# Dry Weight Prediction of Wedelia trilobata and Wedelia chinensis by Using Artificial Neural Network and MultipleLinear Regression Models

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}) of 0.98, root mean square error (RMSE) of 0.003, and mean absolute error (MAE) of 0.001. On the other hand, the ANN model for WT (8-6-1) has R

^{2}0.98, RMSE 0.018, and MAE 0.004. According to errors and coefficient of determination values, the ANN model was more accurate than the MLR one. According to the sensitivity analysis, plant height and number of nodes are the most important variables that support WT and WC growth under submergence and eutrophication conditions. This study provides us with a new method to control invasive plant species’ spread in different habitats.

## 1. Introduction

_{2}, light, and temperature, affect the growth of native plant species, but assist invasive plant species in sustaining their development because they prefer to grow in disturbed habitats [6]. In wetland or riparian zones, the main issues are submergence and eutrophication. The former, called submergence, is a type of flooding during which the shoot of a plant is under water [12]. Expulsion of water from riversides, dams, and canals will create submergence close to these areas, and vegetation will face submergence. Submergence imposes considerable stress by decreasing energy and carbohydrate values [13]. Functional traits, such as shoot elongation and leaves, assist both invasive and native plant species in sustaining their growth under submergence, by enabling exposure to sunlight for photosynthesis [5,14]. Eutrophication is another environmental factor that negatively affects the aquatic ecosystem [15]. Eutrophication decreases the growth of native plant species. It boosts the growth of invasive plant species because invasive plant species prefer to grow in an environment with rich resources [16]. Eutrophication helps to overcome the stress of submergence by enhancing the shoot of invasive species because these plants can obtain more CO

_{2}, light for photosynthesis, and oxygen for transpiration [14]. Meanwhile, invasive plant species enhance their root length in order to capture resources below ground, and overcome the growth of their native competitor by enhancing their root length [17]. Therefore, for managing invasive plant species under submergence and eutrophication habitats, the traits of different growth parameters assist us in understanding their invasion.

## 2. Materials and Methods

#### 2.1. Study Site and Material Preparation

_{3}, NH

_{4}Cl, and KH

_{2}PO

_{4}to prepare each of these treatments, respectively [5]. There were 90 pots in total. Every day, tap water was added to each treatment bin to maintain the submergence level, and the nutrient solution was renewed one time after seven days. Plants were harvested after 30 days.

#### 2.2. Morphological Trait Measurement

^{−2}s

^{−1}, photosynthetically active radiation up to 1000 μmol m

^{−2}s

^{−1}, CO

_{2}concentration 402 μmol mol

^{−1}, vapor pressure 7.0 to 8.8 mbar, and ambient temperature 30.2 to 34.8 °C.

#### 2.3. Processing of Data and Statistical Analysis

#### 2.3.1. Criteria for Input Variables

#### 2.3.2. Artificial Neural Network (ANN)

_{norm}is the normalized value of an independent or dependent variable. X

_{min}and X

_{max}are the variable’s minimum and maximum values, and Xi’s are the original data.

_{0}and b

_{0j}, are always equal to 1. Based on earlier research [21,22,32], the current study used a feed-forward multi-layer perceptron (MLP) topology with three layers, and the back propagation (BP) training technique, along with the Levenberg–Marquardt, Momentum, and Conjugate Gradient learning algorithms. Trial-and-error testing was used to identify hidden layers (1–3) and neurons [25]. Sigmoid Axon, Tangent Hyperbolic Axon, Linear Sigmoid Axon, and Linear Tangent Hyperbolic Axon activation functions were used to determine the best equation with high accuracy within the hidden and output layers [33,34].

#### 2.3.3. Multiple Linear Regression (MLR)

_{0}+ a

_{n}is the regression coefficient, X

_{1}− X

_{n}are independent variables, and € is the error of the nth observation.

#### 2.3.4. Performance and Sensitivity Analysis

^{2}), and mean absolute error (MAE).

_{i}denotes the actual value, and Y

_{j}denotes the predicted value. Y

_{io}and Y

_{jo}are the mean values of observed and predicted values, respectively. A model with lower values of RMSE and MAE and a higher value of R

^{2}is considered the best prediction model.

^{2}, RMSE, and MAE determined the accuracy of the model [37].

## 3. Results and Discussion

#### 3.1. Selection of Input Variables

^{2}= 0.951), followed by ND (R

^{2}= 0.943), CHI (R

^{2}= 0.777), LN (R

^{2}= 0.643), L (R

^{2}= 0.626), PN (R

^{2}= 0.819), and GS (R

^{2}= 0.795). WT also demonstrates a positive correlation with PH (R

^{2}= 0.906), followed by ND (R

^{2}= 0.859), CHI (R

^{2}= 0.488), LN (R

^{2}= 0.550), L (R

^{2}= 0.761), PN (R

^{2}= 0.781), and GS (R

^{2}= 0.448). At the same time, WT negatively correlates with RL (R

^{2}= −0.780). A negative correlation of WT and RL, under competition due to phenotyping plasticity, help WT to capture resources below ground and destroy the growth of WC [5]. The negative correlation of RL also makes WT a stronger competitor in capturing resources below ground [12]. Under submergence and eutrophication, the plant height and number of leaves facilitate the plant’s exposure to sunlight in order to alleviate the negative effects of submergence and eutrophication [14] and continue their photosynthetic process for growth development [9]. Therefore, according to previous studies [9,14,38], and this study’s correlation results, it can be postulated that PH, ND, CHI, LN, L, RL, PN GS are the most important trait parameters to determining the DW of WT and WC, as presented in Figure 2 and Figure 3.

#### 3.2. Prediction of Dry Weight of Wedelia trilobata and Wedelia chinensis Using ANN

^{2}, were determined by using the Sigmoid Axon as a transfer function for both plant species in the testing, training, and validation phase, as presented in Table 6. These findings could be related to the transfer function. It is possible that the input variables and output in this study revealed a complex non-linear relationship; meanwhile, it can be obtained that the Sigmoid Axon function can cover complex non-linear variations related to other transfer functions [24]. Many crop growth prediction models utilized the Sigmoid Axon transfer function [21,22,25,46].

^{2}under different hidden layers, the optimum results in testing (RMSE = 0.003, MAE = 0.001, and R

^{2}= 0.98), training (RMSE = 0.047, MAE = 0.027, and R

^{2}= 0.98), and validation (RMSE = 0.28, MAE = 0.16, and R

^{2}= 0.99), for WC were determined, with one hidden layer, along with four neurons. Similarly, for WT, testing (RMSE = 0.018, MAE = 0.004, and R

^{2}= 0.98), training (RMSE = 0.008, MAE = 0.004, and R

^{2}= 0.99), and validation (RMSE = 0.23, MAE = 0.16, and R

^{2}= 0.99) were determined, also with one hidden layer, along with six neurons, as presented in Table 6. The transfer function between hidden layers and nodes, exhibiting the complexity of the ANN, is one of the most important elements influencing the accuracy and performance of the ANN [32]. Increasing the number of hidden layers and neurons did not affect performance and accuracy of the model discussed in this work [26]. The total input, the output variables, the algorithm used for training, the complexity of the ANN structure, and the number of samples used for the training network are the elements that can disturb hidden layers and units in the ANN [32,47,48,49].

#### 3.3. Multiple Linear Regression (MLR)

^{2}value for both WC and WT because it demonstrated less impact for DW production in both plant species [19]. On the other hand, PH has the highest R

^{2}value for both WC and WT because it helps expose the plants to sunlight so that they can run their photosynthetic process in order to overcome the effects of submergence and eutrophication [5]. Many researchers used SWR to understand the role of the independent variables on the dependent variable for the development of regression models, i.e., in sesame (Sesamum indicum L.) and Ajowan (Trachyspermum ammi L.) [21,55]. Graphs between the predicted and measured DW values for WT and WC were created with the help of the MLR model in Figure 6. The predicted MLR model for WT has R

^{2}= 0.96, RMSE = 0.08, and MAE = 0.009, while the Predicted MLR model for WC has R

^{2}= 0.97, RMSE = 0.09, and MAE = 0.01, as presented in Figure 6. These errors and coefficient of determination values indicate that MLR models have low performance compared to the ANN model.

#### 3.4. Comparsion of MLR and ANN Models

^{2}, RMSE, and MAE), the MLR and ANN models were compared. These are the best criteria to determine the performance of differently trained models [46]. According to the results presented in the scatter plots in Figure 5 and Figure 6, the lower values of RMSE and MAE and higher values of R

^{2}in the ANN model described that the predicted values of the ANN model are very similar to the measured values, compared to the MLR model. In short, the ANN model is more accurate in describing both plant species’ dry weights, by using different growth trait variables when compared to the MLR model because the MLR model could not describe non-linear relationships more accurately [24,25,26]. Many other researchers have agreed that the ANN model is a better method, compared to the MLR model, for the growth prediction of different crops [21,22,25,46,56].

#### 3.5. Sensitivity Analysis

^{2}value (0.78, 0.85), with high RMSE (0.11, 0.028) and MAE (0.014, 0.008) for WT, similar to WC, which had the lowest R

^{2}value (0.72,0.86), with high RMSE (0.13, 0.037) and MAE (0.016, 0.012), as presented in Table 7 and Table 8. Furthermore, results described that PH, followed by ND, was recognized as the most important parameter in predicting DW under both models. SWR and correlation results also agreed with the sensitivity analysis, as presented in Table 3 and Table 4 and Figure 2 and Figure 3, respectively. It can be concluded with sensitivity analysis, SWR, and correlation analysis that PH and ND are the most important factors affecting the DW of both plant species. PH played an important role in sustaining plant growth under submergence and eutrophication because greater height can increase exposure to sunlight in order to perform the photosynthetic process for better growth development [1,5]. The higher number of nodes helped the plant to increase the plant height and number of leaves, which help overcome the stress of submergence and eutrophication by increasing exposure to air in order to obtain CO

_{2,}light for photosynthesis, and oxygen for transpiration [1,4].

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Parameters | Abbreviation | Units |

Plant height | PH | Cm |

Nodes | ND | No |

Chlorophyll content | CHI | SPAD |

Leaf nitrogen | LN | mg/g |

Leaves | L | No |

Root length | RL | Cm |

Specific leaf area | SLA | Cm^{2}/g |

Leaf area | LA | Cm^{2} |

Photosynthesis | PN | umol (CO_{2})m^{2}_{S}^{−1} |

Transpiration | TR | mol (H_{2}O)m^{2}s^{−1} |

Stomatal conductance | GS | mmolm^{2}s^{−1} |

Dry weight | DW | G |

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**Figure 1.**Experimental site (

**A**); experimental plants, Wedelia chinensis (

**B**) and Wedelia trilobata (

**C**).

**Figure 2.**Pearson correlation of Wedelia chinensis between dry weight and other trait variables. Note: ** significant at <0.01; NS at >0.05. PH = plant height; ND = nodes; CHI = chlorophyll content; LN = leaf nitrogen; L = leaves; RL = root length; PN = photosynthesis; TR = transpiration; SLA = specific leaf area; GS = stomatal conductance; LA = leaf area. NS = non-significant.

**Figure 3.**Pearson correlation of Wedelia trilobata between dry weight and other trait variables. Note: ** significant at <0.01. PH = plant height; ND = nodes; CHI = chlorophyll content; LN = leaf nitrogen; L = leaves; RL = root length; PN = photosynthesis; TR = transpiration; SLA = specific leaf area; GS = stomatal conductance; LA = leaf area. NS = non-significant.

**Figure 4.**The convergence of the average MAE value during training and testing of the final ANN structure for Wedelia trilobata (

**A**) and Wedelia chinensis (

**B**). Note: MAE = mean absolute error.

**Figure 5.**Scatter plot between measured and predicted dry weight values for both plant species, Wedelia trilobata (

**A**) and Wedelia chinensis (

**B**) by ANN model. Note: RMSE = root mean square error; MAE = mean absolute error.

**Figure 6.**Measured and predicted values of dry weight for both plant species, Wedelia trilobata (

**A**) and Wedelia chinensis (

**B**) by MLR model. Note: RMSE = root mean square error; MAE = mean absolute error.

Parameters | Minimum | Maximum | Mean | Std. Deviation |
---|---|---|---|---|

PH | 10.00 | 60.00 | 23.66 | 13.22 |

ND | 2.00 | 14.00 | 5.62 | 3.16 |

CHI | 5.60 | 13.50 | 8.75 | 2.44 |

LN | 0.90 | 1.50 | 1.15 | 0.16 |

L | 8.00 | 20.00 | 11.62 | 3.76 |

RL | 8.00 | 22.00 | 14.45 | 3.51 |

SLA | 138.54 | 342.03 | 205.22 | 45.61 |

LA | 3.64 | 12.50 | 8.08 | 2.67 |

PN | 5.01 | 7.87 | 6.08 | 1.02 |

TR | 1.30 | 1.65 | 1.45 | 0.10 |

GS | 0.04 | 0.08 | 0.06 | 0.01 |

DW | 0.42 | 1.87 | 0.763 | 0.47 |

Parameters | Minimum | Maximum | Mean | Std. Deviation |
---|---|---|---|---|

PH | 12.00 | 38.00 | 23.79 | 6.22 |

ND | 3.00 | 9.00 | 5.75 | 1.75 |

CHI | 4.40 | 17.00 | 9.11 | 3.05 |

LN | 0.80 | 1.70 | 1.19 | 0.24 |

L | 6.00 | 14.00 | 10.58 | 1.71 |

RL | 7.00 | 16.00 | 11.77 | 2.72 |

SLA | 145.66 | 341.21 | 244.93 | 57.18 |

LA | 1.90 | 6.04 | 4.28 | 1.28 |

PN | 5.10 | 6.75 | 5.76 | 0.60 |

TR | 1.28 | 1.59 | 1.40 | 0.10 |

GS | 0.03 | 0.61 | 0.07 | 0.11 |

DW | 0.18 | 2.04 | 0.69 | 0.53 |

**Table 3.**Stepwise regression analysis for dry weight of Wedelia chinensis as the dependent variable.

Step | Entered Variable | Variable in Model | Partial-R-Square ^{a} | R-Square ^{b} |
---|---|---|---|---|

1 | GS | GS | 0.632 | 0.795 |

2 | PN | GS PN | 0.716 | 0.846 |

3 | L | GS PN L | 0.732 | 0.856 |

4 | LN | GS PN L LN | 0.738 | 0.859 |

5 | CHI | GS PN L LN CHI | 0.760 | 0.872 |

6 | ND | GS PN L LN CHI ND | 0.898 | 0.948 |

7 | PH | GS PN L LN CHI ND PH | 0.909 | 0.953 |

Durbin–Watson value = 1.60; variance inflation factor (VIF); VIF for all variables (5 < VIF); tolerance for all variables (1 > TOL) |

^{a}Partial determination coefficient;

^{b}determination coefficient; Durbin–Watson value = 1.260. Note: PH = plant height; ND = nodes; CHI = chlorophyll content; LN = leaf nitrogen; L = leaves; PN = photosynthesis; GS = stomatal conductance.

**Table 4.**Stepwise regression analysis for dry weight of Wedelia trilobata as the dependent variable.

Step | Entered Variable | Variable in Model | Partial-R-Square ^{a} | R-Square ^{b} |
---|---|---|---|---|

1 | GS | GS | 0.420 | 0.648 |

2 | PN | GS PN | 0.613 | 0.783 |

3 | RL | GS PN RL | 0.681 | 0.825 |

4 | L | GS PN RL L | 0.702 | 0.838 |

5 | LN | GS PN RL L LN | 0.726 | 0.852 |

6 | CHI | GS PN RL L LN CHI | 0.801 | 0.895 |

7 | ND | GS PN RL L LN CHI ND | 0.813 | 0.902 |

8 | PH | GS PN RL L LN CHI ND PH | 0.861 | 0.928 |

Durbin–Watson value = 1.60; variance inflation factor (VIF); VIF for all variables (5 < VIF); tolerance for all variables (1 > TOL) |

^{a}Partial determination coefficient;

^{b}determination coefficient; Durbin–Watson value = 1.34. Note: PH = plant height; ND = nodes; CHI = chlorophyll content; LN = leaf nitrogen; L = leaves; RL = root length; PN = photosynthesis; GS = stomatal conductance.

**Table 5.**Summary of the components of the artificial neural network model used to predict the growth of Wedelia trilobata and Wedelia chinensis.

ANN Method | Number of Hidden Layers | Number of Neurons in Each Layer | Transfer Function | Learning Algorithm | Training Algorithm |
---|---|---|---|---|---|

Multi-layerperceptron (MLP) | 1–5 | 1–20 | Sigmoid Axon | Levenberg–Marquardt | Back Propagation |

Linear Sigmoid Axon | |||||

Tangent Hyperbolic Axon | |||||

Linear Tangent Hyperbolic Axon |

**Table 6.**The performance of the best ANN models for predicting dry weight of Wedelia trilobata and Wedelia chinensis.

Output | Network Structure | Transfer Function | Learning Algorithm | Training Algorithm | Testing | Training | Validation | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

R^{2} | RMSE | MAE | R^{2} | RMSE | MAE | R^{2} | RMSE | MAE | |||||

WC | MLP-7-4-1 | SigmoidAxon | Levenberg–Marquardt | Back Propagation | 0.98 | 0.003 | 0.001 | 0.98 | 0.047 | 0.027 | 0.99 | 0.28 | 0.16 |

WT | MLP-8-6-1 | SigmoidAxon | Levenberg–Marquardt | Back Propagation | 0.98 | 0.018 | 0.004 | 0.99 | 0.008 | 0.004 | 0.99 | 0.23 | 0.16 |

Method | ANN | MLR | ||||
---|---|---|---|---|---|---|

R^{2} | RMSE | MAE | R^{2} | RMSE | MAE | |

The best ANN/MLR with (PH, ND, CHI, LN, L, RL, PN, GS | 0.98 | 0.018 | 0.004 | 0.96 | 0.08 | 0.009 |

ANN/MLR without (PH) | 0.85 | 0.028 | 0.008 | 0.78 | 0.11 | 0.014 |

ANN/MLR without (ND) | 0.88 | 0.034 | 0.006 | 0.84 | 0.12 | 0.015 |

ANN/MLR without (CHI) | 0.90 | 0.044 | 0.002 | 0.88 | 0.093 | 0.008 |

ANN/MLR without (LN) | 0.92 | 0.057 | 0.006 | 0.90 | 0.103 | 0.011 |

ANN/MLR without (L) | 0.93 | 0.089 | 0.003 | 0.91 | 0.102 | 0.010 |

ANN/MLR without (RL) | 0.95 | 0.091 | 0.005 | 0.93 | 0.13 | 0.014 |

ANN/MLR without (PN) | 0.97 | 0.031 | 0.013 | 0.80 | 0.107 | 0.011 |

ANN/MLR without (GS) | 0.96 | 0.059 | 0.001 | 0.90 | 0.106 | 0.011 |

Method | ANN | MLR | ||||
---|---|---|---|---|---|---|

R^{2} | RMSE | MAE | R^{2} | RMSE | MAE | |

The best ANN/MLR with (PH, ND, CHI, LN, L, PN, GS | 0.98 | 0.003 | 0.001 | 0.97 | 0.09 | 0.010 |

ANN/MLR without (PH) | 0.86 | 0.037 | 0.012 | 0.72 | 0.13 | 0.016 |

ANN/MLR without (ND) | 0.88 | 0.052 | 0.005 | 0.75 | 0.120 | 0.010 |

ANN/MLR without (CHI) | 0.91 | 0.087 | 0.07 | 0.81 | 0.103 | 0.010 |

ANN/MLR without (LN) | 0.90 | 0.046 | 0.04 | 0.85 | 0.091 | 0.08 |

ANN/MLR without (L) | 0.93 | 0.032 | 0.06 | 0.76 | 0.11 | 0.013 |

ANN/MLR without (PN) | 0.95 | 0.021 | 0.08 | 0.78 | 0.12 | 0.012 |

ANN/MLR without (GS) | 0.96 | 0.056 | 0.06 | 0.82 | 0.10 | 0.011 |

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## Share and Cite

**MDPI and ACS Style**

Azeem, A.; Mai, W.; Tian, C.; Javed, Q.
Dry Weight Prediction of *Wedelia trilobata* and *Wedelia chinensis* by Using Artificial Neural Network and MultipleLinear Regression Models. *Water* **2023**, *15*, 1896.
https://doi.org/10.3390/w15101896

**AMA Style**

Azeem A, Mai W, Tian C, Javed Q.
Dry Weight Prediction of *Wedelia trilobata* and *Wedelia chinensis* by Using Artificial Neural Network and MultipleLinear Regression Models. *Water*. 2023; 15(10):1896.
https://doi.org/10.3390/w15101896

**Chicago/Turabian Style**

Azeem, Ahmad, Wenxuan Mai, Changyan Tian, and Qaiser Javed.
2023. "Dry Weight Prediction of *Wedelia trilobata* and *Wedelia chinensis* by Using Artificial Neural Network and MultipleLinear Regression Models" *Water* 15, no. 10: 1896.
https://doi.org/10.3390/w15101896