Membrane channel biological pollution multi-physical field simulation method based on physical information deep learning

Abstract

The invention discloses a membrane channel biological pollution multi-physical field simulation method based on physical information deep learning, which comprises the following steps: acquiring sampling data, and mapping the sampling data into a biological membrane morphology characterization field which is continuously distributed along with space coordinates; constructing a deep neural network model, taking the space coordinates of the membrane channel as input, taking multi-physical field state variables in the membrane channel as output, and establishing a mapping relation from the space coordinates to physical fields; a composite loss function driven by physical information is constructed, the composite loss function comprises a physical equation residual error used for constraining a physical field to meet a preset physical conservation law and a boundary condition residual error item used for constraining a boundary condition, and physical field distribution output by the model is made to conform to a physical evolution law in a membrane channel and biological membrane pollution characteristics at the same time; inputting space coordinates of a to-be-predicted area into the trained deep neural network model to obtain full-field physical quantity distribution information in the polluted membrane channel; the quantitative digital basis is provided for the anti-pollution bionic separation net.

Description

Technical Field

[0001] This invention relates to the field of reverse osmosis water treatment technology, specifically to a multi-physics simulation method for membrane channel biological fouling based on deep learning of physical information. Background Technology

[0002] Reverse osmosis and nanofiltration technologies are currently the mainstream technologies for seawater desalination, industrial pure water production, and wastewater reuse worldwide. However, microbial fouling remains the Achilles' heel of membrane systems, hindering their long-term stable operation. Microorganisms adhere to and grow on the membrane channel's mesh surface, forming biofilms that not only cause channel blockage and a sharp increase in system pressure drop (increased energy consumption), but also trigger severe concentration polarization, leading to a decrease in permeate flux and desalination rate. In recent years, deep learning has shown potential in fluid prediction, but its direct application to membrane fouling simulation still faces significant challenges. On the one hand, traditional convolutional neural networks or recurrent neural networks lack physical constraints, and their predictions often fail to meet mass or momentum conservation, easily producing predictions that violate physical principles. Simultaneously, purely data-driven models require training with tens of thousands of sets of high-quality CFD or experimental data. However, in the practical engineering context of biofouling, due to the dynamic evolution of channel geometry and the limitations of multiphysics measurement methods, obtaining large-scale and comprehensive physical field annotation data is not only extremely costly but also difficult to achieve under many extreme conditions. Summary of the Invention

[0003] Purpose of the invention: The purpose of this invention is to provide a multiphysics simulation method for membrane channel biofouling based on deep learning of physical information. This method provides an intelligent method for simulating the velocity, pressure, and concentration fields within membrane channels under biofouling conditions without requiring massive amounts of labeled data, satisfying physical conservation laws, and improving computational speed by an order of magnitude, thereby solving the problems existing in the background technology.

[0004] Technical solution: The present invention provides a multiphysics simulation method for membrane channel biofouling based on deep learning of physical information, comprising the following steps: Step 1: Obtain sampling data characterizing the distribution of biofouling within the membrane channel and map it into a biofilm morphology characterization field continuously distributed with spatial coordinates; Step 2: Construct a deep neural network model, using the spatial coordinates of the membrane channel as input and the multi-physics field state variables within the membrane channel as output, to establish a mapping relationship from spatial coordinates to physical fields; Step 3: Construct a physical information-driven composite loss function, which includes physical equation residuals used to constrain the physical field to satisfy a preset physical conservation law, and boundary condition residuals used to constrain the boundary conditions. Step 4: Embed the biofilm morphology characterization field into the residual terms of the physical equation, and train the deep neural network model using the composite loss function. By minimizing the composite loss function, the physical field distribution output by the model can simultaneously conform to the physical evolution law within the membrane channel and the biofilm pollution characteristics. Step 5: Input the spatial coordinates of the region to be predicted into the trained deep neural network model to obtain the distribution information of the physical quantities of the entire field within the contaminated membrane channel.

[0005] Furthermore, step 1 also includes the smoothing and continuous processing of biofilm properties, that is, using a smooth transition function to transform the discrete biofilm boundary into a continuous field of physical property parameters, so as to achieve a smooth transition of various parameters in the physical equation at the interface between the fluid and the biofilm, and avoid numerical oscillations caused by abrupt changes in interface parameters.

[0006] Furthermore, in step 2, the multiphysics state variables include the velocity field, pressure field, and substrate concentration field, which are used to characterize the fluid dynamics and solute mass transfer behavior under the influence of biofouling.

[0007] Furthermore, in step 2, the training of the deep neural network model adopts a phased optimization strategy. First, an optimization algorithm with global search capability is used for preliminary optimization to enable the model to quickly locate the physically reasonable region. Then, the algorithm is switched to an optimization algorithm with local precise locking capability for fine solution to improve prediction accuracy.

[0008] Furthermore, in step 3, the physical equation residuals include: fluid dynamics residuals, mass transfer and biochemical reaction residuals, and mass conservation constraint terms; among them, the fluid dynamics residuals are used to describe the fluid motion behavior in the flow channel region and biofilm region within the membrane channel; the mass transfer and biochemical reaction residuals are used to describe the transport process of solutes driven by the flow field and the nutrient uptake and consumption process of the biofilm; and the mass conservation constraint terms are used to force the predicted physical field to satisfy the fluid continuity equation.

[0009] Furthermore, the fluid dynamics residual term is constructed based on the modified momentum equation that introduces the resistance mechanism of porous media. By automatically loading different resistance coefficients in different regions, a unified mathematical description of the clean flow channel region and the biofilm contaminated region is achieved, thereby avoiding the need to divide the fluid region and the biofilm region into separate grids.

[0010] Furthermore, the mass transfer and biochemical reaction residual terms are constructed based on the convection-diffusion-reaction equation coupled with biochemical reaction kinetics, and are used to quantitatively describe the changes in solute concentration gradient inside the biofilm caused by microbial metabolic activities, thereby realizing the two-way physical coupling of the fluid field and the concentration field.

[0011] Furthermore, in step 3, the boundary condition residual terms include inlet velocity constraints, outlet pressure constraints, solid wall no-slip constraints, and membrane surface flux constraints based on solute mass balance; the membrane surface flux constraints based on solute mass balance are used to force the model prediction results to conform to the actual physical operating environment inside the membrane channel.

[0012] Furthermore, the method also includes transfer learning, that is, after training the basic model under standard working conditions, when facing new pollution scenarios or geometric configurations, the weight parameters of the basic model are transferred to the new model as initial weights, and then the boundary conditions and physical constraints under the new working conditions are used for rapid fine-tuning to achieve rapid adaptation to multiple scenarios and multiple configurations.

[0013] Beneficial Effects: Compared with existing technologies, this invention has the following significant advantages: Through "few-sample fine-tuning and physical information constraints," the computation speed is increased by 1-2 orders of magnitude compared with traditional CFD software, greatly improving the optimization and iteration efficiency of the mesh structure; due to the embedding of control equation residuals within the network, the model prediction results strictly follow the physical conservation laws, effectively solving the physical distortion problem inherent in pure data-driven AI, and accurately capturing the microscopic physical details of the contaminated area (such as local dead zone shear force); this invention utilizes self-supervised learning based on physical mechanisms, enabling the solution of physical fields with only a very small amount of labeled data, breaking the dependence of traditional deep learning on massive experimental data; this solution method not only yields results but also allows for the inference of biofilm characteristics (such as permeability) through sensitivity analysis, providing quantitative digital basis for the development of anti-pollution biomimetic meshes and the formulation of precise cleaning plans. This invention achieves rapid end-to-end reconstruction from spatial coordinates to physical field distribution by solidifying the trained neural network model, thereby obtaining the full-field velocity, pressure and concentration distribution within the fouled membrane channel, and further calculating pressure drop, membrane shear force and flux performance indicators for quantitative assessment of membrane fouling degree and optimization of operating conditions. Attached Figure Description

[0014] Figure 1 This is an overall flowchart of the intelligent solver for the biocontamination physical field of the membrane channel mesh of the present invention; Figure 2 This is a schematic diagram of the geometric structure of the simulation computation domain of the present invention; Figure 3 This is a schematic diagram of the neural network architecture of the present invention; Figure 4 This is a schematic diagram of the transfer learning process of the present invention. Detailed Implementation

[0015] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0016] like Figure 1As shown, this invention provides a multi-physics simulation method for membrane channel biofouling based on deep learning of physical information. This method uses spatial coordinates and sampled data as input, and constructs a general objective function by embedding physical information constraints through a fully connected network. Model training employs a collaborative strategy of global search and local optimization to reconstruct high-fidelity velocity, pressure, and concentration field distributions, and derives performance indicators such as shear force, pressure drop, and mass transfer coefficient, achieving physics-driven intelligent solution and engineering evaluation of multi-field membrane fouling. The specific process includes the following steps: Step 1: Perform 3D geometric modeling of the reverse osmosis membrane channel to be simulated. Define the computational domain. This refers to the flow channel space containing the grid. In this embodiment, the grid adopts the following... Figure 2 The biomimetic V-shaped structure is shown. Then, the physical parameters are initialized. The fluid density is set. Dynamic viscosity Solute diffusion coefficient Based on the characteristics of biofouling, the physical properties of biofilms are pre-defined, including biofilm permeability. Substrate diffusion coefficient within biofilm Simultaneously, based on biochemical kinetic mechanisms, the maximum specific growth rate in the Monod equation was defined. quality conversion ratio and half-saturation constant .

[0017] Step 2: Based on the three-dimensional spatial coordinate system The input is a discrete sampling dataset of microbial concentration obtained from microscopic imaging recognition, cellular automata evolution simulation, or experimental sensor monitoring. This dataset contains biomass density or occupancy status information at multiple spatial sampling points. An interpolation function is used to map these discrete sampling points to a continuous coordinate space within the membrane channel computational domain, constructing a preliminary original microbial concentration field distribution exhibiting step distribution characteristics. To eliminate numerical abrupt changes (discontinuities) in the microbial concentration field at the biofilm edge, a smoothing function is introduced to spatially smooth the preliminary mapped field.

[0018] in, Input value is the length of the smooth transition interval. The output spatial distribution mask represents the concentration of the biofilm: 0 indicates the fluid region, and 1 indicates the biofilm-contaminated region.

[0019] Step 3: Build a like Figure 3 The deep fully connected neural network shown serves as the core of the intelligent solver. This network uses spatial coordinates... As input, the output vector contains the velocity of that spatial coordinate. ,pressure and substrate solute concentration .

[0020] Step 4: Using automatic differentiation techniques, construct a multi-field coupled composite loss function that integrates limited sample data, fluid dynamics, and mass transfer processes. This loss function aims to embed the underlying partial differential equations controlling the evolution of biofouling in membrane channels into the constraint space of the neural network, enabling the model to achieve physically consistent field solutions under weak supervision.

[0021] Step 4.1: First, embed weakly supervised constraints based on known real observations into the composite loss function. This is done by obtaining a very small number of nominal velocity field values ​​derived from experimental measurements or high-fidelity numerical simulations. With the nominal value of the concentration field Data, construct mean squared error loss function and This approach serves as an effective supplement to physical modeling, forcing the neural network to align with observed values ​​at key points. It uses a data-driven approach to help correct systematic biases that may arise in the underlying physical equations when describing complex and irregular biofilm boundaries.

[0022] Step 4.2: Apply the smooth, continuous microbial concentration distribution field generated in Step 2. As a space physics mask, it constructs the modified momentum equation residual term. This embodiment uses the Brinkman-Forchheimer framework to uniformly describe the hydrodynamic behavior of the flow channel region and the biofilm region:

[0023] in, Indicates fluid density, This represents the instantaneous velocity vector predicted by the neural network. Indicates fluid pressure. For gradient operators, For the Laplace operator, Indicates fluid dynamic viscosity, Indicates biofilm permeability, This represents the inertial drag coefficient. Simultaneously, the fluid mass conservation constraint is enforced, and the residual term of the continuity equation is constructed:

[0024] Ensure that the flow field at each spatial sampling point within the complex contaminated mesh flow channel strictly adheres to the incompressibility condition.

[0025] Step 4.3: Simultaneously construct the residual terms of the convection-diffusion-reaction equation describing solute transport and microbial metabolic processes:

[0026] in, This represents the local nutrient concentration predicted by the network. This represents the substrate diffusion coefficient distribution of the fluid. This represents the diffusion coefficient of the substrate within the fluid. This represents the diffusion coefficient of the substrate within the biofilm. The equation directly uses the instantaneous velocity vector predicted by the neural network in the preceding steps. As parameters of the convection term, this enables unidirectional or bidirectional coupling constraints between the fluid field and the concentration field. Considering the nutrient consumption characteristics within the biofilm, a biochemical reaction source term based on Monod kinetics is coupled into the loss function:

[0027] Where c is the local nutrient concentration predicted by the network. For the maximum specific growth rate, For mass conversion ratio and Half-saturation constant, This represents the biomass concentration. This constraint enables the intelligent solver to quantitatively capture the concentration gradient created by microorganisms due to nutrient uptake.

[0028] Step 4.4: The supervised data items from Step 4.1, the fluid dynamics residuals and mass conservation residuals from Step 4.2, and the mass transfer biochemical reaction residuals from Step 4.3 are weighted and summed to obtain the total physical-driven residual loss item. During training, the loss function calculates the deviation between the neural network's predictions and physical laws, and backpropagates to update the network weights, forcing the physical distribution field output by the neural network to satisfy the Brinkman-Forchheimer equations and the convection-diffusion-reaction equations everywhere in the entire space. This coupled solution mechanism ensures that the velocity, pressure, and concentration fields output by the model are not only numerically coordinated but also have rigorous consistency in physical mechanisms, thus enabling accurate simulation of the complex fluid-mass transfer coupling transport characteristics inside the contaminated mesh.

[0029] Step 5: Add a specific boundary penalty term to the neural network loss function to force the model's predictions to conform to the actual physical operating environment within the membrane channel. The setting of boundary conditions not only determines the definite solutions of the flow field and mass transfer field, but also forms the basis for simulating the system pressure drop and permeate flux under polluted conditions. Randomly selecting boundary conditions... Each data point is added to the calculation, and the subscript indicates the boundary type.

[0030] Step 5.1: For the flow channel inlet boundary, this invention sets the boundary as a fully developed flow, forcing the velocity vector to satisfy a preset constant inlet velocity loss term:

[0031] in, Indicates the number of samples at the entrance boundary. This represents the predicted distribution of the inlet boundary velocity. The average velocity is The velocity distribution of the flow is fully developed. A constant reference pressure is set for the outlet boundary of the flow channel. Boundary pressure loss term:

[0032] in, Indicates the number of samples taken at the export boundary. This represents the predicted distribution of the outlet boundary pressure. A no-slip boundary condition loss term is uniformly applied to the solid walls within the membrane channel, including the spacer surface and the membrane surface: in, This indicates the number of samples taken from the boundaries of the mesh surface and the membrane surface. This represents the predicted distribution of velocities at the boundaries of the mesh surface and the membrane surface. For the internal region of the biofilm, the velocity decay is already covered by the porous media resistance term in step 4.2, and does not need to be set again here.

[0033] Step 5.2: For the mass transfer process, a constant initial solute concentration is assigned to the inlet boundary. The corresponding loss term: in, Indicates the number of samples at the entrance boundary. This represents the predicted distribution of substrate concentration at the inlet boundary. For the gridded solid surface, a no-flux boundary condition is set to indicate that the solute cannot penetrate the grid support, and a boundary loss term is included. in, This indicates the number of samples taken from the surface of the mesh. Represents the unit normal vector of a geometric surface. This represents the predicted distribution of substrate concentration on the membrane surface. Considering the highly selective permeability of reverse osmosis membranes, solutes cannot pass through the membrane layer with the permeate but instead accumulate on the membrane surface. This invention constructs a Robin boundary condition constraint loss based on mass balance in the loss function:

[0034] in, This indicates the number of samples taken at the membrane surface boundary. The unit normal vector of the membrane surface. This represents the diffusion coefficient of the substrate within the fluid. This represents the predicted distribution of membrane surface velocities. This represents the predicted distribution of substrate concentration at the membrane surface. This term induces a neural network to learn and reconstruct the solute distribution at the membrane surface under high concentration gradients by forcing the total solute flux normally to the membrane surface to be zero.

[0035] Step 6: During the model training phase, this invention integrates the physical residual loss constructed in Step 4 with the boundary constraint loss determined in Step 5 using a weighted average to construct the overall objective function. To address the differences in physical dimensions and numerical magnitudes among the pressure, velocity, and concentration fields, this embodiment performs dimensionless processing on the parameters. The optimization process is executed in two stages: first, the Adam optimization algorithm is used for global coarse-grained optimization, utilizing its stochastic gradient descent characteristics to ensure the model quickly locates a physically reasonable region on a wide loss plane; then, the algorithm switches to the L-BFGS quasi-Newton algorithm, using its second derivative information to lock in the optimal solution locally.

[0036] Step 7: After the neural network training converges and the weight parameters are solidified, the model evolves into a continuous analytic function about the membrane channel space. In the physical field reconstruction stage, the solver inputs any discrete coordinate vector within the membrane channel into the neural network with solidified weights, and can output high-precision physical information for that location in parallel. Furthermore, the output pressure field can be used to calculate the total pressure drop between the inlet and outlet, assessing the increased energy consumption caused by biofilm blockage; simultaneously, the solute concentration on the membrane surface can be used to calculate the local osmotic pressure, and then combined with the transmembrane pressure difference to predict the effective permeate flux distribution after biofouling. This end-to-end reconstruction method eliminates the dependence on cumbersome time-step iterations in traditional numerical simulations, achieving a rapid closed loop from contamination conditions to performance feedback.

[0037] Step 8: As Figure 4 As shown, to further improve the solving efficiency of the intelligent solver when facing different operating environments and complex geometric configurations, this invention introduces a transfer learning mechanism. When dealing with multiple sets of varying mesh structure parameters, this embodiment does not train from scratch for each operating condition. Instead, it first trains and solidifies a "basic model" with underlying general physical characteristics under a standard baseline operating condition. When a new biological pollution scenario or geometric variable is input, the solver uses a weight transfer strategy to directly transfer the learned fluid dynamics prior knowledge and mass transfer law parameters from the basic model to the target model as initial weights. Subsequently, fine-tuning is performed using a small number of boundary condition constraints and specific physical equation residuals under the target operating condition, enabling the model to adapt to the new physical environment within a very short iteration cycle.

Claims

1. A multiphysics simulation method for membrane channel biofouling based on deep learning of physical information, characterized in that, Includes the following steps: Step 1: Obtain sampling data characterizing the distribution of biofouling within the membrane channel and map it into a biofilm morphology characterization field continuously distributed with spatial coordinates; Step 2: Construct a deep neural network model, using the spatial coordinates of the membrane channel as input and the multi-physics field state variables within the membrane channel as output, to establish a mapping relationship from spatial coordinates to physical fields; Step 3: Construct a physical information-driven composite loss function, which includes physical equation residuals used to constrain the physical field to satisfy a preset physical conservation law, and boundary condition residuals used to constrain the boundary conditions. Step 4: Embed the biofilm morphology characterization field into the residual terms of the physical equation, and train the deep neural network model using the composite loss function. By minimizing the composite loss function, the physical field distribution output by the model can simultaneously conform to the physical evolution law within the membrane channel and the biofilm pollution characteristics. Step 5: Input the spatial coordinates of the region to be predicted into the trained deep neural network model to obtain the distribution information of the physical quantities of the entire field within the contaminated membrane channel.

2. The method for simulating biocontamination of membrane channels based on deep learning of physical information according to claim 1, characterized in that, Step 1 also includes the smoothing and continuous processing of biofilm properties, that is, using a smooth transition function to transform the discrete biofilm boundary into a continuous field of physical property parameters, so as to achieve a smooth transition of various parameters in the physical equation at the interface between the fluid and the biofilm, and avoid numerical oscillations caused by abrupt changes in interface parameters.

3. The method for simulating biocontamination of membrane channels based on deep learning of physical information according to claim 1, characterized in that, In step 2, the multiphysics state variables include the velocity field, pressure field, and substrate concentration field, which are used to characterize the fluid dynamics and solute mass transfer behavior under the influence of biofouling.

4. The method for simulating biocontamination of membrane channels based on deep learning of physical information according to claim 1, characterized in that, In step 2, the training of the deep neural network model adopts a phased optimization strategy. First, an optimization algorithm with global search capability is used for preliminary optimization to enable the model to quickly locate the physically reasonable region. Then, the algorithm is switched to an optimization algorithm with local precise locking capability for fine solution to improve prediction accuracy.

5. The method for simulating biocontamination of membrane channels based on deep learning of physical information according to claim 1, characterized in that, In step 3, the physical equation residuals include: fluid dynamics residuals, mass transfer and biochemical reaction residuals, and mass conservation constraint terms. Among them, the fluid dynamics residuals are used to describe the fluid motion behavior in the flow channel region and biofilm region within the membrane channel; the mass transfer and biochemical reaction residuals are used to describe the transport process of solutes driven by the flow field and the nutrient uptake and consumption process of the biofilm; and the mass conservation constraint terms are used to force the predicted physical field to satisfy the fluid continuity equation.

6. The method for simulating biocontamination of membrane channels based on deep learning of physical information according to claim 5, characterized in that, The fluid dynamics residual term is constructed based on the modified momentum equation that introduces the resistance mechanism of porous media. By automatically loading different resistance coefficients in different regions, a unified mathematical description of the clean flow channel region and the biofilm contaminated region is achieved.

7. The method for simulating biocontamination of membrane channels based on deep learning of physical information according to claim 5, characterized in that, The mass transfer and biochemical reaction residual terms are constructed based on the convection-diffusion-reaction equation coupled with biochemical reaction kinetics. They are used to quantitatively describe the changes in solute concentration gradient inside the biofilm caused by microbial metabolic activities, thus realizing the two-way physical coupling between the fluid field and the concentration field.

8. The method for simulating biocontamination of membrane channels based on deep learning of physical information according to claim 1, characterized in that, In step 3, the boundary condition residual terms include inlet velocity constraints, outlet pressure constraints, solid wall no-slip constraints, and membrane surface flux constraints based on solute mass balance. The membrane surface flux constraints based on solute mass balance are used to force the model prediction results to conform to the actual physical operating environment inside the membrane channel.

9. The method for simulating biocontamination of membrane channels based on deep learning of physical information according to claim 1, characterized in that, The method also includes transfer learning, which involves training a basic model under standard operating conditions and then transferring the weight parameters of the basic model to the new model as initial weights when faced with new pollution scenarios or geometric configurations. Then, the boundary conditions and physical constraints under the new operating conditions are used for rapid fine-tuning to achieve rapid adaptation to multiple scenarios and configurations.

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