Method for in-situ obtaining biofilm mechanical parameters in porous media and application thereof

Abstract

The application discloses a method for in-situ obtaining mechanical parameters of a biofilm in a porous medium and application of the method to biofilm deformation simulation and parameter inversion in the porous medium. The mechanical parameters include Young's modulus and Poisson's ratio. The method for in-situ obtaining mechanical parameters of a biofilm in a porous medium comprises the following steps: obtaining biofilm deformation related data in the porous medium, including space-time coordinates, flow velocity, pressure and displacement data; using a deep neural network to construct a mapping relationship between the space-time coordinates and the flow velocity, pressure and displacement; training the deep neural network model by calculating and minimizing a loss function to obtain the mechanical parameters of the biofilm in the porous medium. The application can quickly and accurately obtain the deformation response and mechanical properties of the biofilm under the premise of not damaging the original medium structure through a deep learning algorithm, is suitable for multiple fields such as water quality control, biological remediation and soil remediation, and provides a theoretical basis and technical support for related applications.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of microbial research and machine learning simulation, and particularly relates to a method for in-situ acquisition of biofilm mechanical parameters in porous media and application thereof. BACKGROUND

[0002] The study of biofilm deformation simulation is one of the key technologies in the understanding of biofilm behavior. By deeply understanding the deformation response of biofilm under external force (such as force caused by factors such as fluid flow, particle or bubble impact), scientific basis can be provided for the application of biofilm in the fields of biological remediation, pollutant filtration and water quality control. The mechanical properties of biofilm, such as Young's modulus and Poisson's ratio, as important parameters of linear elastic materials, have gradually become the focus of research. However, due to the influence of various factors on the mechanical properties of biofilm, the mechanical properties of biofilm cannot be directly determined by simple prediction models, and need to be measured by specific experimental methods. In order to better understand and predict the deformation behavior of biofilm in porous media, researchers have proposed some models based on numerical simulation methods such as computational fluid dynamics (CFD) and finite element analysis (FEA). However, these models usually have large amount of calculation when dealing with large-scale, multi-scale complex problems, and need a large amount of experimental data for verification.

[0003] Therefore, it is important to quickly and accurately simulate the deformation of biofilm in porous media and evaluate the mechanical properties of biofilm according to the simulation results.

[0004] The reason for using the model is that it is not clear how quickly the mechanical properties of biofilm will change after being detached from the original environment, so the ex situ measurement of biofilm has great limitations, such as Figure 1 As shown in the following Navier-Stokes equation, under the assumption of incompressibility, the fluid motion in the cavity is described by the conservation of mass and momentum:

[0005]

[0006] where ρ f is the fluid density, u is the cavity flow rate, t is the time, σ f is the stress tensor, p is the pressure, μ is the dynamic viscosity, and I is the unit matrix.

[0007] In the biofilm, the fluid motion is described by Darcy's law:

[0008]

[0009]

[0010] where u is the flow velocity within the biofilm, p is the pressure, μ is the dynamic viscosity, and κ is the permeability.

[0011] For the biofilm, it is assumed that it is a linear elastic material, and the equilibrium equation of the biofilm is:

[0012]

[0013] where ρ s is the biofilm density, v s is the displacement, t is the time, σ s is the stress tensor of the biofilm, f is the volume force on the biofilm, and for linear elastic materials, considering the pore pressure within the biofilm, the relationship between stress and strain is:

[0014] σ s =2μ s ε+λ s tr(ε)I-αpI

[0015] where μ s ,λ s is the Lamé parameter, which can be expressed by Young's modulus (E) and Poisson's ratio (v). ε is the strain tensor of the biofilm, I is the identity matrix, α is the Biot-Willis coefficient, which is assumed to be 1 here, and p is the pressure. Summary of the Invention

[0016] The present invention provides a method for in situ acquisition of the mechanical parameters of biofilms in porous media and its application. A mapping relationship between spatiotemporal coordinates and flow velocity, pressure, and displacement is constructed through a deep neural network. The biofilm mechanical parameters Young's modulus and Poisson's ratio are used as learnable parameters for inversion to simulate biofilm deformation, thereby obtaining the Young's modulus and Poisson's ratio of the biofilm in situ.

[0017] [1] A method for in situ acquisition of mechanical parameters of a biofilm in a porous medium, wherein the mechanical parameters include Young's modulus and Poisson's ratio, the method comprising:

[0018] Obtain data related to biofilm deformation in porous media, including time and space coordinates, flow velocity, pressure, and biofilm displacement data;

[0019] Use deep neural networks (DNNs) to construct implicit conversion relationships between spatiotemporal coordinates and flow velocity, pressure, and biofilm displacement;

[0020] The deep neural network parameters are determined by calculating and minimizing the loss function L of the deep neural network, and the deep neural network model training is completed at the same time. During the training process, the mechanical parameters of the biofilm in the porous medium are obtained by inversion. The loss function L is expressed as follows:

[0021] L = λ data L data + λ physics L physics

[0022]

[0023] where L data is the data loss, L physics is the total physical constraint, λ data and λ physics are the corresponding weight coefficients, u, p, v s represent the acquired flow velocity, pressure, biofilm displacement data, respectively, represent the deep neural network predicted values of flow velocity, pressure, biofilm displacement, respectively, λ u , λ p , λ s are the weight coefficients of the fitting loss of the corresponding type of data, f1, f2, f3, f4, f5 represent the residuals of the velocity field, pressure field, displacement field, and the flow velocity and stress condition differential equations of the fluid-structure boundary, respectively, λ1, λ2, λ3, λ4, λ5 are the weight coefficients of the corresponding differential equation residuals;

[0024]

[0025] where ρ f is the fluid density, t represents time, σ f represents the stress tensor of the fluid, Ω f represents the cavity flow domain, T represents the maximum time, κ is the permeability, μ is the dynamic viscosity, Ω s represents the biofilm domain, ρ s is the biofilm density, σ s represents the stress tensor of the biofilm, f s is the volume force acting on the biofilm, represents the boundary between the cavity flow domain and the biofilm domain, n f represents the unit outer normal vector of the cavity flow domain and biofilm boundary, pointing from the flow domain to the biofilm domain, n s represents the unit outer normal vector of the biofilm domain and biofilm boundary, pointing from the biofilm domain to the flow domain; the fluid and biofilm stress tensors are calculated through the following relationship:

[0026]

[0027] Considering the pore pressure in the biofilm,

[0028]

[0029] wherein: I is an identity matrix; a is a Biot-Willis coefficient (which may be assumed to be 1, for example); μ s , λ s are the Lame parameters, expressed in terms of Young's modulus E and Poisson's ratio v:

[0030]

[0031] In some embodiments, the input of the deep neural network model is a spatiotemporal coordinate (x, y, t), where x and y are the horizontal and vertical coordinates of a point in a two-dimensional experimental image in a Cartesian coordinate system, and t is time; and the output of the deep neural network is a predicted field

[0032] In some embodiments, the method can further comprise fabricating a microfluidic chip device and performing a flow experiment;

[0033] The microfluidic chip device is obtained by photolithography and casting (for example, using experimental tools such as a photoetching machine, a uniform glue machine, a glue drying machine, and a developing device), and can represent a physical model of the spatial structure of the porous medium;

[0034] The flow experiment uses a programmable pumping device to inject the bacterial liquid and the nutrient liquid into the microfluidic chip device at a constant flow rate from the inlet according to the actual situation, and changes the flow rate to obtain biofilm deformation-related data.

[0035] In some embodiments, the photolithography is to uniformly apply a layer of photoresist of a certain thickness on a substrate, and after heating and cooling, ultraviolet exposure is performed. During exposure, a mask is placed between the light source and the photoresist, and the ultraviolet light selectively irradiates the photoresist through the mask, causing the irradiated photoresist to undergo crosslinking reaction, changing the solubility of this part of the photoresist in the developing solution, and then the excess photoresist is washed away by the developing solution.

[0036] In some embodiments, the casting is to pour a high polymer (such as polydimethylsiloxane, etc.) onto the substrate after photolithography, and after solidification, stripping and slicing are performed to transfer the pore structure into the microfluidic chip device.

[0037] In some embodiments, the microfluidic chip device can include a glass slide and a microfluidic chip;

[0038] Two holes are punched on the microfluidic chip as liquid inlet and outlet holes, and then the glass slide is attached to the microfluidic chip to form a closed pore channel between the glass slide and the microfluidic chip; the cavity composed of the glass slide and the microfluidic chip contains pores and throats, and can represent the pore structure of the porous medium.

[0039] In some embodiments, the flow experiment is performed by pumping a bacterial solution of a certain concentration through a pumping device, allowing the microorganisms to attach to the microfluidic chip device for a certain period of time (e.g., 2 hours or the like), allowing the biofilm to grow, changing the flow rate, automatically capturing the deformation process of the biofilm in the microfluidic chip device using an automatic imaging device, obtaining images of the porous medium with the biofilm, collecting flow rate and pressure data in the microfluidic chip device using integrated microsensors, and obtaining displacement field data by image processing.

[0040] In some embodiments, the method can employ a deep learning simulation system embedded with a deep neural network model, which includes a control terminal and a server for data processing and deep neural network model training. After the server collects the biofilm deformation related data and user set parameters, it performs deep neural network model training by calculating and minimizing the loss function L, and returns the results to the user. The results include the inverted biofilm mechanical parameters in the porous medium and the predicted flow rate, pressure, biofilm displacement data and related visual images.

[0041] Further, the control terminal can be used to configure the related parameters for deep neural network model training, including training parameters (such as including the used data set, the number of iterations, etc.) and the proportion of training set, test set and validation set, and receive the results returned by the server as flow rate, pressure and displacement corresponding to space-time coordinates (which can be displayed in the form of images, charts, etc.).

[0042] When the server performs deep neural network model training, it first performs data preprocessing, threshold segmentation of the porous medium with biofilm images by RGB value, divides the solid phase, liquid phase and film phase, integrates the obtained flow field, pressure field and displacement field into a data set, and divides it into a training set, a validation set and a test set. The deep neural network model uses the training set to train the model according to the user set parameters through random or optimized network parameter initialization method, sends the trained deep neural network model to the control terminal, and stores it in the MySQL database together with the training data.

[0043] [2] The method of [1] is used for the application of biofilm deformation simulation and parameter inversion in porous media. The method of the present application can be used to simulate the deformation of biofilm in porous media under external force.

[0044] The application can quickly predict the deformation process of the biofilm in the porous medium from limited experimental data and evaluate the mechanical properties such as Young's modulus and Poisson's ratio, etc. The application has the advantages that: the deformation response and mechanical properties of the biofilm can be quickly and accurately obtained by the deep learning algorithm without destroying the original medium structure; the physical constraint term is introduced into the deep neural network loss function to replace part of the experimental data to guide the deep neural network training, so that the prediction accuracy of the model is effectively improved under the condition of a small amount of experimental data; the application is suitable for water quality control, biological remediation, soil remediation and other fields, and provides theoretical basis and technical support for related applications.

[0045] The application provides a method for quickly and accurately simulating the deformation of the biofilm in the porous medium, which can effectively predict the deformation response of the biofilm under different fluid mechanics and external forces, and further provide a scientific basis for the application in the fields of water quality control and biological remediation, and solve the problem of difficult simulation of the deformation process of the biofilm in the porous medium under the action of external force.

[0046] For example, the method of the application can comprise: simulating the deformation process of the biofilm in the porous medium by the microfluidic technology, and combining the deep learning technology to monitor the deformation of the biofilm in real time, and further obtaining the mechanical properties and deformation characteristics of the biofilm under the external environment such as fluid flow, particle impact, etc.

[0047] In some cases, the microfluidic chip device of the application can comprise a glass slide, a microfluidic chip and a plurality of integrated microsensors. The integrated microsensors can be installed at appropriate positions of the glass slide. By changing the injection speed of the nutrient solution, the integrated microsensors can measure the fluid flow rate and pressure in the deformation process of the biofilm in the microfluidic chip device, and the biofilm will have relevant displacement changes as the injection time elapses.

[0048] In the process of training the deep neural network, the application fully considers the physical law constraints followed by the fluid and the biofilm, and realizes it by taking the residual error of the constitutive equation in the process model as an additional regularization constraint. The equation residual errors of multiple physical processes constitute the total physical constraint L physics .

[0049] Compared with the prior art, the application has the following beneficial effects:

[0050] The application can simulate the deformation of the biofilm in the porous medium under different flow rates by using the microfluidic technology, use a set of microscopic imaging system and sensors to obtain the velocity field, pressure field and displacement field in the experiment, and upload the images and other data to an analysis system based on deep learning technology, construct the mapping relationship between the input and output through the deep neural network, obtain the biofilm deformation prediction and obtain the related biofilm mechanical property parameters.

[0051] The application can evaluate the mechanical property according to the displacement field of the biofilm without destroying the original biofilm growth process, and can predict the displacement field of the biofilm in the pore in a short time based on the deep neural network model containing physical constraints under the condition that only a small amount of data can be generated in the experiment.

[0052] Therefore, the application can simply and quickly evaluate the mechanical property of the biofilm in the porous medium, evaluate the shear resistance of the biofilm in the environment such as a filter membrane and a farmland, predict the evolution of the biofilm morphology in the natural porous medium such as soil, and provide a theoretical basis for the implementation of bioremediation in these natural environments. BRIEF DESCRIPTION OF DRAWINGS

[0053] Figure 1 It is a schematic diagram of biofilm adhesion;

[0054] Figure 2 It is a schematic diagram of the process and structure of the microfluidic experiment;

[0055] Figure 3 It is a schematic diagram of the deep neural network training optimization control process of the application;

[0056] Figure 4 It is a schematic diagram of the principle of the deep neural network model. DETAILED DESCRIPTION

[0057] The application will be further described below in combination with the drawings and specific embodiments. It should be understood that these embodiments are only used to illustrate the application and are not used to limit the scope of the application.

[0058] 1. Fabrication of microfluidic chip device:

[0059] 1) Prepare a mask: make a two-dimensional pore model into an optical mask.

[0060] 2) Photoetching and development: use a uniform coating machine to uniformly coat a layer of 50 mu m thick SU-8 2050 photoresist on a single-side polished silicon wafer, use a hot plate for pre-baking to make the photoresist solidify, then use a photoetching machine for ultraviolet exposure, immediately perform post-baking, and after the silicon wafer cools down, use a developing solution to develop and wash away the excess photoresist. After cleaning the silicon wafer, fumigate the wafer with trimethylchlorosilane (TMCS) overnight to obtain a chip mold.

[0061] 3) PDMS pouring: mix Sylgard 184 silicone base and curing agent at a weight ratio of 10:1 to prepare PDMS (polydimethylsiloxane), pour into the mold after removing bubbles in a vacuum environment, and solidify at 80 DEG C for 2 hours.

[0062] 4) Sensor installation: fix a plurality of integrated micro sensors at the corresponding large pore positions of the glass sheet, and the sensor can collect the flow rate and pressure at the point.

[0063] 5) Chip bonding: After cooling, the PDMS was peeled off from the mold, and after slicing and punching, the glass and PDMS were exposed to oxygen plasma for 30 seconds, and then the PDMS was attached to the glass. Subsequently, the chip was placed in a 70°C oven for ten minutes to make the PDMS and glass adhere more tightly.

[0064] 2. Flow experiment, see Figure 2 :

[0065] 1) Bacterial solution preparation: Bacillus subtilis CMCC(B)63501 is a microorganism used for biofilm research, inoculated in 50ml nutrient solution (composition: tryptone 10g / L, yeast powder 5g / L, NaCl 10g / L), the bacterial solution was cultured at 27°C constant temperature with 180rpm speed, and the solution was diluted in fresh nutrient solution at a ratio of 1:10 on the experimental day.

[0066] 2) Preparation of experimental device: connect the L-shaped steel needle to the inlet and outlet of the microfluidic chip with a polyethylene plastic hose, fix the chip under the microscope, and select the appropriate magnification. Use a syringe to sterilize and remove bubbles by passing 75vol% alcohol into the chip, then pass sterile water to wash away excess alcohol, and then pass fresh nutrient solution to create a suitable environment for microbial growth.

[0067] 3) Run the experiment: aspirate the bacterial solution into the syringe, remove the air bubbles in the syringe, and pass it into the microfluidic chip, and stand for 2 hours to allow the microorganisms to fully adhere to the microfluidic channel. Then aspirate fresh nutrient solution into the syringe, fix the syringe on the injection pump (Harvard Apparatus, Pump 11), set the appropriate flow rate, and then start the fluid pumping.

[0068] 4) Image acquisition: after the biofilm grows for 24 hours, change the flow rate, and during the deformation of the biofilm, the microscopic automatic imaging system captures images of the biofilm deformation at an interval of 1 second, and the Ncorr software obtains the displacement field data of the biofilm, while the sensor collects the flow rate and pressure data in the chip and uploads them to the server.

[0069] 3. Model training, see Figure 3 :

[0070] Model training using deep learning simulation system includes the following steps:

[0071] 1) User inputs the parameters of this training in the control terminal, including the training parameters such as the data set used, the number of iterations, the proportion of training set, test set and validation set. The input terminal is a graphical user interface developed by Java language, which transmits data with the server in TCP / IP protocol. The terminal can display displacement image data, and the user can exclude image data with poor imaging quality when selecting data sets.

[0072] 2) The model training server is configured with open source CentOS system, MySQL database, Tomcat server, Python development environment, etc. The pictures captured by the automatic microscopic imaging system are first segmented into liquid phase, membrane phase and solid phase by a Python script, and then the displacement field data obtained from the segmented images and the data collected by the sensor are stored in the MySQL database by using Ncorr software.

[0073] 3) The deep learning algorithm based on neural network is written by Python. According to the user's data set selection from the control terminal, the selected data is obtained through the Crontab service of CentOS. The input of the model is the space-time coordinate (x, y, t), and the output is the predicted physical field First, the actual observation data (u, p, v s ) need to be normalized:

[0074]

[0075] Where U is the original measured data to be normalized, X is the space-time coordinate original data; X max / U max and X min / U min are the maximum and minimum values in the data, respectively, is the normalized data. Then, according to the proportion input by the user, the processed data is divided into training set, validation set and test set.

[0076] 4) Use DNN architecture to build the mapping between space-time coordinate and observation field. It is composed of multiple linear transformations and nonlinear activation functions. A linear transformation can be represented as:

[0077] T l (X l-1 ):=W l X l-1 +b l

[0078] Where W represents the weight of the input to the current layer l from the previous layer l-1 in the neural network, represents the bias of the current layer l, and X0 represents the initial input of the neural network; plus an activation function the neural network of the lth layer which can be represented as:

[0079] N l (X l-1 ): = σ(T l (X l-1 ))

[0080] Thus a general L-layer DNN neural network can be represented as:

[0081]

[0082] where Θ represents all the weights W l and biases b l . As shown in Figure 4 , the training set is applied in the network training process to obtain the data fitting loss:

[0083]

[0084] where λ u , λ p , λ s are the weight coefficients of the corresponding type of data fitting loss, u, p, v s represent the actual observed flow rate, pressure, displacement data, respectively, and u , p

[0085] , v represent the neural network predicted values of flow rate, pressure, displacement, respectively.

[0086]

[0087] where ρ f is the fluid density, t represents time, σ f represents the stress tensor of the fluid, Ω f represents the cavity flow domain in the porous medium, T represents the maximum time, k is the permeability, μ is the dynamic viscosity, Ω s represents the biofilm domain in the porous medium, ρ s is the biofilm density, σ s represents the stress tensor of the biofilm, f s is the volume force experienced by the biofilm, represents the boundary between the cavity flow domain and the biofilm domain, n f represents the unit outer normal vector of the cavity flow domain and biofilm boundary, pointing from the flow domain to the biofilm domain, n sThe unit outer normal vector of the biofilm domain representing the boundary of the cavity domain and the biofilm. The stress tensors of the fluid and the biofilm are calculated by the following relations:

[0088]

[0089] Considering the pore pressure in the biofilm,

[0090]

[0091] where is the predicted pressure; I is the identity matrix; a is the Biot-Willis coefficient, which is assumed to be 1 here; μ s , λ s are the Lamé parameters, which are expressed by the Young's modulus E and the Poisson's ratio v:

[0092]

[0093] At the same time, the parameters representing the mechanical properties of the biofilm, the Young's modulus and the Poisson's ratio, are taken as the trainable parameters of the neural network to update iteratively, so as to realize the unified solution of the forward and inverse problems.

[0094] The above control equation residuals are added to the loss function of the neural network as regularization constraints to guide the training of the neural network, so as to minimize the equation residuals and make the output of the neural network satisfy the PDE as much as possible. The total physical mechanism constraint term composed of each equation residual is:

[0095]

[0096] where λ1, λ2, λ3, λ4 and λ5 are the weight coefficients of the corresponding differential equation residuals, respectively;

[0097] Finally, the data fitting loss L data and the PDE residual term L physics are added together to obtain the total loss function:

[0098] L = λ data L data + λ physics L physics

[0099] where λ data and λ physics are the relevant weight coefficients. Before training, the model parameters are initialized using Glorot, and the Adam optimization algorithm is used to minimize the loss function L, so that the prediction of the neural network meets both the data matching requirements and the PDE description. After multiple iterations of training, the prediction model is finally obtained.

[0100] The obtained model training result is sent to the control terminal and is also stored in the MySQL database. The data returned to the control terminal include a visual image reflecting the training effect, a model prediction accuracy evaluation index, a mechanical property parameter inversion value, and network parameters of the trained model.

[0101] The present application combines microfluidic technology to produce a microscale chip that can represent the pore space structure of an actual porous medium, and relies on the microfluidic chip to carry out micro-flow simulation experiments. The processed data and sensor data of the images in the flow experiment are uploaded to a simulation system based on deep learning, the neural network model is trained by minimizing the loss function in the system, and the obtained training model result is returned to the terminal for visual presentation. Thus, the present application can quickly and accurately simulate the deformation of the biofilm in the medium and invert the biofilm mechanical parameters without damaging the original medium, through simulation experiments and deep learning algorithms, thereby providing a feasible technical reference for the implementation of environmental engineering such as biological remediation and aquatic ecosystem health judgment.

[0102] Furthermore, it is to be understood that even though numerous characteristics and embodiments of the application have been set forth in the foregoing description, many modifications and / or changes of the embodiments of the application described herein will occur to those skilled in the art once armed with the above description. Such modifications are intended to fall within the scope of the appended claims.

Claims

1. A method for in situ acquisition of mechanical parameters of biofilms in porous media, wherein the mechanical parameters include Young's modulus and Poisson's ratio, characterized in that: The method comprises: Obtain data related to biofilm deformation in porous media, including time and space coordinates, flow velocity, pressure, and biofilm displacement data; Use deep neural networks to construct implicit conversion relationships between spatiotemporal coordinates and flow velocity, pressure, and biofilm displacement; The deep neural network parameters are determined by calculating and minimizing the loss function L of the deep neural network, and the deep neural network model training is completed at the same time. During the training process, the mechanical parameters of the biofilm in the porous medium are obtained by inversion. The loss function L is expressed as follows: L=λ data L data +λ physics L physics Among them, L data is the data loss, L physics is the total physical constraint, λ data and λ physics are the corresponding weight coefficients, u, p, v s Respectively represent the acquired flow rate, pressure, and biofilm displacement data, Denote the deep neural network prediction values ​​of flow velocity, pressure, and biofilm displacement, respectively, and λ u ,λ p ,λ s are the weight coefficients of the corresponding type of data fitting loss, f1, f2, f3, f4, and f5 represent the residuals of the differential equations of velocity field, pressure field, displacement field, and flow velocity and stress conditions at the fluid-solid boundary, respectively; λ1, λ2, λ3, λ4, and λ5 are the weight coefficients of the residuals of the corresponding differential equations, respectively; Among them, ρ f is the fluid density, t represents time, σ f represents the stress tensor of the fluid, Ω f represents the cavity flow domain, T represents the maximum time, k represents the permeability, μ represents the dynamic viscosity, Ω s represents the biofilm domain, ρ s is the biofilm density, σ s represents the stress tensor of the biofilm, f s is the volume force acting on the biofilm, represents the boundary between the cavity domain and the biofilm domain, n f The unit external normal vector of the cavity flow domain and the biofilm boundary points from the flow domain to the biofilm domain, n s The unit external normal vector of the biofilm domain, which represents the boundary between the cavity flow domain and the biofilm, points from the biofilm domain to the flow domain. The fluid and biofilm stress tensors are calculated using the following relationship: Considering the pore pressure in the biofilm, Where I is the identity matrix; α is the Biot-Willis coefficient; μ s ,λ s is the Lamé parameter, expressed by Young's modulus E and Poisson's ratio v:

2. The method according to claim 1, characterized in that The input of the deep neural network model is the space-time coordinates (x, y, t), where x and y are the horizontal and vertical coordinates of the corresponding point of the two-dimensional experimental image in the Cartesian coordinate system, and t is the time; the output of the deep neural network is the predicted field.

3. The method according to claim 1, characterized in that The method also includes the fabrication of a microfluidic chip device and flow experiments; The microfluidic chip device is obtained by photolithography and casting, and can represent a physical model of the spatial structure of the porous medium; The flow experiment uses a programmable pumping device to inject bacterial liquid and nutrient solution into the microfluidic chip device from the inlet at a constant flow rate, and changes the flow rate to obtain biofilm deformation-related data.

4. The method according to claim 3, characterized in that The photolithography process involves applying a layer of photoresist of a certain thickness on a substrate, heating and cooling the substrate, and then performing ultraviolet exposure. During exposure, a mask is placed between a light source and the photoresist. When ultraviolet light passes through the mask, it selectively irradiates the photoresist, causing a cross-linking reaction in the exposed photoresist, thereby changing the solubility of this part of the photoresist in a developer. The developer is then used to wash away the excess photoresist. The pouring method is to pour the high molecular polymer onto the photoetched substrate, and then peel and slice it after solidification to transfer the pore structure into the microfluidic chip device.

5. The method according to claim 3, characterized in that The microfluidic chip device comprises a glass slide and a microfluidic chip; Two holes are punched on the microfluidic chip as the liquid inlet and outlet, and then a glass slide is attached to the microfluidic chip to form a closed pore channel between the glass slide and the microfluidic chip; the cavity formed by the glass slide and the microfluidic chip contains pores and throats, which can represent the pore structure of the porous medium.

6. The method according to claim 3 or 5, characterized in that The flow experiment involves delivering a certain concentration of bacterial solution through a pumping device, allowing it to stand for a period of time to allow the microorganisms to fully adhere to the microfluidic chip device. After the biofilm grows, the flow rate is changed, and an automatic imaging device is used to automatically capture the deformation process of the biofilm in the microfluidic chip device to obtain an image of the porous medium with the biofilm. An integrated microsensor is used to collect flow rate and pressure data in the microfluidic chip device, and the image is processed to obtain displacement field data.

7. The method according to claim 1, characterized in that The method adopts a deep learning simulation system embedded with a deep neural network model. The deep learning simulation system includes a control terminal and a server for data processing and deep neural network model training. After collecting biofilm deformation-related data and user-set parameters, the server trains the deep neural network model by calculating and minimizing the loss function L, and returns the results to the user; the results include the inverted biofilm mechanical parameters in the porous medium and the predicted flow rate, pressure, biofilm displacement data and related visualization images.

8. The method according to claim 7, characterized in that The control terminal is used to configure relevant parameters for deep neural network model training, including training parameters and the ratio of training sets, test sets, and validation sets, and receives the results returned by the server, which are flow velocity, pressure, and biofilm displacement corresponding to the spatiotemporal coordinates; When training a deep neural network model, the server first performs data preprocessing, performs threshold segmentation on the porous medium image with the biofilm using the RGB value, divides the solid phase, liquid phase and membrane phase, integrates the acquired flow velocity field, pressure field and displacement field into a data set, and divides the data set into a training set, a validation set and a test set; the deep neural network model is trained using the training set according to the parameters set by the user through a random or optimized network parameter initialization method, and the trained deep neural network model is sent to the control terminal and stored in a MySQL database together with the training data.

9. Application of the method according to any one of claims 1 to 8 in biofilm deformation simulation and parameter inversion in porous media.

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