CN117272813B - Soil humidity prediction method based on water balance constraint deep learning - Google Patents

Soil humidity prediction method based on water balance constraint deep learning Download PDF

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CN117272813B
CN117272813B CN202311250109.6A CN202311250109A CN117272813B CN 117272813 B CN117272813 B CN 117272813B CN 202311250109 A CN202311250109 A CN 202311250109A CN 117272813 B CN117272813 B CN 117272813B
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李清亮
闫森
张程
上官微
朱金龙
李叶光
金小淳
陈霄
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Abstract

The invention provides a soil humidity prediction method based on water balance constraint deep learning, which comprises the following steps: obtaining model input variables, wherein the variables comprise surface data, forced data and soil water holding capacity; inputting an input variable into a long-short-term memory LSTM model, and simultaneously introducing a loss function designed by a physical mechanism to guide the LSTM model to learn physical information in data, so as to guide the LSTM model to train and obtain an LSTM network model based on physical guidance; the loss function is an absolute water balance loss function of inflow water equal to outflow water or a monotonic loss function designed by utilizing a monotonic relation among rainfall, evaporation and soil humidity; and the prediction of soil humidity is realized by using an LSTM network model based on physical guidance. The two deep learning models based on the physical mechanism provided by the invention are improved in accuracy and physical consistency in the process of simulating global surface water flow.

Description

Soil humidity prediction method based on water balance constraint deep learning
Technical Field
The invention relates to the technical field of machine deep learning, in particular to a soil humidity prediction method based on water balance constraint deep learning.
Background
Soil Moisture (SM) is a key variable of the climate system, which has an important impact on water, energy and bio-geochemical circulation. Participate in a global set of feedback and play an important role in climate change prediction. In the agricultural field, the irrigation plan and the price regulation of agricultural products can be improved, and agricultural pests and water pollution diffusion can be prevented and controlled; in the hydrologic field, providing indication meaning for the improvement of hydrologic process parameterization scheme in land mode, and influencing the performance of physical mode and the evaluation of wet and dry conditions; has important indication function in the field of climate change. However, the space-time variation of SM is highly heterogeneous, controlled by various factors such as soil properties, precipitation and vegetation, which presents a great challenge for accurate prediction of SM. Over the past several decades, researchers have attempted to develop various models to capture the trend of SM changes. These models can be divided into two main categories: a model based on a physical process, and an empirical model based on data driving.
In recent years, with rapid development of computer hardware, a data driving model represented by deep learning (DEEP LEARNING, DL) has strong nonlinear fitting capability, wherein a long-short-term memory network (LSTM) can effectively capture and process long-term dependency relationships by introducing a gating mechanism and memory neurons, and SM just has short-term memory. Therefore, the LSTM model is widely used in the SM forecasting field. However, there are also problems with the "pure" DL model, which is sensitive to hyper-parameters, which is often a model with multiple hyper-parameters, and in order to optimize the parameterization scheme, a large number of parameters must be tuned to achieve optimal model performance, in which process traceability to the laws of physics is often lost.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a soil humidity prediction method based on water balance constraint deep learning, which comprises the following steps:
obtaining model input variables, wherein the variables comprise surface data, forced data and soil water holding capacity;
Inputting the input variable into a long-short-term memory LSTM model, and simultaneously introducing a loss function designed by a physical mechanism to guide the LSTM model to learn physical information in data, so as to guide the LSTM model to train and obtain an LSTM network model based on physical guidance; the loss function is an absolute water balance loss function of inflow water equal to outflow water or a monotonic loss function designed by utilizing a monotonic relation among rainfall, evaporation and soil humidity;
And predicting the soil humidity by using the LSTM network model based on physical guidance.
As a further illustration of the present invention, the forced data includes a 2m temperature, a10 m U type wind component, a10 meter V type wind component, a humidity ratio, a surface pressure, and a total rainfall; the surface data includes soil temperature, short wave radiation, long wave radiation, and total evaporation.
As a further illustration of the present invention, the specific structure of the LSTM model is as follows:
i[t]＝σ(Wix[t]+Uih[t-1]+bi) (1)
f[t]＝σ(Wfx[t]+Ufh[t-1]+bf) (2)
g[t]＝tanh(Wgx[t]+Ugh[t-1]+bg) (3)
o[t]＝σ(Woχ[t]+Uoh[t-1]+bo) (4)
Where i [ t ], f [ t ] and ot [ t ] represent the input gate, forget gate and output gate of LSTM, respectively, g [ t ] is a neuron input, x [ t ] is a network input of time step t, h [ t-1] is an output of LSTM, also called a cyclic input, c [ t-1] is a neuron state of the last time step, the neuron state represents the memory of the system at the current time, and is initialized in the form of an all-zero vector; sigma (·) is a Sigmoid activation function; w, U and b are calibrated parameters, the subscripts indicating which gate a particular parameter matrix/vector is associated with; tanh (·) is a hyperbolic tangent activation function for introducing nonlinearities in neuron inputs and circulatory inputs; representing element-by-element multiplication; /(I) Representing the final predicted value of SM.
As a further illustration of the invention, the absolute moisture balance loss function is as follows:
Loss1＝LossRMSE+LossWB (8)
equation (8) is an absolute moisture balance Loss function, where Loss RMSE is the sum of soil moisture observations SM and the predicted soil moisture value Root mean square error between (d) and (d) as shown in formula (9); loss WB is a Loss function designed by the surface water balance principle that affects SM by describing the increase or decrease in water volume into and out of the system, as follows:
Wt＝Wint-Woutt (10)
In formula (10), W int represents the amount of moisture from precipitation and condensation flowing into the soil; w outt represents the evaporated moisture, i.e., moisture that does not enter or exit the soil; w t represents the amount of water flowing into the system at the current time; in the formula (11), the predicted value of the moisture W t and the soil humidity entering the system at the current moment is calculated by using the absolute value function And the difference between the soil humidity observation value SM t-1 at the previous time; when the difference is closer to 0, it indicates that the moisture and soil humidity entering the system are closer to the water balance.
As a further illustration of the invention, the monotonicity loss function is as follows:
Loss2＝LossRMSE+LossPHY (12)
Equation (12) is a monotonic Loss function, and Loss RMSE is the sum of the soil moisture observations SM and the predicted soil moisture value Root mean square error between the soil humidity observation values, loss PHY is a Loss function designed by fusing monotonic relations existing between rainfall, evaporation and soil humidity observation values SM; in the formula (13), Δw t represents the difference between the amount of water entering the surface water balance system at the current time and the amount of water entering the surface water balance system at the previous time, when the difference is 0, which indicates that the amount of water entering and exiting the system at the current time is not changed from the amount of water at the previous time, then the current time Loss PHY should be 0;0 is a set limit, and only when the current moment of water entering the surface water balance system and the water quantity change entering the surface water balance system at the previous moment of water entering the surface water balance system are increased or reduced, the water quantity change is involved in the calculation of the Loss PHY;
In equation (14), by assigning an initial value to ΔW t, it is noted that the amount of water entering and exiting the system at the current time is changed from the amount of water at the previous time;
In the formula (15), SM t-1 is an observed value of soil humidity at the previous time, Is the predicted value of the soil humidity at the current moment.
Compared with the prior art, the invention has the following beneficial technical effects:
the two deep learning models based on the physical mechanism provided by the invention are improved in accuracy and physical consistency in the process of simulating global surface water flow.
Drawings
FIG. 1 is a flow chart of a surface water model established by using a physically guided LSTM network in the invention; (T2M is 2M temperature (K), U10 is 10M U type wind power component (M/s), V10 is 10M V type wind power component (M/s), Q is humidity ratio (kg/kg), SP is surface pressure (Pa), TP is total rainfall (M), STL is soil temperature (K), SSRD is short wave radiation (J/M 2), STRD is long wave radiation (J/M 2), E is total evaporation (M), and SC is soil water holding property.
FIG. 2 is a physical knowledge-guided performance index improvement graph of 2 models and an LSTM model for a prediction day (0 d) SM (a, b, c represent Bias, RMSE, R improvement graphs of PHYs-LSTM model and LSTM model prediction day SM, d, e, f represent Bias, RMSE, R improvement graph of WB-LSTM model and LSTM model prediction day SM, respectively. Light gray part in the graph indicates that the prediction effect of the model in the region is better than that of the LSTM model, dark gray indicates that the prediction effect of the model in the region is inferior to that of the LSTM model, the darkness of color indicates the improvement degree, and the darkness of color indicates that the improvement effect of the model is better or worse.)
FIG. 3 is a graph of improvement in performance index of 2 models and LSTM model guided by physical knowledge (a, b, c represent Bias, RMSE, R improvement graphs of PHYs-LSTM model and LSTM model for predicting SM 1 day in the future, respectively; d, e, f represent Bias, RMSE, R improvement graphs of WB-LSTM model and LSTM model for predicting SM 1 day in the future, respectively. Light gray part in the graph indicates that the prediction effect of the model in the region is better than that of LSTM model, dark gray indicates that the prediction effect of the model in the region is inferior to that of LSTM model, dark and light of color indicates improvement degree, and darker color indicates that the improvement effect of the model is better or worse.)
FIG. 4 is a graph of physical knowledge-directed physical consistency improvement of 2 models and LSTM models for predicting the same day (0 d) and future 1 day (1 d) of SM (a, c represent the physical consistency improvement of PHYs-LSTM model and LSTM model for predicting the same day (0 d) and future 1 day of SM, respectively; b, d represent the physical consistency improvement of WB-LSTM model and LSTM model for predicting the same day and future 1 day of SM, respectively)
Detailed Description
In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of one or more embodiments. It may be evident, however, that such embodiment(s) may be practiced without these specific details.
Specific embodiments of the present application will be described in detail below with reference to the accompanying drawings.
The soil humidity prediction method based on water balance constraint deep learning provided by the invention comprises the following steps:
s110, acquiring model input variables, wherein the variables comprise surface data, forced data and soil water holding capacity;
specifically, the forced data comprises 2m temperature, 10m U type wind power components, 10m V type wind power components, humidity ratio, surface pressure and total rainfall; the surface data includes soil temperature, short wave radiation, long wave radiation, and total evaporation. Variables used in the present application, the data of which are from the ERA5-Land reanalyzed dataset; wherein the soil water holding capacity (a spatial parameter connecting the atmosphere and the terrestrial ecosystem) is input as a static variable into the model.
S120, inputting an input variable into a long-short-term memory LSTM model, and simultaneously introducing a loss function designed by a physical mechanism to guide the LSTM model to learn physical information in data, so as to guide the LSTM model to train and obtain an LSTM network model based on physical guidance; the loss function is an absolute water balance loss function of inflow water equal to outflow water or a monotonic loss function designed by utilizing a monotonic relation among rainfall, evaporation and soil humidity;
The specific structure of the LSTM model is as follows:
i[t]＝σ(Wix[t]+Uih[t-1]+bi) (1)
f[t]＝σ(Wfx[t]+Ufh[t-1]+bf) (2)
g[t]＝tanh(Wgx[t]+Ugh[t-1]+bg) (3)
o[t]＝σ(Woχ[t]+Uoh[t-1]+bo) (4)
Where i [ t ], f [ t ] and ot [ t ] represent the input gate, forget gate and output gate of LSTM, respectively, g [ t ] is a neuron input, x [ t ] is a network input of time step t, h [ t-1] is an output of LSTM, also called a cyclic input, c [ t-1] is a neuron state of the last time step, the neuron state represents the memory of the system at the current time, and is initialized in the form of an all-zero vector; sigma (·) is a Sigmoid activation function; w, U and b are calibrated parameters, the subscripts indicating which gate a particular parameter matrix/vector is associated with; tanh (·) is a hyperbolic tangent activation function for introducing nonlinearities in neuron inputs and circulatory inputs; representing element-by-element multiplication; /(I) Representing the final predicted value of SM.
The theoretical basis of the LSTM model is the law of conservation of mass. The mass conservation is a main law of realizing a water balance model and a hydrologic model, is a key component for evaluating SM prediction physical rationality, designs two loss functions based on water balance, and is used for guiding an LSTM model to train, and the two loss functions are coupled to form a prediction model main body framework (figure 1) of the application.
The main idea of the design of the loss function is to consider that the variation of SM (the difference between SM at the previous moment and SM at the current moment) and the moisture of the inflowing soil (precipitation at the current moment) minus the moisture of the outflowing soil (evapotranspiration at the current moment) should be equal (absolute moisture balance) or the variation of both should be correlated (with a certain monotonicity). That is, when the amount of water entering the system at the current moment is increased compared with the amount of water entering the system at the last moment, SM should be increased; when the water quantity entering the system at the current moment is reduced compared with the water quantity entering the system at the last moment, SM should be reduced; when the amount of water entering the system at the present moment is not significantly changed, the SM should also be changed very little. Thus, the present application creates two loss functions according to the above principle, one is that SM inflow water is equal to outflow water (absolute moisture balance loss function), and the other is that there is physical monotonicity by SM inflow water (rainfall), outflow water (evaporation) and SM variation (physical monotonicity loss function); in particular, the method comprises the steps of,
The absolute moisture balance loss function is as follows:
Loss1＝LossRMSE+LossWB (8)
equation (8) is an absolute moisture balance Loss function, where Loss RMSE is the sum of soil moisture observations SM and the predicted soil moisture value Root mean square error between (d) and (d) as shown in formula (9); loss WB is a Loss function designed by the surface water balance principle that affects SM by describing the increase or decrease in water volume into and out of the system, as follows:
Wt＝Wint-Woutt (10)
In formula (10), W int represents the amount of moisture from precipitation and condensation flowing into the soil; w outt represents the evaporated moisture, i.e., moisture that does not enter or exit the soil; w t represents the amount of water flowing into the system at the current time; in the formula (11), the predicted value of the moisture W t and the soil humidity entering the system at the current moment is calculated by using the absolute value function And the difference between the soil humidity observation value SM t-1 at the previous time; when the difference is closer to 0, it indicates that the moisture and soil humidity entering the system are closer to the water balance.
As a further illustration of the invention, the monotonicity loss function is as follows:
Loss2＝LossRMSE+LossPHY (12)
Equation (12) is a monotonic Loss function, and Loss RMSE is the sum of the soil moisture observations SM and the predicted soil moisture value Root mean square error between the soil humidity observation values, loss PHY is a Loss function designed by fusing monotonic relations existing between rainfall, evaporation and soil humidity observation values SM; in the formula (13), Δw t represents the difference between the amount of water entering the surface water balance system at the current time and the amount of water entering the surface water balance system at the previous time, when the difference is 0, which indicates that the amount of water entering and exiting the system at the current time is not changed from the amount of water at the previous time, then the current time Loss PHY should be 0;0 is a set limit, and only when the current moment of water entering the surface water balance system and the water quantity change entering the surface water balance system at the previous moment of water entering the surface water balance system are increased or reduced, the water quantity change is involved in the calculation of the Loss PHY;
In equation (14), by assigning an initial value to ΔW t, it is noted that the amount of water entering and exiting the system at the current time is changed from the amount of water at the previous time; in theory, SM should also change and there is a positive correlation with the former change. However, since the design of the loss function does not completely include all variables (e.g., surface runoffs and groundwater fractions) in the whole surface water system, either the model uses hysteretic weather forces and land data, or the observed data and the actual data deviate. Therefore, the data of the non-positive correlation change between the inflow and outflow water and the SM in the training data needs to be removed, and the calculation of the Loss PHY is not involved. The function of equation (14) is to achieve this function.
In the formula (15), SM t-1 is an observed value of soil humidity at the previous time,Is the predicted value of the soil humidity at the current moment. The ReLU function is added to keep the predicted change in SM consistent with the change in ΔW t in equation (13). For example, when ΔW t is 1, it indicates that the current amount of water into the system is increasing, and there is a positive correlation between the changes in both, at which point SM should be greater than SM t-1 at the previous time. When ΔW t is-1, this indicates that the current amount of water into the system is decreasing, and the SM at this time should be less than SM t-1 at the previous time.
S130, predicting the soil humidity by using an LSTM network model based on physical guidance.
The prediction accuracy of the prediction method provided by the invention is analyzed as follows:
the present application uses the following criteria to evaluate the predictive performance of the above DL model, including pearson correlation coefficient (R), root Mean Square Error (RMSE), and Bias (Bias). R may measure how the model captures the changes in the data, RMSE may measure the accuracy of model predictions, bias may measure how far the predicted values deviate from the observed values, and the calculation formula for these criteria is as follows:
Wherein y i is the observed value in the ERA5-Land dataset at the ith moment, Is the predicted value of DL model at the ith moment,/>Is the average of observed values,/>Is the average of the predicted values.
In order to ensure that a physical mechanism is integrated into a deep learning model, the application introduces a new evaluation index, namely physical consistency, besides adopting a traditional evaluation criterion. The index is calculated by substituting the predicted result into a formula (19), if the calculated result is positive, the change trend of SM and the change trend of DeltaW t are indicated to be in negative correlation, namely, a result of physical inconsistency exists; if the calculation result is negative, the variation trend of SM and the variation trend of DeltaW t are positively correlated, namely, a result of physical consistency exists; if the calculation result is 0, it means that Δw t or SM is not changed, and therefore no statistics is performed. Such a judgment index can effectively measure the consistency between the model output result and the physical rule.
Evaluation results: wherein the PHYs-LSTM model represents: physical monotonicity loss function-LSTM model; WB-LSTM model representation: absolute water balance loss function-LSTM model.
(1) Influence of different training periods on model performance
Table 1 is SM prediction results for different times (day and future 1 day, respectively) of training different DL models using different training periods. Three DL models were trained using 2, 3, 5 years of data, predicting the SM for the day (0 d) and the future 1 day (1 d), respectively. The accuracy of all models decreases with decreasing training data sets. The performance metrics of the predictive results for PHYs-LSTM were superior to LSTM (higher R, lower RMSE, bias) in all experiments, and the performance metrics of the PHYs-LSTM model trained with two years of data volume (2018-2019) exceeded the LSTM model trained with five years of data volume (2015-2019). Whereas WB-LSTM only occasionally produces results superior to LSTM in the index R (A1, B0, B1, C1).
Table 1 results of different time predictions for different training phases for three models
(2) Influence of different prediction times on model performance
FIGS. 2 and 3 are graphs of performance index improvement of the PHYs-LSTM model and WB-LSTM model and LSTM model, respectively, for the predicted day and the future 1 day. It can be seen from a, b, c of fig. 2,3 that the overall effect of the PHYs-LSTM model is better than that of the LSTM model both on the predicted day and on the future 1 day worldwide. In addition, d, e, f in fig. 2 and 3, it can be seen that the overall improvement effect of the WB-LSTM model is worse than that of the LSTM model, both on the day of prediction and on the future 1 day of SM, but the improvement effect of the WB-LSTM model is better than that of the LSTM model in extremely arid desert regions such as north africa, middle asia, west north america, etc., especially when the future day of prediction is performed (fig. 3), and these regions are improved more than that of the LSTM model, even the PHYs-LSTM model. We compared SM changes in desert areas with water in and out of the system in the training data and found that the difference between the two is small (both are very close to 0) while the difference between the other areas is relatively large. This is probably due to the fact that the desert area has less rainfall, the vegetation is sparse, the increase and decrease of SM mostly depend on a small amount of rainfall and evaporation, and the ground surface water balance state of the area can be approximated by only two variables of rainfall and evaporation.
(3) Physical consistency
Figure 4 is a graph of physical consistency improvement of 2 models and LSTM model for predicting the current day (0 d) and future 1 day (1 d) SM, guided by physical knowledge. As can be seen from fig. 4 (a), the PHYs-LSTM model has a significant effect of improving physical consistency in most regions worldwide when the SM is predicted on the day, but has a significant negative effect of improving physical consistency in northeast and european regions in north america and in north asia when the SM is predicted for 1 day in the future, which may be due to cold weather in high latitude regions, long periods of freezing and snow accumulation compared to the rest of the regions, and less monotonous states between rainfall, evaporation and SM, resulting in physical consistency in the region that is inferior to that of the conventional LSTM model. In connection with fig. 2 and 3, we found that although the WB-LSTM model is lower in accuracy of predicting SM than the LSTM model, the prediction effect of the WB-LSTM model is optimal in 3 DL models both on the prediction day and on the prediction future 1 day, and the effect is very obvious in the region except malaysia worldwide, probably because all around malaysia islands are oceans, evaporation from the oceans is counted to land areas, disturbing the surface water balance in this area. It follows that poor accuracy of the DL model does not necessarily represent that this model is not desirable in all respects, but rather that the worst-accuracy WB-LSTM model out of the 3 models performs most prominently in terms of physical consistency. This illustrates that rainfall and evaporation are two essential variables in the design of the surface water balance.
In summary, the two physical-boot-based long-short-term memory (LSTM) networks proposed by the present application are referred to as PHYs-LSTM and WB-LSTM, respectively. The results of the PHYs-LSTM network show that the performance of the network is obviously superior to that of the traditional LSTM method. Specifically, when the soil humidity on the day and 1 day in the future is predicted using the PHYs-LSTM model in the global area, the values of pearson correlation coefficient (R), root Mean Square Error (RMSE), and Bias (Bias) are 0.860, 0.030, 0.022, and 0.787, 0.034, 0.025, respectively, achieving the best performance. In addition to the performance improvement, the two physical boot models also provide a significant improvement in physical consistency over conventional LSTM. Experimental results show that the physical mechanism is introduced to enhance the prediction capability of the soil humidity model based on data driving.
It will be evident to those skilled in the art that the invention is not limited to the details of the foregoing illustrative embodiments, and that the present invention may be embodied in other specific forms without departing from the spirit or essential characteristics thereof.
The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive, the scope of the invention being indicated by the appended claims rather than by the foregoing description, and all changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein. Any reference signs in the claims shall not be construed as limiting the claim concerned.
Furthermore, it is evident that the word "comprising" does not exclude other elements or steps, and that the singular does not exclude a plurality. A plurality of units or means recited in the system claims can also be implemented by means of software or hardware by means of one unit or means. The terms second, etc. are used to denote a name, but not any particular order.
Finally, it should be noted that the above-mentioned embodiments are merely for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made to the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention.

Claims (2)

1. The soil humidity prediction method based on water balance constraint deep learning is characterized by comprising the following steps of:
Obtaining model input variables, wherein the variables comprise surface data, forced data and soil water holding capacity; the forced data comprise 2m temperature, 10m U type wind power components, 10m V type wind power components, humidity ratio, surface pressure and total rainfall; the surface data comprise soil temperature, short wave radiation, long wave radiation and total evaporation capacity;
Inputting the input variable into a long-short-term memory LSTM model, and simultaneously introducing a loss function designed by a physical mechanism to guide the LSTM model to learn physical information in data, so as to guide the LSTM model to train and obtain an LSTM network model based on physical guidance; the loss function is a monotonic loss function designed by utilizing a monotonic relation among rainfall, evaporation and soil humidity;
The monotonicity loss function is as follows:
(12)
(13)
Equation (12) is a monotonicity loss function, Is the sum of soil moisture observations SM and predicted soil moisture value/>Root mean square error between/(The loss function is designed by fusing monotonic relation between rainfall, evaporation and soil humidity observation value SM; in equation (13)/(Representing the difference between the water quantity entering the surface water balance system at the current moment and the water quantity entering the surface water balance system at the last moment, when the value is 0, the water quantity entering and exiting the surface water balance system at the current moment is unchanged from the water quantity at the last moment, and the current moment/>Should be 0;0 is a set limit, and the water quantity change entering the surface water balance system at the current moment and the water quantity change entering the surface water balance system at the last moment are only increased or reduced, so that the water quantity change is participated in/>Is calculated;
(14)
in formula (14), by giving Giving an initial value to mark that the water quantity entering and exiting the system at the current moment is changed compared with the water quantity at the last moment;
(15)
In the formula (15) of the present invention, Is the observed value of soil humidity at the last moment,/>Is the predicted value of the soil humidity at the current moment;
And predicting the soil humidity by using the LSTM network model based on physical guidance.
2. The soil humidity prediction method based on water balance constraint deep learning of claim 1, wherein the specific structure of the LSTM model is as follows:
(1)
(2)
(3)
(4)
(5)
(6)
(7)
Wherein, And/>Input gate, forget gate and output gate representing LSTM respectively,/>Is a neuron input,/>Is the network input of time step t,/>Is the output of the LSTM, also known as the loop input,Is the neuron state of the last time step, the neuron state represents the memory of the system of the current time, and is initialized in the form of an all-zero vector; /(I)Is a Sigmoid activation function; w, U and b are calibrated parameters, the subscripts indicating which gate a particular parameter matrix/vector is associated with; tanh (·) is a hyperbolic tangent activation function for introducing nonlinearities in neuron inputs and circulatory inputs; /(I)Representing element-by-element multiplication; /(I)Representing the final predicted value of SM.
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