CN115935626B - Inversion method of river water-underground water vertical transient interaction water flow - Google Patents
Inversion method of river water-underground water vertical transient interaction water flow Download PDFInfo
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Abstract
The invention belongs to the technical field of saturated zone water flux monitoring, and discloses a river-groundwater vertical transient interaction water flux inversion method based on a VAE-PINN algorithm, which comprises the following steps: determining dimensions of a river-groundwater interaction water flux-time sequence, generating a set comprising a plurality of sequences; training the VAE model by utilizing the set; acquiring monitoring data of the temperature of the river bed in a certain monitoring period; constructing PINN, assimilating riverbed temperature data, and inverting to obtain a low-dimensional vector representing the interactive water flux-time sequence; reconstructing the interactive water flux-time sequence according to the low-dimensional vector by means of the trained VAE; and repeating the steps S3-S5 to obtain the interactive water flow-time sequence of the next monitoring period. The invention greatly improves the inversion precision of the river-groundwater vertical transient interactive water flux, and can realize continuous monitoring of the river-groundwater vertical interactive water flux in a certain area.
Description
Technical Field
The invention belongs to the technical field of saturated zone water flow monitoring, and particularly relates to a river-groundwater vertical transient interactive water flow inversion method, a continuous monitoring method and a monitoring system based on a VAE-PINN algorithm.
Background
Under natural conditions, there is a general interaction between river water and groundwater, and the mutual replenishment of the river water and groundwater has an important influence on the water quantity and water quality change in the area. The interactive water flux between river water and underground water is very strong in transient and difficult to accurately quantify due to the influence of factors such as regional climate change, fluctuation of surface (subsurface) water level, human activities (such as reservoir regulation) and the like.
The conventional method for quantifying the vertical interactive water flux of river water and groundwater mainly comprises the following steps: (1) direct measurement, namely directly measuring the river water-underground water interaction water flux (interaction water quantity/monitoring duration) at a certain point by using a seepage meter; (2) the method based on Darcy law needs to firstly measure the hydraulic gradient and saturated water conductivity parameters on the observation point, and then calculate the interactive water flux according to Darcy law; (3) the solute conservation method quantitatively analyzes the conversion quantity of river water and underground water by applying the principle of mass conservation to the trace solute, and further converts the conversion quantity into the interactive water flow. The direct measurement method and the solute mass conservation method can only estimate the average value of the river water-groundwater vertical interaction water flow flux in the monitoring period, the detailed interaction process can not be described, and the estimation result has higher uncertainty; meanwhile, the measuring error of the river bed hydraulic parameter value is large, and the error estimation result of the method based on the Darcy law can be caused.
The hot tracing method which is rising in recent years shows unique advantages in quantifying the river-groundwater interaction water flow, and is specifically expressed as follows: the temperature monitoring is convenient and economical, the measurement accuracy is high, and the environment is not polluted. In the past decade, many studies have utilized analytical solutions of one-dimensional thermal migration equations to estimate river-groundwater vertical interactive water flux from the natural temperature signals of the river bed. However, the analytical solution of the one-dimensional vertical heat migration equation is obtained based on a plurality of basic assumptions, such as that the interactive water flow is required to have only uniform and stable vertical split speed, and the river-groundwater interactive water flow under natural conditions generally shows transient characteristics, which can lead to erroneous estimation results of the analytical method.
In order to overcome the limitation of the analytic solution method, the numerical inversion method is also used in inversion research of river-groundwater vertical interactive water flow. Numerical inversion programs (e.g., 1 DTempPro) have been developed by researchers and used to invert vertical interactive water flux based on riverbed temperature data. However, such numerical inversion software often fails to implement automatic inversion of the interaction water flux, limiting its application in transient interaction scenarios. In addition, some researchers have coupled numerical models with numerical inversion algorithms (e.g., enKF, ES, IES) that invert the interactive water flux based on the riverbed temperature observations, but the numerical inversion algorithms relied on in this process often need to be based on certain assumption conditions (e.g., gaussian assumptions) that will promote uncertainty in the inversion results. In addition, the inversion process of the traditional inversion algorithm requires a large number of numerical model calls, and the calculation cost is high.
Disclosure of Invention
The invention aims to provide a method for inverting the river-groundwater vertical transient interaction water flow based on a VAE-PINN algorithm, and compared with the PINN, the VAE-PINN can greatly improve the inversion precision of the river-groundwater vertical transient interaction water flow and can realize continuous monitoring of the river-groundwater vertical interaction water flow in a certain area.
In order to achieve the above purpose, the present invention adopts the following technical scheme:
the invention provides a method for inverting river-groundwater vertical transient interactive water flow based on a VAE-PINN algorithm, which comprises the following steps:
s1, determining the monitoring period and frequency of the river-groundwater vertical interactive water flow flux to obtain the monitoring time step number, namely the river-groundwater interactive water flow flux-time sequence F i N dimension of (2) F Generating a numerical simulation based on the data including N e Interactive water flux-time series F of individuals i Set { F) 1 ，F 2 ，…，F Ne }；
S2, constructing a variational self-encoder (VAE) model by using the set { F 1 ，F 2 ，…，F Ne Training the VAE model;
s3, acquiring river bed temperature monitoring data in a certain monitoring period;
s4, constructing a neural network PINN embedded with physical knowledge, and assimilating the riverbed temperature monitoring data obtained in the step S3 to obtain an interactive water flow-time sequence F representing the monitoring period in an inversion mode True Is a low-dimensional vector Y of (2) True ；
S5, inverting the PINN in the step S4 to obtain a low-dimensional vector Y by means of the trained VAE decoder in the step S2 True Reconstructing into a river-groundwater vertical interactive water flow flux-time sequence F in the monitoring period True ；
S6, repeating the steps S3-S5 to obtain a river-groundwater vertical interactive water flow-time sequence of the next monitoring period.
Preferably, step S2 specifically includes: s21Dimension n by encoder of VAE F Interactive water flux-time series F i Mapping to a dimension n Y Hidden variable Y of (2) i ，n Y ≤n F Hidden variable Y i Is p (Y) i ) The posterior probability is p (Y i |F i )；
S22, based on hidden variable Y i To obtain new random samples Y i '：
Y i '～p(Y i |F i )；
S23, decoding the hidden variable Y through a VAE decoder i ' reconstruct to F i ' i.e.:
F i '＝Decoder(Y i '；Wt,b)，
wherein: wt is a weight matrix, b is a bias vector;
s24, defining a loss function for the VAE to optimize network parameters in an encoder and a decoder, wherein the loss function is in the following form:
wherein: l (F) i ,F i ') reconstruction loss, i.e. interactive water flux-time series F i And reconstructing sequence F i ' root mean square error between D KL [p(Y i |F i )||p(Y i )]Is a probability distribution p (Y i |F i ) And p (Y) i ) KL divergence between;
and S25, optimizing the loss function by using an Adam optimization algorithm to complete training of the VAE model.
Preferably, step S4 specifically includes:
s41, simulating a heat transfer process in a river bed in a certain monitoring period, wherein the heat transfer process meets the heat transfer equation in a saturated porous medium:
wherein: t is the temperature, DEG C; ρc=n ρ w c w +(1-n)ρ s c s Jm is the volumetric heat capacity of the riverbed sediment -3 ·℃ -1 The method comprises the steps of carrying out a first treatment on the surface of the n is the porosity of the river bed solid phase medium; ρ s c s And ρ w c w The volumetric heat capacities of the river bed solid medium and water, jm -3 ·℃ -1 ；Is the effective heat conductivity of the river bed, wm -1 ·℃ -1 ；k w And k s Thermal conductivity of water and river bed solid phase medium respectively, wm -1 ·℃ -1 ；F True To monitor the true value of the interactive water flux-time sequence over a period, md -1 ；
S42, constructing a deep neural network DNN to approach the temperature monitoring data T (z, T) of the riverbed in the monitoring period, namely
Wherein:the temperature predicted value output by DNN is represented, z is a space coordinate, t is a time coordinate, and θ is a parameter of DNN;
s43, obtaining according to the chain rule by automatic differentiationDifferentiation with respect to z and t will +.>And the differentiation of the derivative with respect to z and t is substituted into the heat transfer equation in S41 to obtain an equation residual, namely:
wherein: f in the heat transfer equation of step S41 True Is replaced by a Decoder (Y) True ；Wt,b)，Y True Is represented by F True Is a low-dimensional vector of (2);
s44, obtaining parameters θ and low-dimensional vector Y of DNN True The overall loss function of the PINN is defined as follows:
wherein:representing the root mean square error between the predicted value and the true value of the boundary condition given by DNN; />Representing the root mean square error between the predicted value and the true value of the initial condition given by the DNN; />Representing equation residuals;
s45, optimizing the overall loss function by using an L-BFGS optimization algorithm, and enabling theta and Y to be enabled to be in loop iteration True The value of (2) reaches the optimum value and outputs Y True Is used for the optimization of the values of (a).
The invention also provides a method for realizing continuous monitoring of the river-groundwater transient state interaction water flux by using the inversion method of the river-groundwater transient state interaction water flux based on the VAE-PINN algorithm, which comprises the following steps:
step 1: selecting a test river reach, placing a temperature measuring net inserted with a plurality of temperature measuring pipes, and ensuring that the temperature measuring pipes are vertical and the top ends of the temperature measuring pipes are flush with the upper interface of the river bed;
step 2: the thermistors in the temperature measurement network are connected to the data acquisition unit one by one through an integrated lead, the data acquisition unit is connected with a power supply, and the sampling frequency of the riverbed temperature data is set;
step 3: the river bed temperature data acquired by the data acquisition unit are timely transmitted to the cloud server through the GPRS module;
step 4: continuously assimilating the riverbed temperature data in each monitoring period based on the VAE-PINN framework through the cloud server, inverting to obtain a vertical interactive water flow-time sequence of the riverbed-groundwater in each monitoring period, and storing the temperature monitoring data and a continuous inversion result of the interactive water flow-time sequence in a MySQL database.
The invention also provides a system for realizing the monitoring of the river water-underground water vertical transient interactive water flow, which comprises a temperature measurement network consisting of a plurality of temperature measurement pipes, a data collector, a solar cell panel, a GPRS module, a cloud server and a MySQL database; 7 thermistors are arranged on each temperature measuring tube from bottom to top;
the temperature measuring net is used for measuring the temperatures at different positions of the river bed;
the data acquisition device is used for acquiring temperature data of each thermistor in the temperature measurement network;
the solar panel is used for supplying power to the data collector and the GPRS module;
the GPRS module is used for transmitting the temperature data acquired by the data acquisition unit to the cloud server;
the cloud server obtains a river-groundwater vertical interactive water flow-time sequence in each monitoring period by utilizing a VAE-PINN framework according to continuous inversion of river bed temperature data in the monitoring period;
the MySQL database is used for storing temperature data and continuous inversion results of water flow.
Compared with the prior art, the invention has the beneficial effects that:
the invention provides a new inversion framework-VAE-PINN for the river-groundwater vertical transient interaction water flow combined with a variation self-encoder (VariationalAutoencoder, VAE) and a neural network (Physics Informed Neural Network, PINN) embedded with physical knowledge, and compared with the PINN, the VAE-PINN can greatly improve the inversion precision of the river-groundwater vertical transient interaction water flow.
According to the invention, a new frame is inverted by using the VAE-PINN, so that the change condition of the river water-underground water vertical interaction water flow field can be continuously monitored in time and space, and the monitoring result is uploaded to a cloud server through a GPRS network; the monitoring system is built on the basis of a cloud server, and is not limited by space in the use process; high temperature measurement precision, low cost and no environmental pollution.
Drawings
FIG. 1 is a schematic diagram of a monitoring system according to the present invention.
FIG. 2 is a schematic diagram of a temperature measuring tube in the monitoring system of the present invention.
FIG. 3 is a flow chart of the inversion method of the river-groundwater vertical transient interactive water flux based on the VAE-PINN algorithm.
FIG. 4 is a graph showing the results of inversion of river-groundwater vertical transient interaction water flux at three measurement points according to the present invention using PINN and VAE-PINN, respectively.
Detailed Description
The following examples are illustrative of the present invention and are not intended to limit the scope of the invention. The technical means used in the examples are conventional means well known to those skilled in the art unless otherwise indicated. The test methods in the following examples are conventional methods unless otherwise specified.
Example 1
As shown in fig. 1, the monitoring system for river-groundwater vertical transient interaction water flow based on a VAE-PINN algorithm comprises a temperature measurement network 1, a data collector 3, a solar cell panel 4, a GPRS module 5, a cloud server 6 and a MySQL database 7, wherein the temperature measurement network 1 is composed of a plurality of temperature measurement pipes 10. Each temperature measuring tube 10 is connected with the data collector 3 through an integrated lead 2. Specifically, the temperature measurement net 1 is used for measuring temperatures at different positions of a river bed; the data collector 3 is used for collecting temperature data of each thermistor 12 in the temperature measurement network 1; the solar panel 4 is used for supplying power to the data collector 3 and the GPRS module 5; the GPRS module 5 is used for transmitting the temperature data acquired by the data acquisition unit 3 to the cloud server 6; the cloud server 6 obtains a river-groundwater vertical interactive water flow-time sequence of each monitoring period by utilizing a VAE-PINN framework according to continuous inversion of the river bed temperature data in each monitoring period; the MySQL database 7 is used to store temperature data and continuous inversion results of water flux-time series.
In this embodiment, a temperature measuring net 1 with a size of 2m×2m is composed of a fixing ring 8 (diameter 1.8 cm) and a connecting wire 9 (length 40 cm), which comprises 25 sub-grids with a size of 0.4m×0.4m, and 36 temperature measuring tubes 10 can be inserted.
As shown in fig. 2, the temperature measuring tube 10 includes: 11 parts of PVC pipe, 12 parts of thermistor, 13 parts of flower pipe, 14 parts of rubber plug and 15 parts of lead wire. PVC pipe 11 is 60cm long and 1.5cm in diameter; the probes of 7 thermistors 12 are respectively fixed at 0cm, 5cm, 10cm, 20cm, 30cm, 40cm and 60cm of the PVC pipe 11. The PVC pipe 11 at the probe position of the thermistor 12 is a flower pipe 13 to promote convection transmission of temperature signals; a sealing rubber plug 14 is arranged between two adjacent probes to prevent water from flowing vertically in the PVC pipe 11.
The method for continuously monitoring the river water-underground water vertical transient interactive water flow by using the monitoring system comprises the following steps:
step 1: selecting a test river reach, placing a temperature measuring net 1 inserted with 36 temperature measuring pipes 10, and ensuring that the temperature measuring pipes 10 are vertical and the top ends of the temperature measuring pipes are flush with the upper boundary of the river bed;
step 2: the thermistors 12 in the temperature measurement net 1 are connected to the data collectors 3 one by one through the integrated lead 2, the data collectors 3 are connected with a power supply, and the sampling frequency of the riverbed temperature data is set to be 5 min/time;
step 3: the GPRS module 5 is used for timely transmitting the temperature data acquired by the data acquisition unit 3 to the cloud server 6;
step 4: the cloud server 6 continuously assimilates temperature data in each monitoring period based on the VAE-PINN framework, the vertical interactive water flow flux-time sequence of the river water and the underground water in each monitoring period is obtained through inversion, and continuous inversion results of the temperature monitoring data and the water flow flux-time sequence are stored in the MySQL database.
In order to better demonstrate the reliability of the monitoring method in the aspect of monitoring the river-groundwater vertical transient interactive water flow flux, in this embodiment, a section of three-dimensional river bed simulated by numerical software COMSOL Multiphysics is selected as a research area, and the size of the research area is 2m×2m×0.6m (length×width×depth). The temperature signals at the upper boundary of the selected river reach fluctuate according to a sine rule, the average value of the temperature signals is 20 ℃, the amplitude is 5 ℃, and the fluctuation period is 1 day. The initial temperature value of the riverbed was 20 ℃. The monitoring period in this example was set to 1 day, the monitoring frequency of the interactive water flux was set to 5 min/time, and the number of monitoring time steps was 288.
As shown in fig. 3, in step 4 of the present invention, the specific steps for inversion by using the VAE-PINN algorithm to obtain the river-groundwater vertical transient interactive water flux are as follows:
s1, determining that the monitoring period of the river water-underground water vertical interactive water flow is 1 day, the monitoring frequency is 5 min/time, and obtaining 288 monitoring time steps, namely the interactive water flow-time sequence F i N dimension of (2) F =288, and using finite difference software MODFLOW to simulate and monitor river-groundwater interaction process of river reach under natural and artificial interference conditions (corresponding to various river level fluctuation conditions), generating a model containing N e =6000F i Set { F) 1 ，F 2 ，…，F Ne }。
S2, constructing a variational self-Encoder (VAE) model, which comprises two parts of an Encoder (Encoder) and a Decoder (Decoder), wherein the Encoder of the VAE comprises 1 input layer, 2 convolution layers and 1 full-connection layer, the Decoder comprises 1 full-connection layer, 1 reconstruction layer and 3 deconvolution layers, and the obtained interactive water flow-time sequence set { F 1 ，F 2 ，…，F Ne Training the VAE model. The step S2 specifically comprises the following steps:
s21, using the VAE encoder to make the dimension n F Interactive water flux-time series F i Mapping to a dimension n Y Hidden variable Y of (2) i ，n Y ≤n F Hidden variable Y i Is p (Y) i ) The posterior probability is p (Y i |F i )；
S22, acquiring new random samples Y based on probability distribution of hidden variables i '：
Y i '～p(Y i |F i )；
S23, decoding Y by VAE decoder i ' reconstruct to F i ' i.e.:
F i '＝Decoder(Y i '；Wt,b)，
wherein: wt is a weight matrix, b is a bias vector;
s24, defining a loss function for the VAE to optimize network parameters in the encoder and the decoder, wherein the loss function is in the following form:
wherein: l (F) i ,F i ') reconstruction loss, i.e. interactive water flux-time series F i And reconstructing sequence F i ' root mean square error between D KL [p(Y i |F i )||p(Y i )]Is a probability distribution p (Y i |F i ) And p (Y) i ) KL divergence between;
and S25, optimizing the loss function in the S23 by utilizing an Adam optimization algorithm, and completing training of the VAE model.
And S3, acquiring river bed temperature data which are obtained by monitoring by a monitoring system in a certain monitoring period and uploaded to a cloud server.
S4, constructing a neural network PINN embedded with physical knowledge, assimilating the riverbed temperature data obtained in the S3 by using the neural network PINN, and inverting to obtain a riverbed vertical interactive water flow-time sequence F in the representative monitoring period True Is a low-dimensional vector Y of (2) True . The step S4 specifically comprises the following steps:
s41, simulating a heat transfer process in a river bed in a certain monitoring period, wherein the heat transfer process meets the heat transfer equation in a saturated porous medium:
wherein: t is the temperature, DEG C; ρc=n ρ w c w +(1-n)ρ s c s Jm is the volumetric heat capacity of the riverbed sediment -3 ·℃ -1 The method comprises the steps of carrying out a first treatment on the surface of the n is the porosity of the river bed solid phase medium; ρ s c s And ρ w c w The volumetric heat capacities of the river bed solid medium and water, jm -3 ·℃ -1 ；Is the effective heat conductivity of the river bed, wm -1 ·℃ -1 ；k w And k s Thermal conductivity of water and river bed solid phase medium respectively, wm -1 ·℃ -1 ；F True To monitor the true value of the interactive water flux-time sequence over a period, md -1 ；
S42, constructing a deep neural network DNN to approximate the temperature monitoring data T (z, T) of the riverbed in the monitoring period, namely
Wherein:the temperature predicted value output by DNN is represented, z is a space coordinate, t is a time coordinate, and θ is a parameter of DNN;
s43, obtaining according to the chain rule by automatic differentiationDifferentiation with respect to z and t. Will->And the differentiation of the derivative with respect to z and t is substituted into the heat transfer equation in S41 to obtain an equation residual, namely:
it should be noted that F in the heat transfer equation of step S41 True Is replaced by a Decoder (Y) True ；Wt,b)，Y True Is represented by F True In the low-dimensional vector of (a), i.e. in the equation residualIs based on the low-dimensional vector Y by the decoder of the VAE model trained in step S25 True And (5) reconstructing to obtain the product.
S44, obtaining parameters θ and low-dimensional vector Y of DNN True The overall loss function of the PINN is defined as follows:
wherein:representing the root mean square error between the predicted value and the true value of the boundary condition given by DNN; />Representing the root mean square error between the predicted value and the true value of the initial condition given by the DNN; />Representing equation residuals;
s45, optimizing the overall loss function by using an L-BFGS optimization algorithm, and enabling theta and Y to be enabled to be in loop iteration True The value of (2) reaches the optimum value and outputs Y True Is used for the optimization of the values of (a).
S5, inverting the low-dimensional vector Y obtained by PINN in S45 by means of the trained VAE decoder in S2 True Reconstructing into a river-groundwater vertical interactive water flow flux-time sequence F in the monitoring period True ；
S6, repeating the steps S3-S5 to obtain a river-groundwater vertical interactive water flow-time sequence of the next monitoring period.
Three temperature measuring tubes are randomly selected from 36 temperature measuring tubes in the embodiment, and the interactive water flow-time sequence on the corresponding point positions is inverted according to the temperature monitoring data, and the inversion result is shown in fig. 4. Compared with the result obtained by PINN inversion, the interactive water flow-time sequence obtained by VAE-PINN inversion is closer to a true value, which shows that the change situation of the river water-underground water vertical interactive water flow with time can be accurately inverted.
In order to avoid the influence of accidental errors, the embodiment respectively inverts the interactive water flow-time sequence of the whole research area according to the temperature data of 36 temperature measuring tubes, and calculates the Root Mean Square Error (RMSE) and the determination coefficient (R) between the inversion result and the true value at 36 points 2 ) The values, the average of these evaluation indexes are shown in Table 1.
TABLE 1 mean of evaluation indicators corresponding to the interactive Water flux-time series obtained by inversion of PINN and VAE-PINN on 36 observation points
Analysis shows that the RMSE value between the vertical transient interaction water flux value and the true value obtained by the VAE-PINN inversion is smaller, R, compared with the PINN alone 2 Values closer to 1 indicate more accurate results from the VAE-PINN inversion. Therefore, the invention can realize more accurate monitoring of the vertical transient interaction water flow between river water and underground water.
The above-mentioned embodiments are merely preferred embodiments of the present invention, which are not intended to limit the scope of the present invention, and other embodiments can be easily made by those skilled in the art through substitution or modification according to the technical disclosure in the present specification, so that all changes and modifications made in the principle of the present invention shall be included in the scope of the present invention.
Claims (3)
1. The inversion method of the river-groundwater vertical transient interactive water flow based on the VAE-PINN algorithm is characterized by comprising the following steps:
s1, determining the monitoring period and frequency of the river-groundwater vertical interactive water flow flux to obtain the monitoring time step number, namely the river-groundwater interactive water flow flux-time sequence F i N dimension of (2) F A base (B)Generating a digital simulation containing N e Individual interactive water flux-time series F i Set { F) 1 ，F 2 ，…，F Ne }；
S2, constructing a variational self-encoder (VAE) model by using the set { F 1 ，F 2 ，…，F Ne Training the VAE model; the step S2 specifically comprises the following steps:
s21, using the VAE encoder to make the dimension n F Interactive water flux-time series F i Mapping to a dimension n Y Hidden variable Y of (2) i ，n Y ≤n F Hidden variable Y i Is p (Y) i ) The posterior probability is p (Y i |F i )；
S22, based on hidden variable Y i To obtain new random samples Y i '：
Y i '～p(Y i |F i )；
S23, decoding the hidden variable Y through a VAE decoder i ' reconstruct to F i ' i.e.:
F i '＝Decoder(Y i '；Wt,b)，
wherein: wt is a weight matrix, b is a bias vector;
s24, defining a loss function for the VAE to optimize network parameters in an encoder and a decoder, wherein the loss function is in the following form:
wherein: l (F) i ,F i ') reconstruction loss, i.e. interactive water flux-time series F i Root mean square error, D, with the reconstructed sequence Fi KL [p(Y i |F i )||p(Y i )]Is a probability distribution p (Y i |F i ) And p (Y) i ) KL divergence between;
s25, optimizing the loss function by using an Adam optimization algorithm to complete training of the VAE model;
s3, acquiring river bed temperature monitoring data in a certain monitoring period;
s4, constructing a neural network PINN embedded with physical knowledge, and assimilating the riverbed temperature monitoring data obtained in the step S3 to invert to obtain a true value F representing the interactive water flux-time sequence in the monitoring period True Is a low-dimensional vector Y of (2) True The method comprises the steps of carrying out a first treatment on the surface of the The step S4 specifically comprises the following steps:
s41, simulating a heat transfer process in a river bed in a certain monitoring period, wherein the heat transfer process meets the heat transfer equation in a saturated porous medium:
wherein: t is the temperature, DEG C; ρc=n ρ w c w +(1-n)ρ s c s Jm is the volumetric heat capacity of the riverbed sediment -3 ·℃ -1 The method comprises the steps of carrying out a first treatment on the surface of the n is the porosity of the river bed solid phase medium; ρ s c s And ρ w c w The volumetric heat capacities of the river bed solid medium and water, jm -3 ·℃ -1 ；Is the effective heat conductivity of the river bed, wm -1 ·℃ -1 ；k w And k s Thermal conductivity of water and river bed solid phase medium respectively, wm -1 ·℃ -1 ；F True To monitor the true value of the interactive water flux-time sequence over a period, md -1 ；
S42, constructing a deep neural network DNN to approach the temperature monitoring data T (z, T) of the riverbed in the monitoring period, namely
Wherein:representing the temperature predicted value, z, of the DNN outputIs a space coordinate, t is a time coordinate, and θ is a parameter of DNN;
s43, obtaining according to the chain rule by automatic differentiationDifferentiation with respect to z and t will +.>And the differentiation of the derivative with respect to z and t is substituted into the heat transfer equation in S41 to obtain an equation residual, namely:
wherein: y is Y True Is represented by F True Is a low-dimensional vector of (2);
s44, obtaining parameters θ and low-dimensional vector Y of DNN True The overall loss function of the PINN is defined as follows:
wherein:representing the root mean square error between the predicted value and the true value of the boundary condition given by DNN; />Representing the root mean square error between the predicted value and the true value of the initial condition given by the DNN; />Representing equation residuals;
s45, optimizing the overall loss function by using an L-BFGS optimization algorithm, and enabling theta and Y to be enabled to be in loop iteration True The value of (2) reaches the optimum and is inputY is taken out True Is a function of the optimization value of (a);
s5, inverting the PINN in the step S4 to obtain a low-dimensional vector Y by means of the trained VAE decoder in the step S2 True Reconstructing into a river-groundwater vertical interactive water flow flux-time sequence F in the monitoring period True ；
S6, repeating the steps S3-S5 to obtain a river-groundwater vertical interactive water flow-time sequence of the next monitoring period.
2. The method for realizing continuous monitoring of river-groundwater transient interactive water flux by using the inversion method of river-groundwater vertical transient interactive water flux based on the VAE-PINN algorithm as claimed in claim 1, which is characterized by comprising the following steps:
step 1: selecting a test river reach, placing a temperature measuring net inserted with a plurality of temperature measuring pipes, and ensuring that the temperature measuring pipes are vertical and the top ends of the temperature measuring pipes are flush with the upper interface of the river bed;
step 2: the thermistors in the temperature measurement network are connected to the data acquisition unit one by one through an integrated lead, the data acquisition unit is connected with a power supply, and the sampling frequency of the riverbed temperature data is set;
step 3: the river bed temperature data acquired by the data acquisition unit are timely transmitted to the cloud server through the GPRS module;
step 4: continuously assimilating the riverbed temperature data in each monitoring period based on the VAE-PINN framework through the cloud server, inverting to obtain a vertical interactive water flow-time sequence of the riverbed-groundwater in each monitoring period, and storing the temperature monitoring data and a continuous inversion result of the interactive water flow-time sequence in a MySQL database.
3. The monitoring system for realizing the method for continuously monitoring the river-groundwater vertical transient interactive water flux according to claim 2 is characterized by comprising a temperature measurement network consisting of a plurality of temperature measurement pipes, a data collector, a solar panel, a GPRS module, a cloud server and a MySQL database; 7 thermistors are arranged on each temperature measuring tube from bottom to top;
the temperature measuring net is used for measuring the temperatures at different positions of the river bed;
the data acquisition unit is used for acquiring temperature data of each thermistor in the temperature measurement network;
the solar panel is used for supplying power to the data collector and the GPRS module;
the GPRS module is used for transmitting the riverbed temperature data acquired by the data acquisition unit to the cloud server;
the cloud server obtains a river-groundwater vertical interaction water flow-time sequence of each monitoring period by utilizing a VAE-PINN framework according to continuous inversion of the river bed temperature data in the monitoring period;
the MySQL database is used for storing temperature data and continuous inversion results of the water flow-time sequence.
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