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Effect of phosphorus starved cultures of Dunaliella tertiolecta on growth represented as optical density under stress of nickel ionsIn the case of normal culture, phosphorus starved control culture (without nickel stress), and phosphorus-starved treated cultures, data presented in Table 1 and graphed in figure (S1, Supplementary Data) clearly showed a progressive increase in optical density with increasing culturing period in case of normal culture, phosphorus-starved control culture, and phosphorus-starved treated cultures. Our findings are consistent with those of18 who found that in phosphorus starved cultures of three algae species, Microcystic aeruginosa, Chlorella pyrenoidesa, and Cyclotella sp., the biomass, specific growth rate, and Chl-a all declined significantly.The optical density achieved during the four periods of culturing was lower in phosphorus-depleted control cultures than in normal cultures (i.e., cultures contained phosphorus). When compared to a normal control (without nickel addition), the optical density was reduced by 9.1% after 4 days of culturing under phosphorus deprivation and by 10.0 percent after 8 days of culturing. In the case of 5 mg/L dissolved nickel, however, the obtained optical density values in phosphorus starved treatment cultures rose with the increase in culturing period during all culturing periods as compared to phosphorus-starved control (without nickel addition) cultures.At 10 mg/L dissolved nickel and after 4 days of culturing, the optical density although less than those in case of concentration 5 mg/L, yet it was higher than control (− P) but by increasing the culturing period more than 4 days, the optical density was less than control (− P). Our results are similar to those of19 who observed that the decrease in cell division rate signaled the onset of P-deficiency. The cultures that showed no significant increase in cell number for at least three consecutive days under the experimental conditions were considered P-depleted. In addition20, observed that the growth rate of Dunaliella prava was found to be dramatically lowered when phosphorus was limited. The content of chlorophyll fractions, total soluble carbohydrates, and proteins all fell considerably as a result of phosphorus restriction.The results concerning the effect of dissolved nickel on the growth of Dunaliella tertiolecta under conditions of phosphorus limitation show that phosphorus starved Dunaliella had lower growth as compared to the control (phosphorus-containing culture medium). These results are in agreement with those obtained by7 who reported that the optical density of Chlorella kessleri cell suspension decreased with phosphorus deficiency compared to control. Also21, found that Chlorella vulgaris cells grew 30–40% slower in phosphorus-starved cultures than in control cultures. Furthermore22, showed that diatoms were unable to thrive when phosphorus levels were insufficient. Diatom dominances were reduced to 45 and 55% in enclosures where phosphate was not provided23 observed that, under salt stress, Chlorella’s metabolic rate was substantially lower than Dunaliella’s.It can be concluded that when microorganisms are deprived of phosphorus, dissolved nickel uptake decreases, resulting in an increase in algal metabolism24. Also25, examined the effects of phosphorus and nitrogen starvation on the life cycle of Emiliania huxleyi (Haptophyta) and proved that various biochemical pathways’ metabolic load increased under P-starvation while it decreased under N-starvation.Effect of phosphorus starved cultures of Dunaliella tertiolecta on chlorophylls content under stress of nickel ionsTable 2 and figure (S2, Supplementary Data) show the sequences of change in the amount of chlorophylls a and b in phosphorus-depleted cultures of Dunaliella tertiolecta in response to various dissolved nickel concentrations. The results show that total chlorophyll content rose steadily until the end of the experiment under normal conditions (a control containing phosphorus). These results are in harmony with those obtained by24. The ratio between chlorophylls “a” and “b” remained nearly constant till the end of the 12th day. At the 16th day of culturing, the ratio decreased from 2.9:1 to 2.4:1. On the contrary, the total chlorophylls under control (in the absence of nickel element) in case of phosphorus-starved cultures showed a progressive increase up to the 12th day. At the 12th day the total chlorophylls in case of phosphorus-starved cultures decreased by 10.7% compared to the normal control. At the 16th day, the total chlorophylls in case of untreated phosphorus starved culture decreased by 20.8% compared to those obtained at normal control26. Reported that the chlorophyll content of Chlorella sorokiniana was significantly reduced due to a lack of nitrogen and phosphorus in the medium.Table 2 Effect of different concentrations of dissolved nickel (mg/L) on chlorophylls content (µg/ml) of Dunaliella tertiolecta under the stress of phosphorus starvation.Full size tableThe total chlorophyll content of Dunaliella tertiolecta in the phosphorus-starved cultures treated with 5 mg/L of dissolved nickel increased gradually until the 12th day, when the content of the total chlorophylls reached 2.11 µg/ml, i.e., higher than the phosphorus-starved control (− P) by 15.3%. At the 16th day, the total chlorophylls, although lower than those obtained at the 12th day, were still higher than the control (− P). At a concentration of 10 mg/L of dissolved nickel, slight increase in the content of total chlorophylls was recorded from the beginning to the end of the culturing period, i.e., from the 4th to the 16th day. At the other concentrations of dissolved nickel (15, 20, and 25 mg/L), a pronounced decrease in the total chlorophylls could be observed from the 4th to the 16th day of culturing compared to control (− P). Our results are going with an agreement with those obtained by27 who found that chlorophylls were inhibited maximum at higher dissolved nickel concentrations but activated at lower values. The normal ratio between chlorophylls “a” and “b” (3:1) was upset after the 8th day of culturing under concentrations 5, 10, and 15 mg/L of dissolved nickel. At 20 and 25 mg/L of dissolved nickel, this ratio was unstable from the beginning to the end of the experiment. The fact that dissolved nickel is extremely mobile and hence only absorbed to a minimal level may explain the sensitivity of the tested alga to nickel in response to phosphorus deficiency, and an increase in phosphorus concentration favors its absorption by microorganisms28. It can be concluded that when microorganisms are deprived of phosphorus, dissolved nickel uptake decreases, resulting in an increase in algal metabolism.Effect of different concentrations of dissolved nickel on photosynthesis (O2-evolution) of phosphorus starved cells of Dunaliella tertiolecta
Data represented in Table 3 and graphed in figure (S3, Supplementary Data S3) showed that the effect of phosphorus limitation on the photosynthetic activity of Dunaliella tertiolecta in response to five different concentrations of dissolved nickel revealed that, under phosphorus limiting conditions, the amount of O2-evolution was lower than in untreated cultures (the control). The evolution of O2 after 4 days of culturing in case of phosphorus starved control decreased by 8.7% compared to normal control, while after 12 days it decreased by 30.4%. The rate of O2-evolution at different concentrations of dissolved nickel over 5 mg/L caused successive reductions in the O2-evolution of phosphorus starved cells. Application of 5 mg/L of dissolved nickel, the results cleared that the rate of O2-evolution increased under the effect of all tested concentrations till the end of the experiment. It is clear from our data that the rate of O2-evolution depended mainly on the concentration of the nickel element and the length of culturing period. The lower the rate of O2-evolution, the higher the element’s concentration, and the longer the culturing period. This coincided with the findings of7 who found that low phosphorus treatment causes Chlorella kessleri to lose its photosynthetic activity. In this regard, it was discovered that phosphorus deficiency resulted in a decrease in photosynthetic electron transport activity29 found that the O2-evolution of Chlamydomon reinhardtii declined by 75%. This decrease reflects damage of PSII and the generation of PSII QB-non reducing centers.Table 3 Effect of different concentrations of dissolved nickel (mg/L) on photosynthetic activity (O2-evolution calculated as µ mol O2 mg chl-1 h-1) on phosphorus supplemented and starved cells of Dunaliella tertiolecta.Full size tableAlso30 found that P- deficiency has been correlated with lower photosynthetic rates. In the case of the treated phosphorus-starved cultures with lower concentrations (5 mg/L) of dissolved nickel, the rate of photosynthesis increased when compared to the phosphorus-starved control, but was less than that of the normal control (without nickel treatment). On the contrary, it was found that, in the treated phosphorus-starved cultures at concentrations of 10, 15, 20 and 25 mg/L of the tested element, the rate of photosynthesis decreased from the beginning to the end of the experiment. With increasing concentration, duration of the culturing period, and kind of element, the condition of decrease in O2-evolution became more pronounced; the same results were also recorded by24. The stimulation of growth and photosynthesis in the presence of some concentrations of dissolved nickel under phosphorus-limiting conditions is observed by31 they report that in Cu2+ sensitive Scenedesmus acutus, intracellular polyphosphate plays a key role in shielding photosynthesis from Cu2+ toxicity but not in copper resistant species.Effect of different concentrations of dissolved nickel on respiration (O2-uptake) of phosphorus starved cells of Dunaliella tertiolectaData obtained in Table 4 and graphed in figure (S4, Supplementary Data S4) concerning the rate of respiration of Dunaliella tertiolecta under phosphorus-limiting conditions was higher than that of untreated phosphorus-starved (control) for a short period of time only, i.e., after 4 days, at concentrations 5, 10 and 15 mg/L of dissolved nickel, After 8 days of culturing, the rate of O2- uptake increased only at 5 mg/L of dissolved nickel, while at the other concentrations it decreased gradually with increasing the concentration of the element. This finding is consistent with the findings of23, who discovered that Dunaliella cells increased their O2 absorption and evolution rates in the presence of 2 M salt NaCl in the media. In terms of oxygen uptake rate, Dunaliella cells demonstrated an increase in salt concentrations. In 1.5 M NaCl, it increased significantly by 60–80%.Table 4 Effect of different concentrations of dissolved nickel (mg/L) on respiration activity (O2-uptake calculated as µ mol O2 h-1) on phosphorus supplemented and starved cells of Dunaliella tertiolecta.Full size tableConcerning the increase in respiration in P-depleted green alga species cultures5 suggested that Scenedesmus, for example, can utilize the energy stored in starch and lipids for active phosphorus uptake from lake sediments. This process is aided by an increase in phosphatase production32 and these cells’ ability to operate anaerobically33. When unicellular green algae or higher plants are exposed to P deficiency, the majority of newly fixed carbon appears to be allocated to the synthesis of non-phosphorylated storage polyglucans (i.e., starch) or sucrose, with less photosynthetic activity directed to respiratory metabolism and other biosynthesis pathways34. It can be concluded from the obtained results that, when the alga was cultivated under phosphorus deficiency and treated with varied amounts of dissolved nickel, the growth was the most sensitive characteristic, followed by photosynthesis, and then dark respiration. In the few comparative studies with several species of green algae, growth was more sensitive than the other physiological processes examined. Out of them35, reported that growth was more susceptible to phosphorus deficiency in Chlorella pyrenoidosa and Asterionella gracilis than photosynthesis and respiration (the least sensitive processes). Growth was also more sensitive than photosynthesis in Nitzschia closterium 36 . Another important fact reported by37 is that under low phosphorus conditions, Dunaliella parva accumulates lipids rather than carbohydrates. These findings imply that phosphorus stress may prevent starch and/or protein production, leading to an increase in carbon flux to lipids. More

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Marine phytoplankton both follow and actively influence the environment they inhabit. Unpacking the complex ecological and biogeochemical roles of these tiny organisms can help reveal the workings of the Earth system.
Phytoplankton are the workers of an ocean-spanning factory converting sunlight and raw nutrients into organic matter. These little organisms — the foundation of the marine ecosystem — feed into a myriad of biogeochemical cycles, the balance of which help control the distribution of carbon on the Earth surface and ultimately the overall climate state. As papers in this issue of Nature Geoscience show, phytoplankton are far from passive actors in the global web of biogeochemical cycles. The functioning of phytoplankton is not just a matter for biologists, but is also important for geoscientists seeking to understand the Earth system more broadly.Phytoplankton are concentrated where local nutrient and sea surface temperatures are optimal, factors which aren’t always static in time. Prominent temperature fluctuations, from seasonal to daily cycles, are reflected in phytoplankton biomass, with cascading effects on other parts of marine ecosystems, such as economically-important fisheries. In an Article in this issue, Keerthi et al., show that phytoplankton biomass, tracked by satellite measurements of chlorophyll for relatively small ( More

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Study areaFigure 2 shows the location of the study area on a map of China generated by ArcGIS software. This study’s field experiments were carried out in the Shuanghe Town agricultural comprehensive water-saving demonstration area (40°42′ N; 107°24′ E), which is located in the middle reaches of the Hetao Irrigation Area of Inner Mongolia. The duration of the experimental process ranged from April in 2018 to October in 2020. The experimental area was characterized by a mid-temperate semi-arid continental climate. The average annual precipitation was determined to be 138 mm and the average evaporation was approximately 2332 mm. The majority of the rainfall was concentrated during summer and autumn seasons, and the accumulation of salt in the surface soil was considered to be serious in the spring and winter months. The average rainfall during maize growth period was 75.3 mm. The 0 to 40 cm soil layers in the experimental area were categorized as silty loam soil, with an average bulk density ranging from 1.42 to 1.53 g cm−3. A maize straw layer with a thickness of 5 cm was buried at a depth of 40 cm, and then the land was leveled. Also, in addition to autumn watering and spring irrigation procedures, water from the Yellow River was used three times for irrigation during the entire growth period of the maize crops. The adopted irrigation method belonged to border irrigation. Urea (46% N) were used as the fertilizer types.Figure 2The location of the study area.Full size imageField trials design and data collectionWe carried out experiment 1 from 2018 to 2019, and the data obtained were used for model training and to determine the hyper-parameters. The experimental design is shown in Table 1. The PNN model trained from the data obtained in experiment 1 predicted the optimal range of irrigation amount and nitrogen application rate (N rate) for each growth period of maize. In these ranges, the soil organic matter and total nitrogen could be kept above 20 g/kg and 1.6 g/kg, respectively, the soil salt content was less than 2 g/kg, and the pH value was between 6.5 and 7.5. In order to verify the accuracy and feasibility of the range of irrigation and nitrogen application simulated by PNN, the field experiment 2 was set in 2020 based on the range simulated by PNN and to evaluate the fitting degree between measured and simulated values of soil indicators under the same amount of irrigation and nitrogen application. The experimental design is shown in Table 2.Table 1 Experimental 1 design scheme.Full size tableTable 2 Experimental 2 design scheme.Full size tableThe experimental design were repeated for three times. The plot area of each treatment measuring 8 × 9 = 72 m2. The surrounding area was separated using 1.2 m buried polyethylene plastic film, and 30 cm was left at the top to prevent fertilizer and water from flowing into each other. The field management process was consistent with that used by the local farmers. The film width of maize was 1.1 m, with each film covering two rows. The plant spacing was approximately 45 cm, and the row spacing was 35 cm. In addition, the planting density of the maize was 60,000 plants/hm2.During the entire growth period of the maize crops, soil samples were collected from the 0 to 20 cm, 20 to 40 cm, 40 to 60 cm, 60 to 80 cm, and 80 to 100 cm soil layers using a soil drill and a three-point method was adopted. The soil samples were stored at 4 °C for the determination of total nitrogen, organic matter, total salt content, and pH values. The total nitrogen, organic matter, total salt content, and pH were determined using a KDN-AA double tube azotometer, MWD-2 microwave universal digestion device, TU1810PC ultraviolet–visible spectrophotometer, and a TU18950 double beam ultraviolet–visible spectrophotometer, respectively.Soil parameters measured include organic matter (SOM), total nitrogen (TN), Salt and pH. The data set includes pre-irrigation and post-irrigation reports from 2018 to 2020. Statistical parameters regarding the soil data are shown in Table 3.Table 3 Various meteorological variables and their descriptive statistics.Full size tableThe dataset obtained in Experiment 1 in 2018 to 2019 was 2490 rows in size, the 80/20 principle was used to data into training, and testing sets were required for ML modeling; 80% of data were employed for model training, while the remaining 20% were used for testing. Specifically, the data corresponding to the treatments with the nitrogen application rate (N rate) of 75 kg/hm2 (N3) in all the treatments (W1N3, W2N3, W3N3) were used as the test set, and the data of the other treatments were used as the training set. The training set was used to initiate ML parameter training. Subsequently, The test set was employed to assess the model. The dataset size in 2020 was 1080 rows, which was used to verify ML modeling.Figure 3 shows the changes of soil indexes over time for each treatment in the field test (take the 0–40 cm soil in the main distribution area of maize roots as an example). There are differences under the influence of different irrigation amounts. When irrigation is 90 mm, soil SOM is 13.25% and 7.00% higher than 60 mm and 120 mm, and soil TN is 4.59% and 6.50% higher than 60 mm and 120 mm, respectively. The soil Salt was 23.30% lower than 60 mm, and the pH was 4.16% and 4.36% lower than that of 60 mm and 120 mm, respectively. It can be seen that irrigation of 90 mm is more favorable for increasing soil SOM and TN contents and reducing soil salinity and alkalinity. Soil SOM and TN contents were the highest at n 75 kg/hm2, which were 4.38% and 8.34% higher than those at N = 93.3 kg/hm2, respectively. Soil Salt was the lowest at N = 60 kg/hm2, which was 3.02% lower than those at N = 75 kg/hm2, with a small gap with other levels. In conclusion, nitrogen application of 75 kg/hm2 was beneficial to increase soil organic matter and nitrogen content, and nitrogen application of 60 kg/hm2 was beneficial to controlling soil salt content.Figure 3Changes in soil organic matter, total nitrogen, salinity, and pH under different treatments over time (a case study of 2019).Full size imageMachine learning (ML) models used for irrigation and nitrogen application strategiesFive ML frames were used to estimate the irrigation and N rate. These models are preference Neural Network (PNN), Support Vector Regression (SVR), Linear Regression (LR), Logistic Regression (LOR), and traditional BP Neural Networks (BPNN). Among them, the prediction effects of linear, Poly, and rbf kernel functions are respectively tried in SVR framework. The torch framework was used to train and test machine learning models in Python.Development of preference neural networkModel frameworkThe preference neural network (PNN) which was proposed for the first time in this study was a typical deep learning model. PNN can be regarded as an approximate natural function in order to describe the complete dependence of the soil fertility indexes, including the effects of soil total nitrogen, organic matter, total salt content, and pH values on irrigation and nitrogen applications. More specifically, PNN has the ability to optimize the function by constructing the mapping y = f (x, θ) and learning parameter θ.First, the input end of PNN model was defined as matrix X ∈ ℝn×d (in which n is the sample size, n = 2490; and d is the dimension of each input vector, d = 6), where {xi} i=1, …, n ∈ X represents the vectorized set of total nitrogen, organic matter, salt content, and pH used for measuring the soil fertility, as well as the nitrogen application and irrigation durations (expressed by days after sowing). At the same time, the output end of the model was defined as the matrix Y ∈ ℝn×2, which represented the levels of the irrigation and nitrogen fertilizer applications. The goal of the proposed PNN model was to learn the fixed mapping Y′ = f (X; θ) ⇒Y through the given input matrix X, where θ is the well optimized learnable parameters which can be obtained via PNN training. Meanwhile, the predicted value Y′ will infinitely approach the measured value Y. The structure and the algorithm of this study’s PNN model is shown in Fig. 4 and Table. 4.Figure 4Schematic diagram for the PNN structural connections. In the figure, it can be seen that when each input vector passed through each layer of the PNN, it is first multiplied by the Hadamard product of the weight matrix and preference value matrix for the purpose of obtaining a weight matrix with preference properties. After the matrix was activated by the Relu Function, Batch Normalization Module Methods and the Dropout Module were used for random suspension and normalization processing, and the input of the next layer was obtained.Full size imageTable 4 Algorithm of Preference neural network.Full size tableLayer-by-layer affine transformationA good definition of the affine transformation of the information flow between layers is considered to be the key to neural network model training. Generally speaking, the learnable parameter θ of each layer of a model includes the weight parameter w and the preference parameter b. The hidden representation hl of the l-th layer in PNN is defined as follows:$${h}_{l}({h}_{l-1};{W}_{l},{b}_{l})={h}_{l-1}^{mathrm{T}}{W}_{l}+{b}_{l}$$
(1)

where Wl and bl represent the learnable weight and bias variables of the l layer, respectively, and hl-1 is the hidden representation of the upper layer. Therefore, when l = 1, then h0 = X.In the present study, using the hierarchical update rules, a given input data stream was allowed to pass through each hidden layer with intermediate operations, and then finally reached the output end.Preference structureThe correlation between different production behavior factors (e.g., irrigation levels) and different natural factors (e.g., soil organic matter) differs in agricultural production. However, the traditional fully connected neural network has the characteristic that nodes of one layer are fully connected with all nodes of subsequent layers, resulting in the neurons between production behavior factors and natural factors with very weak correlation still all being connected. Conversely, connections between neurons corresponding to factors with solid correlations are not strengthened.Therefore, in this study the preference value module was specially developed. By first calculating the correlation and significance between different production behavior factors (irrigation amount, N rate) and different soil fertility factors (organic matter, total nitrogen, total salt and pH), the preference value between the above two types of variables was calculated, and the preference matrix was constructed. Then the Hadamard product of the weight matrix and preference matrix was used to realize the artificial intervention and guidance to the neural network’s learning process.In order to reduce the adverse impact of non-normality of data on correlation analysis as much as possible, this study rank-based inverse normal (RIN) transformations (i.e., conversion to rank score) methods were used to normally process the data28. The RIN transformation function used here is as follows:$$f(x)={Phi }^{-1}left(frac{{x}_{r}-frac{1}{2}}{n}right)$$
(2)

where Φ–1 is the inverse normal cumulative distribution function, and n is the sample size.The normal cumulative distribution function is represented as follows: for discrete variables, the sum of probabilities of all values less than or equal to a, and its formula is as shown below:$${F}_{X}(a)=P(Xle a)$$
(3)
The RIN normalized conversion values meet the requirements of normal distribution, Pearson correlation analysis and t-test can be directly performed, and the formula used was as follows:$$r(X,Y)=frac{mathrm{Cov}(X,Y)}{sqrt{left(mathrm{Var}left[Xright]mathrm{Var}left[mathrm{Y}right]right)}}$$
(4)

where r (X, Y) is the Pearson Correlation Coefficient, Var [X] is the variance of X, and Var [Y] is the variance of Y, Cov (X, Y) is the covariance of X and Y, which represents the overall error of the two variables. The t-test is performed on the normalized data after rank-based inverse normal (RIN) transformation method, and the formula is as follows:$$t=sqrt{frac{n-2}{1-{r}^{2}}}$$
(5)

where n is the number of samples, and r represents the Pearson Correlation Coefficient. Preference value is the concentrated embodiment of correlation and significance between variables, and the calculation formula is as follows:$${PV}_{ij}=frac{r({X}_{i},{Y}_{j})}{{P}_{ij}+e}$$
(6)

where PVij represents the preference values between the variables Xi and Yj, Xi represents the ith production behavior factor (e.g., irrigation amount), and Yj represents the jth soil fertility factor (e.g., soil organic matter content), ({P}_{ij}) is obtained by looking up the table based on the t, and e is a constant, taking 0.001 in order to prevent the denominator of the formula from being 0.In order to make the preference values of the various indicators in the same order of magnitude more stable, the preference values were normalized:$${PV}_{normal}=pm frac{left|{PV}_{i}-{PV}_{avg}right|}{sqrt{frac{sum_{i=1}^{N}{({PV}_{i}-{PV}_{avg})}^{2}}{N-1}}}$$
(7)

where N represents the number of variables related to the experimental treatments, PVi -PVavg takes the absolute value, while the positive or negative values of the PVnormal were determined by the positive or negative values of the correlation r.The PNN integrated the preference matrixes into the neural network structures by identifying the Hadamard products of the learnable weights between the preference matrixes and the input and output data. By referring to Eq. (1) in the hierarchical affine transformation, the preference constraint of PNN could be expressed as follows:$${h}_{l}({h}_{l-1};{W}_{l},{b}_{l})={h}_{l-1}^{T}{W}_{l}odot P+{b}_{l}$$
(8)

where P is the preference matrix calculated by Eq. (8), and ⊙ represents the Hadamard product of the corresponding elements of the matrix. The structure of preference neural network and preference value are shown in Figs. 5 and 6.Figure 5Schematic diagram of the preference connection structures of the preference neural networks. The depth of the network detailed in the figure only illustrates the preference connection structure (for a better demonstration), and does not indicate the depth of the PNN used in the experiment.Full size imageFigure 6PVnormal between production behavior factors and natural factors. Since soil depth, days, irrigation amount and N rate were all artificially set variables, and there was no objective correlation in the data set. Therefore, the preference values among these variables were default e = 0.001.Full size imageHyper-parameters of PNNWe conducted experiments on the datasets with varying the hyper-parameters (such as the number of PNN layers and hidden layers, the number of nodes in each layer, learning rate, dropout rate and batch size) to understand that how the Hyper-parameters impact on the performance of PNN.We select the activation function and learning rate by referring to the neural network structure commonly used in similar fields (1 hidden layer and 64 hidden nodes)29,30. It is found that ReLU has better performance than other activation functions (sigmoid, tanh). The performance is best when the learning rate is around 0.005. It is generally believed that neural networks with more hidden layers are able, with the same number of resources, to address more complex problems31, but excessively increasing network depth will easily lead to overfitting32. Since there is no direct method to select the optimal number of hidden layers and nodes33, this study first calculated the structure of one hidden layer and 64 nodes in each layer, and found that the combined effect was poor (R2 of irrigation and nitrogen application were 0.3971 and 0.4124, respectively). Therefore, the trial-and-error method is adopted. The number of hidden layers starts from 1 and is incremented by 1 to test the maximum number of 10 hidden layers. The number of nodes in each layer were tested with a maximum number of 100 hidden neurons, starting with 5 and increasing by 5.We found that when the number of hidden layers of PNN exceeds 6, and the number of nodes in each layer exceeds 65, the performance will drop significantly. The reason behind this phenomenon could be the current dataset size is insufficient for larger scale of the PNN model. In the consideration of that the size of new dataset we can obtain very year is similar to the current dataset size, we believe that current hyper-paramter settings of PNN is in a reasonable condition.After that, the number of layers was fixed as 6, and the number of nodes in each layer were tested 10 times with 60 as the starting point and 1 as the increment, we found that when the number of nodes was 64, the improvement of the fit degree was no longer noticeable. On this basis, we changed different activation functions and learning rate again, and found that PNN still has the best performance when the activation function is ReLU and the learning rate is 0.005. Then, different batch sizes and dropout rates were tried. The two parameters had weaker effects on the performance than the other parameters, and the performance was optimal at 256 and 0.1, respectively.The hyper-parameters include:

1.

number of PNN layers;

2.

number of hidden layers;

3.

types of activation function;

4.

percentage of dropout;

5.

learning rate;

6.

loss function;

7.

optimizer;

8.

batch size;

9.

number of epochs;

10.

number of workers.

The ideal PNN structure for the study comprises these layers:

1.

number of PNN layers is 8;

2.

number of hidden layers is 6;

3.

Fully connected layers with 64 nodes and ReLU activation function

4.

dropout with 0.1.

5.

the learning rate is 0.005;

6.

loss function is Huber Loss Methods (HLM);

7.

optimizer: ADAM;

8.

epochs is 500;

9.

the batch size is 256;

10.

number of workers is 6.

Hyper-parameters of other modelsLR algorithms and LOR do not have hyper-parameters that need to be adjusted. A part of the hyper-parameters of the SVR model was determined by referring to Guan Xiaoyan’s research34, and a part of the hyper-parameters of the BPNN model was determined by referring to Gu Jian’s research27. RMLP takes the same hyperparameters as PNN. The hyperparameters of SVR and BPNN models are shown in Table 5.Table 5 Hyper-parameters of other model.Full size tableModel performance evaluationThe proposed PNN model was trained and validated using the field measured data from 2020 and the performance achievements of PNN were evaluated by the root mean square errors, mean square errors, and mean absolute errors as follows:$$RMSE=sqrt{frac{{sum }_{i=1}^{n}{({y}_{ipre}-{y}_{imea})}^{2}}{n}}$$
(9)
$${R}^{2}=1-frac{{sum }_{i=1}^{n}{({y}_{ipre}-{y}_{imea})}^{2}}{{sum }_{i=1}^{n}{({y}_{ipre}-{y}_{iavg})}^{2}}$$
(10)
$$MAE=frac{{sum }_{i=1}^{n}left|{y}_{ipre}-{y}_{iavg}right|}{n}$$
(11)
Model multidimensional fertility targetsThe soil fertility grade classification of soil organic matter, soil total nitrogen content and salt content in this study was based on the soil fertility grade classification results by the Agriculture and Animal Husbandry Bureau of Bayannur City, along with the local standard Technical Specifications for the Assessment and Rating Criteria of Cultivated Land Quality (DB 15/T 1086, 2016), as the shown in Tables 6 and 7.Table 6 Soil organic matter and Soil total nitrogen degrees.Full size tableTable 7 Grading of the salinization degrees.Full size tableIn the evaluation system of soil fertility referencing the Technical Specifications for Assessment and Rating Criteria of Cultivated Land Quality (DB 15/T 1086, 2016), the pH was divided into four grades according to the membership degrees of the land productivity evaluations, as detailed in Table 8.Table 8 pH grading degrees of the cultivated land.Full size tableBased on the classification standard of soil fertility obtained by the Bureau of Agriculture and Animal Husbandry of Bayannur City, when the farmland soil is at the high fertility level, the soil organic matter and total nitrogen content should be more than 20 g/kg and 1.6 g/kg, respectively. Soil salt content was less than 2 g/kg. Meanwhile, the pH value is kept between 6.5 and 7.5. More