-1)	光补偿点 I_c (µmol·m^-2·s^-1)		暗呼吸速率 R_d (µmol·m^-2·s^-1)	模型拟合的决定系数 R²
直角双曲线模型 Rectangular hyperbola model	20	0.094 3	61.488 0	107.877 6		8.732 0	0.962 2
	25	0.089 3	68.372 4	120.464 5		9.298 3	0.966 2
	30	0.102 7	66.953 5	107.877 5		9.508 1	0.961 5
	35	0.104 8	68.320 1	107.877 6		9.702 2	0.960 3
	40	0.096 4	62.854 3	107.877 5		8.926 0	0.961 1
非直角双曲线模型 Non-rectangular hyperbolic model	20	0.092 9	61.667 2	107.155 9		8.568 8	0.962 2
	25	0.042 4	39.048 8	103.921 2		4.400 1	0.992 7
	30	0.045 6	39.765 2	84.978 2		3.864 5	0.989 3
	35	0.046 5	40.576 8	84.978 5		3.943 4	0.989 4
	40	0.042 8	37.330 6	84.978 1		3.627 9	0.988 9
直角双曲线修正模型 Modified model of rectangular hyperbola	20	0.055 4	32.908 7	97.673 4		5.216 4	0.980 8
	25	0.058 1	34.590 9	120.743 9		6.720 5	0.984 6
	30	0.060 3	35.833 9	97.673 3		5.680 0	0.981 1
	35	0.061 6	36.565 2	97.673 5		5.796 0	0.981 3
	40	0.056 6	33.640 0	97.673 3		5.332 3	0.980 2
指数模型 Exponential model	20	0.063 4	37.039 3	19.380 2		1.207 8	0.971 5
	25	0.062 3	40.246 5	19.741 8		1.212 0	0.974 2
	30	0.069 0	40.331 7	17.773 8		1.207 8	0.972 3
	35	0.061 6	36.565 2	97.673 5		5.796 0	0.980 8
	40	0.064 8	37.862 4	18.952 0		1.207 8	0.978 8
	40	0.043 6	47.714 3	25.250 0	1.089 4		0.985 4

图2 不同温度下芦苇光响应模型参数差异分析。

Fig. 2 Analysis of differences in model parameters of Phragmites australis light response at different temperatures. Amax, maximum net photosynthetic rate; Ic, light compensation point; Rd, dark respiration rate; Tleaf, leaf temperature.

图3 芦苇的4种光响应模型线性回归分析。A, 直角双曲线模型。B, 非直角双曲线模型。C, 指数模型。D, 直角双曲线修正模型。

Fig. 3 Linear regression analysis of four light response models for Phragmites australis. A, Rectangular hyperbola model. B, Non-rectangular hyperbolic model. C, Exponential model. D, Modified model of rectangular hyperbola.

图4 不同温度下互花米草光响应模型参数差异分析。

Fig. 4 Analysis of differences in model parameters of light response of Spartina alterniflora at different temperatures. Amax, maximum net photosynthetic rate; Ic, light compensation point; Rd, dark respiration rate; Tleaf, leaf temperature.

图5 互花米草的4种光响应模型线性回归分析。A, 直角双曲线模型。B, 非直角双曲线模型。C, 指数模型。D, 直角双曲线修正模型。

Fig. 5 Linear regression analysis of four light response models for Spartina alterniflora. A, Rectangular hyperbola model. B, Non-rectangular hyperbolic model. C, Exponential model. D, Modified model of rectangular hyperbola.

表3 芦苇CO2响应模型参数平均值

Table 3 Mean values of Phragmites australis CO2 response model parameters

模型 Model	叶片温度 T_leaf (℃)	初始斜率 α	最大净光合速率 A_max (µmol·m^-2·s^-1)	CO₂补偿点 $\Gamma *$(µmol·m^-2·s^-1)	光呼吸速率 R_p (µmol·m^-2·s^-1)	模型拟合的决定系数 R²
直角双曲线模型 Rectangular hyperbola model	20	0.183 2	119.943 6	106.343 3	16.737 4	0.998 5
	25	0.193 8	116.599 2	74.536 9	12.861 2	0.996 1
	30	0.207 5	115.981 9	77.440 0	14.119 1	0.993 7
	35	0.230 9	113.510 7	99.638 3	19.009 4	0.983 6
	40	0.202 5	111.775 0	101.130 7	17.300 0	0.998 8
Michaelis-Menten模型 Michaelis-Menten model	20	-	119.943 6	106.343 3	16.737 4	0.998 5
	25	-	116.599 2	74.536 9	12.861 2	0.996 1
	30	-	115.981 9	77.440 0	14.119 1	0.993 7
	35	-	113.510 7	99.638 3	19.009 4	0.983 6
	40	-	111.775 0	101.130 7	17.300 0	0.998 8
直角双曲线修正模型 Modified model of rectangular hyperbola	20	0.153 3	41.087 1	108.154 3	15.344 0	0.998 8
	25	0.159 7	44.594 2	74.905 0	11.331 9	0.997 2
	30	0.174 1	46.207 5	77.867 5	12.638 7	0.994 6
	35	0.179 5	40.513 9	101.701 9	16.789 8	0.986 6
	40	0.169 4	41.739 2	102.650 3	15.800 8	0.999 1

表4 互花米草CO2响应模型参数平均值

Table 4 Mean values of Spartina alterniflora CO2 response model parameters

模型 Model	叶片温度 T_leaf (℃)	初始斜率 α	最大净光合速率 A_max (µmol·m^-2·s^-1)	CO₂补偿点 $\Gamma *$(µmol·m^-2·s^-1)	光呼吸速率 R_p (µmol·m^-2·s^-1)	模型拟合的决定系数 R²
直角双曲线模型 Rectangular hyperbola model	20	2.260 4	74.634 5	22.385 1	30.155 5	0.992 6
	25	2.130 4	74.802 1	22.121 0	28.911 8	0.993 1
	30	2.169 4	75.013 1	20.975 6	28.322 8	0.992 7
	35	1.272 5	69.188 4	19.595 8	18.329 9	0.997 4
	40	1.786 0	69.854 8	18.670 9	22.571 1	0.993 4
Michaelis-Mente模型 Michaelis-Menten model	20	-	74.634 5	22.385 1	30.155 5	0.992 6
	25	-	74.802 1	22.121 0	28.911 8	0.993 1
	30	-	75.013 1	20.975 6	28.322 8	0.992 7
	35	-	69.188 4	19.595 8	18.329 9	0.997 4
	40	-	69.854 8	18.670 9	22.571 1	0.993 4
直角双曲线修正模型 Modified model of rectangular hyperbola	20	0.596 4	39.818 2	11.817 3	6.383 9	0.995 3
	25	0.626 2	40.902 1	13.017 0	7.305 3	0.992 7
	30	0.620 1	41.776 0	10.861 1	6.146 0	0.997 5
	35	0.625 3	43.911 9	13.381 3	7.498 2	0.997 0
	40	0.617 1	42.079 5	10.173 1	5.762 8	0.998 8

图6 不同温度下芦苇CO2响应模型参数差异分析。

Fig. 6 Analysis of differences in model parameters of Phragmites australis CO2 response at different temperatures. Amax, maximum net photosynthetic rate; Γ*, CO2 compensation point; Rp, light respiration rate; Tleaf, leaf temperature.

图7 芦苇的3种CO2响应模型线性回归分析。A, 直角双曲线模型。B, Michaelis-Menten模型。C, 直角双曲线修正模型。

Fig. 7 Linear regression analysis of three CO2 response models for Phragmites australis. A, Rectangular hyperbola model. B, Michaelis-Menten model. C, Modified model of rectangular hyperbola.

图8 不同温度下互花米草CO2响应模型参数差异分析。

Fig. 8 Difference analysis of model parameters of CO2 response of Spartina alterniflora at different temperatures. Amax, maximum net photosynthetic rate; Γ*, CO2 compensation point; Rp, light respiration rate; Tleaf, leaf temperature.

图9 互花米草3种CO2响应模型线性回归分析。A, 直角双曲线模型。B, Michaelis-Menten模型。C, 直角双曲线修正模型。

Fig. 9 Linear regression analysis of three CO2 response models for Spartina alterniflora. A, Rectangular hyperbola model. B, Michaelis-Menten model. C, Modified model of rectangular hyperbola.

图10 芦苇和互花米草光合指标的相关性分析。A, 芦苇光合指标的相关性分析。B, 互花米草光合指标的相关性分析。A, 净光合速率; Ci, 植物胞间CO2浓度; Ca, 环境CO2浓度; E, 蒸腾速率; gs, 气孔导度; H, 湿度; PAR, 有效光合辐射; RH, 相对湿度; Ta, 气温; Tleaf, 叶片温度; VPD, 水蒸气压亏缺; WUE, 水分利用效率。*, p < 0.05。

Fig. 10 Correlation analysis of photosynthetic metrics in Phragmites australis and Spartina alterniflora. A, Correlation analysis of photosynthetic indexes in Phragmites australis. B, Correlation analysis of photosynthetic indexes in Spartina alterniflora. A, net photosynthetic rate; Ci, plant intercellular CO2 concentration; Ca, ambient CO2 concentration; E, transpiration rate; gs, stomatal conductance; H, humidity; PAR, effective photosynthetic radiation; RH, relative humidity; Ta, temperature; Tleaf, leaf temperature; VPD, water vapor pressure deficit; WUE, water use efficiency. *, p < 0.05.

图11 基于理论指导的神经网络(TgNN)的多因素光合速率预测模型训练过程。A, 训练集损失变化。B, 测试集损失变化。

Fig. 11 Training process of a multifactorial photosynthetic rate prediction model based on Theory-guided neural network (TgNN). A, Training set loss variation. B, Test set loss variation.

表5 各类模型在测试集上的误差

Table 5 Errors of various models on the test set

植物类别 Plant category	模型种类 Types of model	平均绝对误差 MAE	平均绝对百分比误差 MAPE	均方误差 MSE	均方根误差 RMSE
芦苇 Phragmites australis	多元线性回归 Multiple linear regression	5.426 1	0.128 1	5.580 1	0.131 8
	神经网络 Neural network	4.687 0	0.110 4	4.736 8	0.111 5
	随机森林 Random forest	4.343 6	0.102 5	4.345 3	0.102 6
	支持向量回归 Support vector regression	5.584 9	0.131 9	5.658 1	0.133 7
	理论指导的神经网络 Theory-guided neural network	2.574 5	0.060 7	2.669 2	0.063 6
互花米草 Spartina alterniflora	多元线性回归 Multiple linear regression	3.737 3	0.332 3	4.215 1	0.583 1
	神经网络 Neural network	3.301 7	0.193 2	4.457 8	0.269 2
	随机森林 Random forest	1.801 0	0.183 3	2.064 0	0.494 4
	支持向量回归 Support vector regression	3.806 0	0.534 4	4.712 5	1.179 1
	理论指导的神经网络 Theory-guided neural network	1.504 3	0.094 9	1.668 8	0.163 0

图12 5种芦苇光合速率预测模型的回归分析。A, 多元线性回归。B, 神经网络。C, 随机森林。D, 支持向量回归。E, 理论指导的神经网络。

Fig. 12 Regression analysis of five Phragmites australis photosynthetic rate prediction models. A, Multiple Linear Regression (MLR). B, Neural Network (NN). C, Random Forest (RF). D, Support Vector Regression (SVR). E, Theory-guided Neural Network (TgNN).

图13 5种互花米草光合速率预测模型的回归分析。A, 多元线性回归。B, 神经网络。C, 随机森林。D, 支持向量回归。E, 理论指导的神经网络。

Fig. 13 Regression analysis of photosynthetic rate prediction models for five species of Spartina alterniflora. A, Multiple Linear Regression (MLR). B, Neural Network (NN). C, Random Forest (RF). D, Support Vector Regression (SVR). E, Theory-guided Neural Network (TgNN).

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光合响应模型与理论指导的神经网络融合的多因素光合速率预测模型

Multi-factor photosynthetic rate prediction model by fusion of photosynthetic response model and theory-guided neural network

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