PINN-based method and system for analyzing the driving mechanism of spatiotemporal changes in water ecology

Abstract

This invention belongs to the field of water ecology prediction. To address the low accuracy of analysis results for the driving mechanisms of water ecology's spatiotemporal variation, it provides a PINN-based method and system for analyzing the driving mechanisms of water ecology's spatiotemporal variation. The PINN-based method includes acquiring spatiotemporal data and influencing factor data for key water ecology indicators at each monitoring point; processing this acquired data using a pre-trained PINN model to obtain predicted concentrations of key water ecology indicators at different spatiotemporal scales; and performing a global sensitivity analysis based on the predicted concentrations of key water ecology indicators at different spatiotemporal scales and their corresponding influencing factor data to determine the impact of influencing factor data at different spatiotemporal scales on changes in key water ecology indicator concentrations. This method can provide an accurate data foundation for water ecological environment management decisions.

Description

Technical Field

[0001] The present invention belongs to the field of water ecology prediction, and in particular relates to a method and system for analyzing the driving mechanism of water ecology spatiotemporal changes based on PINN. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] Changes in aquatic ecosystems are not only affected by meteorological factors, but are also closely related to a variety of factors such as topography, land use, and the distribution of pollution sources. Currently, traditional analyses of the driving mechanisms of spatiotemporal changes in aquatic ecosystems typically rely on statistical methods such as correlation analysis, which typically rely on static features. These methods make it difficult to directly capture the dependencies between spatiotemporal features and are unable to effectively identify the complex influencing factors and driving mechanisms of long-term spatial changes in aquatic ecosystems. Furthermore, existing analytical methods lack comprehensive analysis and accurate quantification of multiple factors, resulting in a failure to fully explore the deep-seated mechanisms of changes in aquatic ecosystems. This reduces the accuracy of the analysis results of the driving mechanisms of spatiotemporal changes in aquatic ecosystems and makes it impossible to provide an accurate data basis for water ecological environment management decisions. Summary of the Invention

[0004] In order to solve the above technical problems, the present invention provides a method and system for analyzing the driving mechanism of spatiotemporal changes in water ecology based on PINN (Physics-Informed Neural Networks), which can deeply explore the contribution of various factors to water ecological changes, help to comprehensively reveal the potential laws of changes in the water ecological environment, and provide scientific and accurate decision-making support for water ecological environment management.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] The first aspect of the present invention provides a method for analyzing the driving mechanism of spatiotemporal changes in water ecology based on PINN.

[0007] In one or more embodiments, a method for analyzing the driving mechanism of spatiotemporal changes in water ecology based on PINN is provided, including:

[0008] Obtain spatiotemporal data of key water ecological indicators and influencing factors at each monitoring point;

[0009] The pre-trained PINN model was used to process the above acquired data to obtain the predicted values ​​of the concentrations of key water ecological indicators at different temporal and spatial scales;

[0010] A global sensitivity analysis was conducted based on the predicted values ​​of the concentrations of key water ecological indicators at different spatiotemporal scales and their corresponding influencing factor data to obtain the impact of the influencing factor data at different spatiotemporal scales on the changes in the concentrations of key water ecological indicators;

[0011] Among them, in the process of training the PINN model, the total loss function is composed of the weighted sum of the data fitting loss function and the physical constraint loss function; the data fitting loss function is used to measure the difference between the predicted value and the true value of the concentration of key water ecological indicators; the physical constraint loss function is used to measure the difference between the neural network predicted value and the theoretical value of the physical constraint equation.

[0012] The second aspect of the present invention provides a PINN-based water ecological spatiotemporal change driving mechanism analysis system.

[0013] In one or more embodiments, a PINN-based water ecological spatiotemporal variation driving mechanism analysis system includes:

[0014] Data acquisition module, which is used to obtain the spatiotemporal data of key water ecological indicators and influencing factor data of each monitoring point;

[0015] A concentration prediction module is used to process the above-obtained data using a pre-trained PINN model to obtain predicted values ​​of the concentrations of key water ecological indicators;

[0016] Sensitivity analysis module, which is used to conduct global sensitivity analysis based on the predicted values ​​of key water ecological indicator concentrations at different spatiotemporal scales and their corresponding influencing factor data, and obtain the impact of influencing factor data at different spatiotemporal scales on the changes in key water ecological indicator concentrations;

[0017] Among them, in the process of training the PINN model, the total loss function is composed of the weighted sum of the data fitting loss function and the physical constraint loss function; the data fitting loss function is used to measure the difference between the predicted value and the true value of the concentration of key water ecological indicators; the physical constraint loss function is used to measure the difference between the neural network predicted value and the theoretical value of the physical constraint equation.

[0018] A third aspect of the present invention provides a computer-readable storage medium.

[0019] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the above-mentioned PINN-based method for analyzing the driving mechanism of spatiotemporal changes in water ecology.

[0020] A fourth aspect of the present invention provides a computer-readable storage medium.

[0021] A computer program product includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the program is executed by the processor, the steps of the above-described method for analyzing the driving mechanism of spatiotemporal changes in water ecology based on PINN are implemented.

[0022] A fifth aspect of the present invention provides an electronic device.

[0023] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the above-described method for analyzing the driving mechanism of spatiotemporal changes in water ecology based on PINN are implemented.

[0024] Compared with the prior art, the present invention has the following beneficial effects:

[0025] (1) The present invention uses PINN to combine physical equations with neural networks, so that the model can use big data for pattern recognition without losing the physical essence of the water ecosystem. It can also maintain good performance when facing missing or incomplete data, making the model more accurate and robust. It can deeply explore the contribution of various factors to water ecological changes, help to fully reveal the potential laws of water ecological environment changes, and provide scientific and accurate decision-making support for water ecological environment management.

[0026] (2) The present invention combines sensitivity analysis to conduct interpretability analysis of the model, accurately quantifying the independent and synergistic effects of various influencing factors at different spatiotemporal scales, fully considering the nonlinear relationships and interactions between various factors, and enhancing the understanding of changes in aquatic ecosystems. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The accompanying drawings, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0028] Figure 1 1 is a flow chart of a method for analyzing the driving mechanism of spatiotemporal changes in water ecology based on PINN according to an embodiment of the present invention;

[0029] Figure 2 This is a schematic diagram of the analysis process of the driving mechanism of spatiotemporal changes in water ecology based on PINN in an embodiment of the present invention;

[0030] Figure 3 PINN model structure diagram of an embodiment of the present invention;

[0031] Figure 4 4 is a schematic diagram of the structure of a PINN-based water ecological spatiotemporal change driving mechanism analysis system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0032] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0033] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.

[0034] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0035] Figure 1 This is a flow chart of a method for analyzing the driving mechanism of spatiotemporal changes in water ecology based on PINN in an embodiment of the present invention. Figure 1 and Figure 2 The PINN-based method for analyzing the driving mechanism of spatiotemporal changes in water ecology in this embodiment may include:

[0036] S101, obtain the spatiotemporal data of key water ecological indicators and influencing factor data of each monitoring point.

[0037] It should be noted here that key water ecological indicators include but are not limited to chlorophyll a, total algae, primary productivity, etc., to characterize the health status and changes of the water ecosystem. Those skilled in the art can set them specifically according to actual conditions.

[0038] Influencing factor data include but are not limited to water quality data (nitrogen, phosphorus, pH value, dissolved oxygen, etc.), meteorological data (such as temperature, precipitation, wind speed, etc.), and human activity data (agricultural fertilization, industrial emissions, etc.).

[0039] Obtaining the spatiotemporal data of key water ecological indicators and influencing factors at each monitoring point, including the following processing:

[0040] Data on key water ecological indicators such as chlorophyll a, total algae, and primary productivity: Delete missing, outlier, or erroneous values, detect and remove or correct outliers to ensure data quality;

[0041] Impact factor data: Standardization and normalization are performed to eliminate deviations caused by different units or dimensions;

[0042] Time information: Fourier encoding is used to map time data into high-dimensional space;

[0043] For each time scale t, it is converted into a high-dimensional feature through the sine and cosine functions:

[0044] ;

[0045] in, is a set of different frequencies. Each frequency corresponds to a different periodic pattern, which can help the model learn different periodic features. Common frequencies Set to: ;

[0046] Where T is the period of the time scale (in days, T=365), and k is the frequency number.

[0047] Spatial location: The longitude and latitude coordinates corresponding to key water ecological indicator data such as chlorophyll a, total algae, and primary productivity. The longitude is set to lon and the latitude is set to lat.

[0048] S102, using a pre-trained PINN model to process the above-obtained data to obtain predicted values ​​of the concentrations of key water ecological indicators at different temporal and spatial scales.

[0049] like Figure 3 As shown in FIG, the PINN model adopts a multi-layer cascaded deep neural network architecture and a nonlinear mapping model with a multi-layer perceptron as the basic framework.

[0050] The PINN model combines physical knowledge with a data-driven approach, employing a deep neural network framework to solve physical problems. Unlike traditional neural network models, PINN incorporates physical information into the loss function, enabling the neural network to not only rely on data to learn function mappings but also adhere to known physical laws, thereby improving the model's predictive accuracy and physical interpretability.

[0051] The specific design of the PINN model structure is as follows:

[0052] Input layer: Contains multiple influencing factors (such as precipitation, temperature, and dissolved oxygen) as well as spatiotemporal coordinates (including time, longitude, latitude, and water depth). These input features provide a description of the aquatic environment and help the neural network learn complex spatiotemporal variations.

[0053] Hidden layer: A three-layer fully connected network structure is constructed, with 100 neurons per layer, using the Tanh activation function. This design enhances nonlinear representation capabilities by increasing network depth, while the smooth gradient characteristics of the Tanh function facilitate stable solutions to differential equations.

[0054] Output layer: A single neuron structure corresponds to the predicted values ​​of the concentrations of key water ecological indicators such as chlorophyll a, total algae, and primary productivity. A linear activation function is used to ensure that the output value range is not restricted.

[0055] During PINN model training, the total loss function is composed of the weighted sum of a data-fitting loss function and a physical constraint loss function. The data-fitting loss function measures the difference between the predicted and true concentrations of key water ecological indicators, while the physical constraint loss function measures the difference between the neural network's predictions and the theoretical values ​​of the physical constraint equations. This fully integrates the dual constraints of data-driven and physical mechanisms.

[0056] Data Loss: This is used to measure the difference between the neural network prediction value and the actual concentration of key water ecological indicators such as chlorophyll a, total algae, and primary productivity. The mean square error (MSE) is often used as a measurement standard. The specific form is: ;

[0057] in, is the data fitting loss; N is the number of training samples, 、 Respectively expressed in i The network predicted and measured concentrations of key water ecological indicators such as chlorophyll a, total algae, and primary productivity at each sampling point.

[0058] Physics Loss: It is used to measure the difference between the predicted value of the neural network and the theoretical value of the physical constraint equation. The mean square error (MSE) can also be used as a measurement standard. The specific form is: ;

[0059] in, Loss of physical restraint; Indicates in i The theoretical value of the physical constraint equation at each sampling point.

[0060] During the training process of PINN, the total loss function The optimization objective is achieved by weighted combination of data fitting loss and physical constraint loss:

[0061] ;

[0062] in, 、 are hyperparameters, i.e., weight values, which control the balance between data fitting accuracy and physical law constraints.

[0063] Among them, the physical constraint equation system of the concentration of key water ecological indicators is characterized as follows:

[0064] The concentration of key water ecological indicators is determined by the weight of the influence of various physical characteristics in the candidate physical item database of key water ecological indicators on the change of the concentration of key water ecological indicators.

[0065] Take the candidate physical item library as input feature matrix , construct a system of physical constraint equations describing the concentrations of key water ecological indicators such as chlorophyll a, total algae, and primary productivity: ;

[0066] Where y is the concentration of key water ecological indicators such as chlorophyll a, total algae, and primary productivity; is the input feature matrix, which contains the candidate physical item library; w is the sparse weight matrix, which represents the weight of the impact of each physical feature on the change of the total concentration of key water ecological indicators.

[0067] In the Bayesian statistical framework, the weight coefficients w are treated as random variables. To achieve feature selection and reduce the impact of redundant features, the weight coefficients w are typically assigned a sparse prior distribution, causing most weight coefficients to approach zero. This allows the model to automatically eliminate features that are irrelevant to the output or have little impact, thereby improving model interpretability and efficiency.

[0068] The automatic correlation decision (ARD) prior is adopted. This prior is achieved by introducing a hyperparameter For each weight Configure a variance to achieve sparsity:

[0069] ;

[0070] in, is a hyperparameter corresponding to each weight, which controls the sparsity of the feature; p is the probability.

[0071] In order to make Can be adaptively adjusted to guide sparsity, usually for each Assign a Gamma distribution as a prior: ;

[0072] Among them, a and b are the hyperparameters of Gamma distribution. Very large, then the corresponding The closer it is to 0, the feature is ignored, otherwise it is retained.

[0073] According to Bayes' theorem, the posterior distribution of the weight coefficient w is expressed as:

[0074] ;

[0075] in, is the likelihood function, which represents the relationship between the observed value and the predicted value; is the prior distribution of the weight coefficient, that is w sparse priors; is the marginal likelihood, which is used to optimize the model.

[0076] The marginal likelihood is obtained by integrating over all possible weight coefficients w:

[0077] ;

[0078] To obtain the optimal weight coefficient w, maximize the marginal likelihood Optimize the hyperparameters a and b. The final equation is: , which is the physical constraint equation required to construct the PINN model.

[0079] In this embodiment, the physical constraint equation of the concentration of key water ecological indicators is represented by a nonlinear function of the concentration of key water ecological indicators and the influencing factors; wherein the change in the concentration of key water ecological indicators is determined by the influence weight of each physical feature in the candidate physical item database.

[0080] Among them, the candidate physical item database of key water ecological indicators includes linear items, nonlinear items, interaction items, time lag effect items, ecological dynamics characteristic items and spatial coupling items of key water ecological indicators.

[0081] A physical feature library containing M candidate physical items is constructed through multi-dimensional feature engineering. The candidate items can be divided into the following categories:

[0082] 1) Linear terms;

[0083] The linear term represents the direct linear effect of the influencing factors on the changes of key water ecological indicators such as chlorophyll a, total algae, and primary productivity. Specifically, the linear combination of influencing factors is directly used, such as: x1, x2, ..., x i .

[0084] 2) Nonlinear terms;

[0085] Considering that the influencing factors may have nonlinear effects on key water ecological indicators such as chlorophyll a, total algae, and primary productivity, some common mathematical transformations can be used to describe the nonlinear response of a single factor, such as: x1 2 , log(x1), x2 2 ,log(x2).

[0086] 3) interaction terms;

[0087] In aquatic ecosystems, multiple factors often work together and influence each other, so the interactions between different factors also need to be considered. Interaction terms can be represented by the product of the factors, such as x1x2 or x1x3.

[0088] 4) Time lag effect term;

[0089] Changes in key water ecological indicators such as chlorophyll a, total algae content, and primary productivity are affected not only by factors at the current moment but also by the lagged effects of factors from the past. Therefore, factors from historical moments can be introduced.

[0090] 5) Ecological dynamics characteristic items;

[0091] In ecological models, many processes follow specific dynamic mechanisms. For example, the Michaelis-Menten equation describes the nutrient absorption process, and the light-temperature response mechanism describes the effects of light and temperature on algal growth. The characteristic terms of ecological dynamics can be expressed as: 、 Among them, K x1 is the half-saturation constant corresponding to the factor x1.

[0092] 6) spatial coupling term (spatial heterogeneity characteristics);

[0093] In environments with significant spatial heterogeneity, the spatial distribution of these factors can significantly influence changes in key aquatic ecological indicators, such as chlorophyll a, total algal abundance, and primary productivity. Spatial coupling can be represented by locational features, such as longitude (lon), latitude (lat), and water depth (z).

[0094] Combine the above-mentioned physical items to form a complete physical item library. Assuming there are N training samples and i influencing factors, these candidate physical items can be represented as an N×M matrix. Specifically:

[0095] X is the impact factor matrix, whose size is N× i , represents N samples, i A combination of influencing factors. ;

[0096] X 2 Together with the interaction term, it can be expressed as:

[0097] ;

[0098] Each of log(X), time lag effect term, ecological dynamics characteristic term and spatial coupling term can form an N×1 vector, representing the physical term value corresponding to each sample.

[0099] By combining these physical items, we can finally get a complete candidate physical item library, which is expressed as , , its mathematical expression is:

[0100] ;

[0101] Among them, C represents a constant term; each Corresponding to a physical item, the size is N×1.

[0102] During training, the model updates the network weights through a back-propagation algorithm to minimize the total loss function. By jointly optimizing data-driven and physical constraints, PINN can simultaneously improve prediction accuracy and consistency with physical constraints, resulting in a final model with good generalization capabilities and physical interpretability.

[0103] The K-Fold Cross-Validation method is used to comprehensively evaluate the robustness and generalization ability of the model. Specifically, the dataset is divided into K subsets, one of which is selected as the validation set, and the remaining subsets are used for training. This is repeated K times, and the average performance indicators of each validation are calculated. This method can reduce the random effects caused by data partitioning and ensure the reliability of the evaluation results. In addition, appropriate evaluation metrics (such as R² coefficient of determination, RMSE root mean square error, MAE mean absolute error, MAPE mean absolute error percentage, etc.) can be used to evaluate model performance. The specific indicators are as follows:

[0104] ;

[0105] ;

[0106] ;

[0107] ;

[0108] In the formula, n represents the number of samples, 、 Respectively i The predicted and measured values ​​of key water ecological indicators such as chlorophyll a, total algae, and primary productivity at each sampling point. It is the average value of the measured concentrations of all key water ecological indicators such as chlorophyll a, total algae, and primary productivity.

[0109] S103, performing a global sensitivity analysis based on the predicted values ​​of the concentrations of key water ecological indicators at different spatiotemporal scales and their corresponding influencing factor data, to obtain the impact of the influencing factor data at different spatiotemporal scales on the changes in the concentrations of key water ecological indicators.

[0110] In this embodiment, the concentration of key water ecological indicators such as chlorophyll a, total algae, and primary productivity are used as system outputs, and the influencing factor data X=[ x 1 ,x 2 ,…x i ] as the key explanatory variable.

[0111] In this example, the Sobol' index was used for sensitivity analysis.

[0112] The Sobol's index is a global sensitivity analysis method based on variance decomposition. Its primary function is to identify and quantify the intensity and direction of the impact of input variables on outputs across the full parameter range, capturing nonlinear relationships between inputs and outputs and interactions between variables.

[0113] For the model , where y is the output, are input variables. The Sobol' indicator performs variance decomposition by the following steps:

[0114] (1) Variance decomposition: First, the variance Var(y) of the model output y is decomposed into the contributions of each input variable and their interactions:

[0115] ;

[0116] in, Indicates that when considering The variance of the model output when the variable is affected.

[0117] (2) Sensitivity index;

[0118] In the process of global sensitivity analysis, the first-order sensitivity index and the total sensitivity index are used to measure the independent contribution of a single influencing factor data and the overall contribution of the interaction between the influencing factor data and other influencing factor data, respectively.

[0119] First-order sensitivity index: represents a single input variable The contribution to the output variance is defined as: ; This indicator reflects the input variable x i The degree of uncertainty that independently affects the output. Larger, description has a significant impact on output.

[0120] Overall sensitivity index:

[0121] The total contribution, which combines the direct contribution of the input variable and all interactions with other inputs, is defined as: ;

[0122] in, Indicates removing x i Additional input variables after the variable. Reflects the input variables The total contribution to the uncertainty of the model output.

[0123] To gain a deeper understanding of the driving mechanisms of key aquatic ecological indicators such as chlorophyll-a, total algae, and primary productivity at different spatiotemporal scales, the Sobol' index was calculated for different spatiotemporal subregions. This process discretized the spatiotemporal coordinates into multiple subregions, for example, by time (e.g., monthly bins) and by geographic location (e.g., longitude and latitude bins). The Sobol' index was then calculated within each subregion to analyze the impact of input variables on key aquatic ecological indicators such as chlorophyll-a, total algae, and primary productivity in different subregions.

[0124] Figure 4 This is a schematic diagram of the structure of a PINN-based water ecology spatiotemporal change driving mechanism analysis system in an embodiment of the present invention. Figure 1 The PINN-based method for analyzing the driving mechanism of spatiotemporal changes in water ecology corresponds to the Figure 4 As shown, the PINN-based water ecological spatiotemporal change driving mechanism analysis system in this embodiment may include:

[0125] Data acquisition module 401, which is used to obtain the spatiotemporal data of key water ecological indicators and influencing factor data of each monitoring point;

[0126] The concentration prediction module 402 is used to process the acquired data using a pre-trained PINN model to obtain a predicted value of the concentration of key water ecological indicators;

[0127] Sensitivity analysis module 403, which is used to perform global sensitivity analysis based on the predicted values ​​of the concentrations of key water ecological indicators at different spatiotemporal scales and their corresponding influencing factor data, to obtain the impact of the influencing factor data at different spatiotemporal scales on the changes in the concentrations of key water ecological indicators;

[0128] Among them, in the process of training the PINN model, the total loss function is composed of the weighted sum of the data fitting loss function and the physical constraint loss function; the data fitting loss function is used to measure the difference between the predicted value and the true value of the concentration of key water ecological indicators; the physical constraint loss function is used to measure the difference between the neural network predicted value and the theoretical value of the physical constraint equation.

[0129] It should be noted here that, Figure 4 The modules in the PINN-based water ecological spatiotemporal change driving mechanism analysis system are Figure 1 The various steps in the PINN-based water ecological spatiotemporal change driving mechanism analysis method correspond one to one, and the specific implementation process is the same, which will not be repeated here.

[0130] In other embodiments, an electronic device is provided that includes a central processing unit (CPU) capable of executing various appropriate actions and processes based on a program stored in a read-only memory (ROM) or a program loaded from a storage unit into a random access memory (RAM). The RAM also stores various programs and data required for system operation. The CPU, ROM, and RAM are interconnected via a bus 404. An input / output (I / O) interface is also connected to the bus.

[0131] The following components are connected to the I / O interface: an input section including a keyboard and mouse; an output section including cathode ray tubes (CRTs), liquid crystal displays (LCDs), and speakers; a storage section including a hard disk; and a communication section including network interface cards such as local area network (LAN) cards and modems. The communication section performs communication processing via a network such as the Internet. A drive is also connected to the I / O interface as needed. Removable media such as magnetic disks, optical disks, magneto-optical disks, and semiconductor memories are installed in the drive as needed, allowing computer programs read from these media to be installed in the storage section as needed.

[0132] When the central processing unit in the electronic device of this embodiment executes the program, the following is achieved: Figure 1 The steps in the PINN-based method for analyzing the driving mechanisms of spatiotemporal changes in water ecology are shown.

[0133] In particular, according to an embodiment of the present application, the process described above with reference to the flowchart can be implemented as a computer software program. For example, an embodiment of the present application includes a computer program product, which includes a computer program carried on a computer readable medium, the computer program including a computer program for executing Figure 1 In such an embodiment, the computer program can be downloaded and installed from a network via the communication portion and / or installed from a removable medium. When the computer program is executed by the central processing unit, the various functions defined in the apparatus of the present application are performed.

[0134] in, Figure 1 The computer program instructions corresponding to the method shown can also be stored in a computer readable memory that can guide a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0135] Those skilled in the art will appreciate that all or part of the processes in the above-described method embodiments can be implemented by instructing the relevant hardware through a computer program. The program can be stored in a computer-readable storage medium, and when executed, the program can include the processes in the above-described method embodiments. The storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM).

[0136] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A PINN-based method for analyzing the driving mechanism of spatiotemporal changes in water ecology, characterized by: include: Obtain spatiotemporal data of key water ecological indicators and influencing factors at each monitoring point; The pre-trained PINN model was used to process the above acquired data to obtain the predicted values ​​of the concentrations of key water ecological indicators at different temporal and spatial scales; A global sensitivity analysis was conducted based on the predicted values ​​of the concentrations of key water ecological indicators at different spatiotemporal scales and their corresponding influencing factor data to obtain the impact of the influencing factor data at different spatiotemporal scales on the changes in the concentrations of key water ecological indicators; In the process of training the PINN model, the total loss function is composed of the weighted sum of the data fitting loss function and the physical constraint loss function; the data fitting loss function is used to measure the difference between the predicted value and the actual value of the concentration of key water ecological indicators; the physical constraint loss function is used to measure the difference between the neural network prediction value and the theoretical value of the physical constraint equation; The construction process of the physical constraint equation of the concentration of key water ecological indicators is as follows: Based on key water ecological indicators, a multi-dimensional database of candidate physical items of key water ecological indicators is constructed; The candidate physical item database of key water ecological indicators is used as the input feature matrix to construct the physical constraint equation of the concentration of key water ecological indicators; The candidate physical item database of the key water ecological indicators includes linear items, nonlinear items, interaction items, time lag effect items, ecological dynamics characteristic items and spatial coupling items of the key water ecological indicators; linear items represent the direct linear effects of influencing factors on changes in key water ecological indicators; nonlinear items represent the nonlinear effects of influencing factors on key water ecological indicators; interaction items represent the joint effects of different influencing factors and their mutual effects on key water ecological indicators; time lag effect items represent the effects of influencing factors at the current moment and influencing factors at past moments on key water ecological indicators; ecological dynamics characteristic items represent the dynamic mechanisms of influencing factors on key water ecological indicators; spatial coupling items represent the effects of the spatial distribution of influencing factors on changes in key water ecological indicators; The physical constraint equation for the concentration of key water ecological indicators is represented by a nonlinear function of the concentration of key water ecological indicators and the influencing factors. The change in the concentration of key water ecological indicators is determined by the influence weight of each physical feature in the candidate physical item database. The PINN model adopts a multi-layer cascaded deep neural network architecture and a nonlinear mapping model with a multi-layer perceptron as the basic framework.

2. The PINN-based method for analyzing the driving mechanism of spatiotemporal changes in water ecology according to claim 1, characterized in that: In the process of global sensitivity analysis, the first-order sensitivity index and the total sensitivity index are used to measure the independent contribution of a single influencing factor data and the overall contribution of the interaction between the influencing factor data and other influencing factor data, respectively.

3. A PINN-based water ecological spatiotemporal change driving mechanism analysis system, characterized by: include: Data acquisition module, which is used to obtain the spatiotemporal data of key water ecological indicators and influencing factor data of each monitoring point; A concentration prediction module is used to process the above-obtained data using a pre-trained PINN model to obtain predicted values ​​of the concentrations of key water ecological indicators; Sensitivity analysis module, which is used to conduct global sensitivity analysis based on the predicted values ​​of key water ecological indicator concentrations at different spatiotemporal scales and their corresponding influencing factor data, and obtain the impact of influencing factor data at different spatiotemporal scales on the changes in key water ecological indicator concentrations; In the process of training the PINN model, the total loss function is composed of the weighted sum of the data fitting loss function and the physical constraint loss function; the data fitting loss function is used to measure the difference between the predicted value and the actual value of the concentration of key water ecological indicators; the physical constraint loss function is used to measure the difference between the neural network prediction value and the theoretical value of the physical constraint equation; The construction process of the physical constraint equation of the concentration of key water ecological indicators is as follows: Based on key water ecological indicators, a multi-dimensional database of candidate physical items of key water ecological indicators is constructed; The candidate physical item database of key water ecological indicators is used as the input feature matrix to construct the physical constraint equation of the concentration of key water ecological indicators; The candidate physical item database of the key water ecological indicators includes linear items, nonlinear items, interaction items, time lag effect items, ecological dynamics characteristic items and spatial coupling items of the key water ecological indicators; linear items represent the direct linear effects of influencing factors on changes in key water ecological indicators; nonlinear items represent the nonlinear effects of influencing factors on key water ecological indicators; interaction items represent the joint effects of different influencing factors and their mutual effects on key water ecological indicators; time lag effect items represent the effects of influencing factors at the current moment and influencing factors at past moments on key water ecological indicators; ecological dynamics characteristic items represent the dynamic mechanisms of influencing factors on key water ecological indicators; spatial coupling items represent the effects of the spatial distribution of influencing factors on changes in key water ecological indicators; The physical constraint equation for the concentration of key water ecological indicators is represented by a nonlinear function of the concentration of key water ecological indicators and the influencing factors. The change in the concentration of key water ecological indicators is determined by the influence weight of each physical feature in the candidate physical item database. The PINN model adopts a multi-layer cascaded deep neural network architecture and a nonlinear mapping model with a multi-layer perceptron as the basic framework.

4. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the PINN-based water ecological spatiotemporal change driving mechanism analysis method as described in any one of claims 1 to 2 are implemented.

5. A computer program product comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the PINN-based water ecological spatiotemporal change driving mechanism analysis method according to any one of claims 1 to 2 are implemented.

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the PINN-based water ecological spatiotemporal change driving mechanism analysis method according to any one of claims 1 to 2 are implemented.

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