Soil water and salt prediction method and system fusing physical information and deep learning

Abstract

The invention discloses a soil water and salt prediction method and system fusing physical information and deep learning, and is applied to the technical field of soil water and salt prediction. The method comprises the following steps: acquiring multi-source time sequence data of an arid farmland area and preprocessing the multi-source time sequence data; constructing a physical information embedded long short-term memory network PI-LSTM, converting a moisture migration equation, a salinity migration equation and boundary conditions into loss functions, and constructing a composite loss function; the PI-LSTM is trained, and parameters of the PI-LSTM are optimized by minimizing the composite loss function; and collecting the PI-LSTM trained by real-time multi-source time sequence data, and predicting soil water and salt data. According to the method, the Richards equation, the solute transport equation and the boundary condition are converted into differentiable physical loss functions, and the differentiable physical loss functions are embedded into the training process of the LSTM network, so that physical law and data driven end-to-end collaborative learning is realized, and the generalization ability and robustness of the model are improved.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of soil water and salt prediction, and more particularly to a soil water and salt prediction method and system fusing physical information and deep learning. BACKGROUND

[0002] Soil water and salt dynamics are the key processes of water and salt migration, distribution and balance in the environment conditions in the agricultural ecosystem in a dry region, and the variation law thereof directly affects crop root water absorption, nutrient availability and sustainability of the agricultural ecosystem. In the dry region with rare precipitation and strong evaporation, water resources become the most critical limiting factor for agricultural development. In order to maximize water use efficiency and ensure crop emergence and growth, the mulching (such as plastic film mulching) technology has been widely used and becomes a crucial drought-resistant and water-saving measure in the region. Under the planting mode of the mulched farmland in the dry region, the application of the mulching technology plays a positive role in soil conservation, temperature increase and weed suppression, and also significantly changes the water and heat exchange process between the soil and the atmosphere, thereby causing a profound change in the water and salt transport path and accumulation mode. The physical barrier formed by the mulching effectively blocks the direct evaporation of soil water under the film, so that the water in the crop root zone can be kept, however, this process also leads to the weakening of the upward water transport driven by soil evaporation. The change of the water transport path also promotes the redistribution of salt in the horizontal direction, the lateral transport of water under the film is enhanced, and combined with the infiltration of irrigation water or precipitation, the salt is easy to transport and accumulate to the exposed area between the films or the edge of the crop root zone, forming a typical salt spot or local high-salt area. In addition, the increase of soil temperature and the condensation of gaseous water under the condition of mulching further increase the complexity of the water and salt coupling transport process, and cause the significant enhancement of the spatial heterogeneity of water and salt.

[0003] Due to the variation of the water and salt transport process induced by the mulching of farmland, the traditional prediction model is also challenged. For the model based on the physical mechanism (such as HYDRUS, SWAP, etc.), the model is usually established on the basis of the assumption of homogeneous or simplified layered soil, and it is difficult to accurately depict the non-uniform water flow field and solute field caused by the plastic film boundary in the mulched farmland; secondly, the key parameters (such as unsaturated hydraulic conductivity, dispersion, etc.) required by the model have strong spatial variability at the mulching interface, and the traditional sampling method is difficult to obtain the representative parameter value; furthermore, under the condition of mulching, the soil water evaporation process is jointly controlled by the gaseous diffusion under the film and the liquid evaporation between the films, and the setting of the boundary condition is much more complex than that of the traditional bare land, which increases the difficulty of model construction and solution.

[0004] For pure data-driven models, the differences in water and salt transport characteristics between the under-mulch and inter-mulch areas under mulch conditions are huge, resulting in highly uneven spatial distribution of monitoring data. The water in the under-mulch area remains relatively stable, and the salt accumulation is weak, while the evaporation in the inter-mulch bare area is strong, and a salt-enriched area is easily formed. This structural imbalance makes the training data set obviously skewed. The model is prone to overfitting to the water and salt characteristics of the under-mulch area with a large amount of data, and lacks the ability to capture the formation mechanism of key salt spots in the inter-mulch area, affecting the overall prediction accuracy. In addition, the transport of water and salt in the mulch system is essentially dominated by physical processes, such as water infiltration and redistribution, salt convection and diffusion mechanisms, which have strong physical constraints. If the model only relies on statistical associations in historical data without embedding the corresponding physical laws, its generalization ability will be severely limited when faced with irrigation strategies or extreme climate situations that have not been experienced, and the prediction results may deviate from the actual physical process, reducing its reliability and applicability in farmland management decisions.

[0005] Therefore, it is important to incorporate physical mechanisms into data-driven models to enable the model to learn patterns and rules from both data and physical mechanisms for predicting soil water and salt data. However, existing fusion methods mostly rely on relatively simple machine learning models, and have not fully exploited the potential of deep neural networks in feature extraction and nonlinear relationship modeling. Current fusion strategies mostly stop at data augmentation at the training set level or statistical averaging at the model output level, and have not fully explored how to effectively combine actual observation data with more structured physical constraints in an end-to-end learning framework, limiting the model's generalization ability and mechanism consistency in soil water and salt dynamic prediction. Therefore, how to provide a soil water and salt prediction method and system that combines physical information and deep learning is a problem that needs to be solved by those skilled in the art. SUMMARY

[0006] Therefore, the present application provides a soil water and salt prediction method and system that combines physical information and deep learning, which converts the Richards equation, solute transport equation, and boundary conditions that describe water and salt transport into differentiable physical loss functions, embeds them into the training process of the LSTM network, and realizes end-to-end collaborative learning of physical laws and data-driven learning, thereby improving the prediction accuracy, robustness, and generalization ability of the model in the mulch farmland environment in arid regions.

[0007] To achieve the above purpose, the present application provides the following technical solutions: A soil water and salt prediction method that combines physical information and deep learning, comprising the following steps: S1, acquiring multi-source time series data of arid farmland areas and preprocessing to construct a training data set; S2, construct a physical information embedded long short-term memory network PI-LSTM, convert the water migration equation, salt migration equation and boundary condition for controlling soil water and salt migration into a loss function, and construct a composite loss function; S3, train the PI-LSTM through the training data set, and optimize the parameters of the PI-LSTM by minimizing the composite loss function; S4, collect real-time multi-source time series data of the target drought farmland area, input the trained PI-LSTM after preprocessing, and predict the soil water and salt data at the future time node.

[0008] Optionally, the multi-source time series data includes soil moisture data, soil salt data, temperature data, weather data, underground water level and irrigation amount.

[0009] Optionally, the water migration equation loss is specifically: The dynamic transport of mulched farmland soil moisture is regarded as one-dimensional vertical motion, and Richards is used for description: ; In the formula, is the water migration equation loss, is the predicted volumetric water content, K is the unsaturated zone permeability coefficient, h is the negative pressure water head, z is the vertical depth, t is the time step, and MSE represents the mean square error.

[0010] Optionally, the salt migration equation loss is specifically: The control equation of salt migration is expressed by the convection-dispersion equation: ; In the formula, is the salt migration equation loss, is the soil dispersion coefficient, is the Darcy flow rate, is the soil water salinity, is the volumetric water content, , is the spatial coordinate.

[0011] Optionally, the boundary condition loss is specifically: The boundary condition is divided into water boundary condition and salt boundary condition, and the water boundary condition is: ; In the formula, and are the residual water content and the saturated water content, respectively; and the salt boundary condition is: ; In the formula, S Salt concentration, It is the maximum possible salinity value set based on historical observation data of the study area; the boundary condition loss is defined as: ; ; In the formula, For boundary condition loss, Represents the ReLU function. n To input the number of samples, It is the first i Predicted moisture content of each sample It is the first i Predicted salt values ​​for each sample.

[0012] Optionally, the composite loss function is as follows: ; ; In the formula, For compound loss, For data loss, , , , These are the weights for data loss, water transport equation loss, salt transport equation loss, and boundary condition loss, respectively. Data loss is used to measure the deviation between the predicted value and the actual observed value, ensuring that the output matches the actual situation.

[0013] A soil water and salt prediction system integrating physical information and deep learning, applying the aforementioned method for soil water and salt prediction integrating physical information and deep learning, includes: The multi-source data acquisition module is used to collect and preprocess multi-source time-series data from arid farmland areas. The model building module, connected to the multi-source data acquisition module, is used to build a long short-term memory network PI-LSTM for embedding physical information and to define a composite loss function. The model training module, connected to the multi-source data acquisition module and the model building module, is used to train PI-LSTM; The water and salt data prediction module, connected to the multi-source data acquisition module and the model training module, is used for short-term prediction of soil water and salt data.

[0014] As can be seen from the above technical solution, compared with the prior art, the present invention provides a soil water and salt prediction method and system that integrates physical information and deep learning, which has the following beneficial effects: 1. Significantly improves prediction performance: This invention effectively enhances the model's ability to express the intrinsic mechanism of water and salt transport by introducing physical constraints, avoiding overfitting and extrapolation bias of pure data-driven models. It shows significantly better performance than traditional LSTM and external variable-enhanced models in both water and salt prediction. 2. Enhanced model robustness: This invention effectively suppresses error propagation in multi-step prediction tasks by introducing physical loss, enabling the model to maintain high accuracy even when the prediction period is extended, thus extending the effective prediction time and improving the practical value of the model in actual farmland environments. 3. Highly adaptable and economically feasible: It can maintain stable performance under various data acquisition frequencies, especially under low-frequency sampling conditions, which reduces the dependence of field monitoring on high-frequency data and provides a feasible technical path for precision agriculture in resource-limited areas. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0016] Figure 1 This is a flowchart of the soil water and salt prediction method of the present invention; Figure 2 This is a schematic diagram illustrating the core architecture and workflow of the PI-LSTM model of the present invention; Figure 3 This is a schematic diagram of the soil water, salt, and heat sensor layout in drip-irrigated farmland under mulching, as described in this embodiment of the invention. Figure 4 This is a schematic diagram comparing the average R² of LSTM and PI-LSTM moisture prediction results in an embodiment of the present invention. Figure 5 This is a schematic diagram comparing the average R² of LSTM and PI-LSTM salt prediction results in an embodiment of the present invention; Figure 6 This is a schematic diagram comparing the root mean square error of LSTM and PI-LSTM moisture prediction results in an embodiment of the present invention. Figure 7 This is a schematic diagram comparing the root mean square error of LSTM and PI-LSTM salt prediction results in an embodiment of the present invention. Figure 8 This is a schematic diagram illustrating the effect of prediction step size on the average R² of soil moisture prediction results of PI-LSTM and LSTM in an embodiment of the present invention. Figure 9This is a schematic diagram illustrating the influence of prediction step size on the root mean square error of soil moisture prediction results of PI-LSTM and LSTM in an embodiment of the present invention. Figure 10 This is a schematic diagram illustrating the effect of prediction step size on the average R² of soil salinity prediction results of PI-LSTM and LSTM in an embodiment of the present invention. Figure 11 This is a schematic diagram illustrating the influence of prediction step size on the root mean square error of soil salinity prediction results of PI-LSTM and LSTM in an embodiment of the present invention. Figure 12 This is a schematic diagram illustrating the influence of input sequence length on the average R² of PI-LSTM and LSTM soil prediction results in an embodiment of the present invention. Figure 13 This is a schematic diagram illustrating the influence of input sequence length on the root mean square error of PI-LSTM and LSTM soil prediction results in an embodiment of the present invention. Figure 14 This is a schematic diagram illustrating the influence of input sequence length on the average R² of PI-LSTM and LSTM soil prediction results in an embodiment of the present invention. Figure 15 This is a schematic diagram illustrating the influence of input sequence length on the root mean square error of PI-LSTM and LSTM soil prediction results in an embodiment of the present invention. Figure 16 This is a schematic diagram comparing the average R² of soil moisture predicted by the model under different data acquisition frequencies in an embodiment of the present invention. Figure 17 This is a schematic diagram comparing the root mean square error of the model predicting soil moisture under different data acquisition frequencies in an embodiment of the present invention. Figure 18 This is a schematic diagram comparing the average R² of the model's prediction of soil salinity under different data acquisition frequencies in this embodiment of the invention; Figure 19 This is a schematic diagram comparing the root mean square error of model prediction of soil salinity under different data acquisition frequencies in an embodiment of the present invention. Detailed Implementation

[0017] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0018] This invention discloses a method for predicting soil water and salt content by integrating physical information and deep learning, such as... Figure 1 As shown, it includes the following steps: S1. Obtain multi-source time-series data of arid farmland areas and preprocess them to construct a training dataset; S2. Construct a Physical Information Embedded Long Short-Term Memory (PI-LSTM) network. The core architecture and workflow of the PI-LSTM model are as follows: Figure 2 As shown, the water transport equation, salt transport equation and boundary conditions that control soil water and salt transport are transformed into loss functions to construct a composite loss function; S3. Train the PI-LSTM using the training dataset, and optimize the parameters of the PI-LSTM by minimizing the composite loss function; S4. Collect real-time multi-source time-series data of the target arid farmland area, preprocess the data, and input it into the trained PI-LSTM to predict soil water and salt data at future time points.

[0019] LSTM is a specially designed recurrent neural network (RNN) architecture. Its core advantage lies in effectively solving the long-term dependency problem commonly faced by traditional RNNs when processing long-sequence data. LSTM achieves fine-grained control over information flow by introducing sophisticated gating mechanisms (including input gates, forget gates, and output gates) and the cell state as a core memory unit. This mechanism allows LSTM to selectively retain, update, and output key information spanning long time intervals, thus performing excellently in modeling complex temporal dynamics. Its computation process is as follows: ; ; ; ; ; ; In the formula, , , and They represent t Outputs of the time forget gate, input gate, unit state, and output gate; Indicates that LSTM in time t The output; and tan h Let these represent the sigmoid activation function and the hyperbolic tangent function, respectively. , , and These are the weights for the forget gate, input gate, unit state, and output gate, respectively. , , and These are the biases for the forget gate, input gate, unit state, and output gate, respectively.

[0020] Furthermore, the multi-source time-series data includes soil moisture data, soil salinity data, temperature data, meteorological data, groundwater level, and irrigation volume.

[0021] Furthermore, the specific loss in the water transport equation is as follows: The dynamic transport of soil moisture in mulched farmland is viewed as a vertical one-dimensional motion, described using Richards: ; In the formula, Losses due to water transport equations To predict volumetric moisture content (cm³) 3 / cm 3 ), K The permeability coefficient (cm / h) in the unsaturated region. h Negative pressure head (cm) z Vertical depth (cm) t For the time step, MSE represents the mean squared error, which is calculated using the following formula: ; Furthermore, the specific loss in the salt transport equation is as follows: The movement of salts in soil is mainly influenced by convection and dispersion; therefore, the governing equation for salt transport is expressed by the convection-dispersion equation (CDE): ; In the formula, For the loss in the salt transport equation, Soil dispersion coefficient, cm 2 / d, Darcy velocity, cm / d. Soil water mineralization, mg / cm³ 3 , This refers to the volumetric water content. , Spatial coordinates ( i, j = 1, 2).

[0022] Furthermore, the boundary condition loss is specifically as follows: To ensure that the predicted values ​​of soil moisture and salinity are within a reasonable range, boundary conditions were applied to them separately. These boundary conditions are divided into moisture boundary conditions and salinity boundary conditions. The moisture boundary condition is as follows: ; In the formula, and These represent the residual water content and the saturated water content, respectively; the salinity boundary condition is: ; In the formula, S Salt concentration (expressed as conductivity unit dS / m). This is the maximum possible salinity value set based on historical observation data of the study area; in this embodiment, it is taken as [value missing]. =10 dS / m; Boundary condition loss is defined as: ; ; In the formula, For boundary condition loss, Represents the ReLU function. n To input the number of samples, It is the first i Predicted moisture content of each sample It is the first i Predicted salt values ​​for each sample.

[0023] In this embodiment of the invention, the technical implementation is based on PyTorch's automatic differentiation function. A differentiable physical loss term is designed to directly calculate the partial derivative terms in the Richards equation and solute transport equation from the spatiotemporal sequence output by the LSTM. This allows physical laws to participate in the backpropagation process of the network in the form of gradients. To improve the feasibility and stability of numerical calculation, a finite difference strategy is introduced in the calculation of physical residuals: the central difference method with higher accuracy is used to approximate the spatial derivative for internal grid points, while forward or backward difference processing is used at the boundaries to effectively avoid the propagation of boundary errors.

[0024] Furthermore, by constructing a multi-constraint collaborative composite loss function, data-driven learning and physical mechanism constraints are deeply integrated. The core of this integration mechanism is a joint optimization objective function that simultaneously minimizes the data fitting error and the physical equation residuals. The composite loss function is as follows: ; ; In the formula, For compound loss, For data loss, , , , These are the weights for data loss, water transport equation loss, salt transport equation loss, and boundary condition loss, respectively. Data loss is used to measure the deviation between the predicted value and the actual observed value, ensuring that the output matches the actual situation.

[0025] The weight hyperparameters can be adjusted during training. Typically, the four weights are initially considered equal, and then further adjusted to achieve optimal performance. Introducing these hyperparameters during training to adaptively weight and fuse the data error term and the physical residual term is crucial to prevent any one type of loss term (especially the physical term) from becoming overly dominant and causing the model to deviate from the actual observed data. Boundary conditions are treated as soft constraints, using the ReLU function to construct a boundary violation penalty term, ensuring that the model's predicted values ​​always remain within a physically reasonable range.

[0026] In one embodiment of the present invention, the performance of the PI-LSTM model in predicting water and salt dynamics in arid farmland is tested experimentally from different aspects, specifically: The data used in this embodiment comes from the Korla Experimental Station in Xinjiang Uygur Autonomous Region and is used for algorithm training and verification. The farmland at this station uses a drip irrigation system with one film and two pipes. Figure 3 As shown, within the mulched area, sensors were installed at depths of 15cm, 25cm, and 40cm in three locations: wide rows, narrow rows, and between the mulch layers, to collect soil moisture, salinity, and temperature data. Data collection spanned from May 2012 to April 2013, covering the entire growing season with drip irrigation and spring flood irrigation. The acquired data included year-round soil volumetric water content and salinity (EC), soil temperature, meteorological data (precipitation and evaporation), groundwater level, and irrigation volume records.

[0027] Soil moisture and salinity data were acquired using the Hydra water-salt-heat monitoring system. Sensors were installed before irrigation during the growing season and monitored continuously from May 2012 until the end of spring irrigation in April 2013. Data was collected every 15 minutes during the growing season and every 4 hours during the non-growing season. Nine monitoring profiles were established: wide-row, narrow-row, and inter-film profiles at depths of 15cm, 25cm, and 40cm, respectively. Meteorological data were collected using a Davis Vantage Pro2 automatic weather station with a time resolution of 1 hour per data point. Elements included precipitation, air temperature and humidity, wind direction, wind speed, and solar radiation. Potential crop evapotranspiration was calculated based on the measured data. Irrigation data was recorded using water meters to record the amount of water used each time, and irrigation water samples were collected. A total of 14 irrigation events were recorded throughout the year. Groundwater level data was monitored using a water level gauge, and simultaneously with a barometer, neutron analyzer, and soil sampling. A total of 29 monitoring sessions were completed during the growing season. In this study, considering the difficulty of obtaining field data, which prevented such dense data collection, and in order to maintain a consistent time step for the data as a whole, the data were uniformly processed to be collected once every 4 hours, that is, 6 data points per day, and a total of 1974 data points throughout the year.

[0028] The aforementioned region has a typical continental arid climate with scarce water resources. The average annual precipitation is only 58.6 mm, while the annual evaporation reaches 2788.2 mm. Due to the widespread distribution of saline-alkali land and the scarcity of water resources, the transport of water and salt in farmland has become a key link in the local water cycle. Therefore, accurate prediction of soil water and salt dynamics is of great significance for the development and sustainable development of water resources in this region.

[0029] In this embodiment, three experiments were conducted. Experiment 1 examined the model's accuracy within a 5-day prediction period and compared it with an LSTM model incorporating different external variables. Experiment 2 evaluated the effective prediction length by varying the input sequence length and prediction lead time to analyze the model's stability in long-term predictions. Experiment 3 explored the impact of different data acquisition frequencies on model performance. Through these multi-faceted experiments, the reliability, adaptability, and practical value of the proposed model were comprehensively evaluated.

[0030] Experiment 1 Basic Performance Evaluation: To meet the practical needs of dynamic water and salt prediction in arid farmland, current models are typically required to have the ability to predict the next five days. To evaluate the performance of PI-LSTM in dynamic water and salt prediction, a baseline LSTM model, data-augmented LSTM models with added evaporation, precipitation, temperature, irrigation volume, and groundwater level, respectively, and the PI-LSTM proposed in this embodiment were selected for comparison. The prediction lead time for all models was uniformly set to 5 days. During data acquisition, multi-source data, including meteorological data, were simultaneously acquired; to fully utilize this information, it was introduced as additional input into the LSTM model. Experimental results are as follows: Figures 4-7 As shown, Figure 4 , Figure 5 , Figure 6 , Figure 7The figures show the average R² for moisture prediction, the average R² for salinity prediction, the root mean square error (RMSE) for moisture prediction, and the root mean square error (RMSE) for salinity prediction. Looking at the average R², the PI-LSTM model improves moisture prediction by 102.42% compared to the baseline LSTM model, significantly higher than the improvement achieved by introducing a single external variable. Adding evaporation, precipitation, temperature, and groundwater level only improves the results by 56.02%, 36.03%, 11.32%, and 13.56%, respectively. In salinity prediction, the PI-LSTM model shows an even more significant improvement in R², reaching 188.42%, while the enhanced model introducing evaporation and precipitation only improves by 12.83% and 17.24%, respectively. Other variables such as temperature, irrigation volume, and groundwater level have limited impact on salinity prediction. From the perspective of root mean square error (RMSE), the PI-LSTM model also performs best. In moisture prediction, PI-LSTM reduced RMSE by 41.39%, while models incorporating evaporation, precipitation, irrigation, and groundwater level only reduced it by 45.49%, 40.11%, 1.41%, and 2.43%, respectively. In salinity prediction, PI-LSTM significantly reduced RMSE by 16.76%, compared to models incorporating evaporation and precipitation, which only resulted in reductions of 3.04% and 4.05%, respectively, with other variables having negligible effects.

[0031] The above results demonstrate that PI-LSTM, by incorporating physical mechanisms, not only comprehensively outperforms augmented LSTM models that rely solely on a single external variable in all aspects of water and salinity prediction, but also exhibits superior predictive stability and generalization ability. This indicates that, compared to relying on individual observed variables, embedding physical processes into the model structure can more systematically and consistently capture the intrinsic dynamics of water and salt transport, thereby achieving more reliable predictions in complex farmland environments.

[0032] Experiment 2 Effective Continuous Prediction Evaluation: As the prediction period lengthens, the prediction accuracy of data-driven models generally declines. To evaluate whether PI-LSTM can extend the high-precision prediction period (i.e., effective prediction length) of deep learning-based methods, input time series lengths of 18, 24, 30, 60, 90, 120, 150, and 180 were selected to predict soil moisture conditions for the next 5 days. Simultaneously, with a fixed input sequence length of 180 steps, different prediction time steps were set: 6, 12, 18, 24, and 30. Through this design, 13 different prediction model combinations were constructed. PI-LSTM and LSTM models were trained using the same input time step with different prediction days, and different input time steps with the same prediction days, respectively, to compare the trends in their prediction accuracy. All input variables underwent normalization preprocessing before entering the model to eliminate the interference of differences in units and magnitudes on model performance.

[0033] Experimental results are as follows Figures 8-15 As shown, Figure 8 and Figure 9 To predict the impact of step length on soil moisture prediction performance, Figure 10 and Figure 11 To predict the impact of step length on soil salinity prediction performance, Figure 12 and Figure 13 The impact of input sequence length on soil moisture prediction performance. Figure 14 and Figure 15 The impact of input sequence length on soil salinity prediction performance was investigated. The results show that the prediction time step size has a significantly greater impact on model performance than the input sequence length. With a fixed input sequence length of 180 time steps, as the prediction step size increased from 6 to 30, the prediction accuracy of both the PI-LSTM and LSTM models decreased, while the uncertainty increased. Specifically, the LSTM model saw a maximum decrease in average R² of 46.64% and 56.27% in moisture and salinity predictions, respectively, and a maximum increase in average RMSE of 72.19% and 62.20%, respectively. In contrast, the PI-LSTM model showed a maximum decrease in average R² of only 3.34% and 3.28% in both predictions, and a maximum increase in average RMSE of 17.04% and 19.59%, respectively.

[0034] In contrast, when the prediction time step is fixed at 30, the impact of increasing the input sequence length from 18 to 180 is relatively small. Under this condition, the LSTM model shows a maximum decrease in average R² of 22.87% and 25.91% for moisture and salinity predictions, respectively, and a maximum increase in average RMSE of 9.70% and 7.89%; while the PI-LSTM model shows a maximum decrease in average R² of 3.49% and 4.94%, respectively, and a maximum increase in average RMSE of 19.86% and 13.81%. Overall, the PI-LSTM model exhibits better adaptability to longer input sequences and significantly improves the time range covered by high-precision predictions.

[0035] Experiment 3: The impact of data acquisition frequency: For soil moisture and salinity data collection, this embodiment standardized the collection frequency. Due to limitations in actual field conditions, high-frequency data acquisition is difficult. To ensure data consistency across time steps, all data were collected every 4 hours. To further explore the impact of collection frequency on model performance, different collection intervals were set: 15 min, 30 min, 1 h, 2 h, and 4 h (i.e., daily sample sizes of 96, 48, 24, 12, and 6, respectively). Using the LSTM model as a benchmark, a comparison was made with the PI-LSTM model. All models had a prediction period of 5 days and an input time step of 30 days. The total sample size within the same time range varied with the collection frequency. For the same prediction period of 5 days, the corresponding sample sizes were 480, 240, 120, 60, and 30, respectively; similarly, the sample size corresponding to the input time step was adjusted accordingly with the daily collection frequency. This setting ensured the consistency of the model input length across different frequencies, thereby guaranteeing the reliability of the evaluation results.

[0036] Experimental results are as follows Figures 16-19 As shown, Figure 16 , Figure 17 , Figure 18 , Figure 19 The comparisons of the average R² of soil moisture prediction, the root mean square error (RMSE) of soil moisture prediction, and the root mean square error (RMSE) of soil salinity prediction under different data collection frequencies are presented. It can be seen that as the daily sample size decreases (from 96 to 12), the performance of both models in moisture and salinity prediction tasks gradually declines. At higher sampling frequencies (e.g., 96 samples per day), the PI-LSTM model significantly outperforms the traditional LSTM model at all detection depths (15cm, 25cm, 40cm), with an average R² increase of approximately 70% and an average RMSE reduction of over 50%, indicating that the introduction of physical constraints significantly enhances the model's ability to capture the dynamic patterns of moisture and salinity in high-frequency data. However, when the sampling frequency decreases to only 6 samples per day (i.e., collected every 4 hours), the performance of all models shows a significant degradation. Especially at the shallowest layer of 15cm, the R² of the LSTM model generally drops to a negative value, and its predictive ability is even lower than that of the baseline model. In contrast, the PI-LSTM can still maintain a higher R², with its R² value being about 15 times higher than that of the LSTM on average, and its RMSE is also reduced by about 40% on average. This shows that physical constraints effectively alleviate the modeling difficulties caused by data sparsity and significantly improve the robustness and generalization ability of the model under low sampling rate conditions.

[0037] This method not only effectively overcomes the inherent limitations of traditional pure data-driven models in terms of poor extrapolation and weak interpretability, but also significantly improves the model's ability to characterize water and salt transport processes in complex farmland environments by introducing physical equations as intrinsic constraints, providing reliable theoretical and methodological support for water-saving and salt-controlling and precision irrigation management in arid regions.

[0038] and Figure 1 Corresponding to the method described above, this embodiment also discloses a soil water and salt prediction system that integrates physical information and deep learning. The soil water and salt prediction method that integrates physical information and deep learning described above includes: The multi-source data acquisition module is used to collect and preprocess multi-source time-series data from arid farmland areas. The model building module, connected to the multi-source data acquisition module, is used to build a long short-term memory network PI-LSTM for embedding physical information and to define a composite loss function. The model training module, connected to the multi-source data acquisition module and the model building module, is used to train PI-LSTM; The water and salt data prediction module, connected to the multi-source data acquisition module and the model training module, is used for short-term prediction of soil water and salt data.

[0039] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0040] Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for predicting soil water and salt by fusing physical information and deep learning, characterized in that, The method comprises the following steps: S1, acquiring multi-source time series data of a drought farmland area and preprocessing, and constructing a training data set; S2, constructing a physical information embedded long short-term memory network PI-LSTM, converting a water migration equation, a salt migration equation and a boundary condition for controlling soil water and salt migration into a loss function, and constructing a composite loss function; S3, training the PI-LSTM through the training data set, and optimizing the parameters of the PI-LSTM by minimizing the composite loss function; S4, collecting real-time multi-source time series data of a target drought farmland area, inputting the preprocessed data into the trained PI-LSTM, and predicting soil water and salt data at a future time node. 2.The method of claim 1, wherein, The multi-source time series data includes soil moisture data, soil salt data, temperature data, meteorological data, underground water level and irrigation amount. 3.The method of claim 1, wherein, The water migration equation loss is specifically: The dynamic transport of mulched farmland soil moisture is regarded as one-dimensional vertical motion, which is described by Richards: ； where, is the water transport equation loss, is the predicted volumetric water content, K is the unsaturated zone hydraulic conductivity, h is the negative pressure head, z is the vertical depth, t is the time step, and MSE denotes the mean square error.

4. The method of claim 1, wherein the method comprises: The salt migration equation loss is specifically: The control equation of salt migration is expressed by the convection-dispersion equation: ； wherein, is the salt transport equation loss, is the soil dispersion coefficient, is the Darcy flow velocity, is the soil water salinity, is the volumetric water content, , is the spatial coordinate.

5. The method of claim 1, wherein the method comprises: The boundary condition loss is specifically: The boundary condition is divided into water boundary condition and salt boundary condition, and the water boundary condition is: ； wherein and are the residual and saturated water contents, respectively; the salinity boundary condition is: ； wherein S is the salinity concentration, is the maximum possible salinity value set according to historical observation data of the study area; the boundary condition loss is defined as: ； ； In the formula, For boundary condition loss, Represents the ReLU function. n To input the number of samples, It is the first i Predicted moisture content of each sample It is the first i Predicted salt values ​​for each sample.

6. The method of claim 1, wherein the method comprises: The composite loss function is specifically: ； ； wherein, is the composite loss, is the data loss, , , , are the weights of the data loss, the water transport equation loss, the salt transport equation loss, and the boundary condition loss, respectively. The data loss is used to measure the deviation between the predicted value and the true observed value, ensuring that the output conforms to the actual situation.

7. A soil water-salt prediction system fusing physical information and deep learning, characterized in that, The application of the soil water and salt prediction method fusing physical information and deep learning according to any one of claims 1-6 comprises: A multi-source data acquisition module for acquiring multi-source time series data of a drought farmland area and preprocessing; A model construction module connected with the multi-source data acquisition module for constructing a physical information embedded long short-term memory network PI-LSTM and defining a composite loss function; A model training module connected with the multi-source data acquisition module and the model construction module for training the PI-LSTM; A water and salt data prediction module connected with the multi-source data acquisition module and the model training module for short-term prediction of soil water and salt data.

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