PINN-based stirring tank particle flow parameter prediction method and system

Abstract

The invention provides a PINN-based stirring tank particle flow parameter prediction method and system, and belongs to the technical field of particle motion prediction in a multiphase flow system. Comprising the following steps: simulating a solid-liquid two-phase flow process in a stirring tank based on a bidirectional coupling simulation model; constructing a physical information neural network model, and embedding a constraint condition based on a particle motion basic physical rule; defining a total loss function including data fitting loss and physical constraint loss based on constraint conditions, and training the established physical information neural network model; and utilizing the trained physical information neural network model to respectively carry out time sequence prediction on particle flow parameters in the stirring tank and real-time prediction on the particle flow parameters under the working condition of high solid content. According to the method, the complex flow of the particles under the high solid content can be rapidly and accurately reduced, the accuracy of predicting the flow parameters of the particles in the stirring tank is improved, and effective data support is provided for regulation and control of the stirring tank.

Description

Technical Field

[0001] This invention belongs to the field of particle motion prediction technology in multiphase flow systems, and particularly relates to a method and system for predicting particle flow parameters in a stirred tank based on PINN. Background Technology

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

[0003] Solid-liquid two-phase stirred tanks, as typical industrial reaction equipment, are widely used in process industries such as chemical, mineral processing, food and pharmaceutical manufacturing. In actual production processes, especially under high solids content conditions, the movement of particle groups within the tank exhibits complex dynamic characteristics such as strong nonlinearity and multi-scale coupling, which poses significant challenges to the accurate acquisition of particle flow parameters and process control.

[0004] Currently, existing research methods for studying particle flow behavior in stirred tanks mainly suffer from the following technical shortcomings: (1) Existing technologies mainly rely on physical experiments. Although physical experimental methods can reflect the real flow state of particle flow behavior in the stirring tank, under high solid content conditions, the dense distribution of particles will cause optical or sensor measurements to be severely blocked, making it difficult to achieve full-domain, real-time parameter capture. In addition, once the working conditions change, the experimental system needs to be reconfigured, resulting in long cycles and high costs, making it difficult to support rapid regulation and optimization in industrial scenarios.

[0005] (2) Existing technologies also include numerical simulation studies of particle flow behavior in stirred tanks. These studies are generally conducted using a computational fluid dynamics-discrete element (CFD-DEM) coupled model. Although this method can simulate particle motion under different operating conditions, the computational load increases dramatically with the number of particles, placing extremely high demands on hardware resources and limiting its real-time prediction capability in actual dynamic working conditions. Summary of the Invention

[0006] To overcome the shortcomings of the prior art, this invention provides a method and system for predicting particle flow parameters in a stirred tank based on PINN. This method can quickly and accurately reconstruct the complex flow of particles under high solids content, improve the accuracy of predicting particle flow parameters in a stirred tank, and provide effective data support for the control of the stirred tank.

[0007] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions: The first aspect of this invention provides a method for predicting particle flow parameters in a stirred tank based on PINN.

[0008] A method for predicting particle flow parameters in a stirred tank based on PINN includes: Based on a two-way coupled simulation model, the two-phase flow process of solid and liquid in a stirred tank is simulated to generate a particle flow simulation dataset, which is then divided into a training set and a test set. A physical information neural network model is constructed, and constraints based on the fundamental physical laws of particle motion are embedded in the constructed physical information neural network model; a total loss function including data fitting loss and physical constraint loss is defined based on the constraints, and the constructed physical information neural network model is trained using the training set; Using the trained physical information neural network model, time-series prediction of particle flow parameters in a stirred tank and real-time prediction of particle flow parameters under high solids content conditions are performed respectively. The prediction results are evaluated using the test set to verify the prediction accuracy of the physical information neural network model under different conditions, and the particle flow parameters are output through visualization tools.

[0009] Furthermore, the two-phase flow process of solid and liquid in the stirred tank is simulated based on a two-way coupled simulation model, including: first, the simulation initialization of the two basic models, the CFD model and the DEM model, respectively; then, the force transmission of the fluid on the particles is carried out sequentially through the CFD model and the DEM model; then, the reaction force transmission of the particles on the fluid is carried out sequentially through the DEM model and the CFD model; finally, the motion state is coordinated by geometric sharing between the CFD model and the DEM model.

[0010] Furthermore, the simulation of the two-phase flow process of solid and liquid in the stirred tank based on the two-way coupled simulation model also includes: optimizing the CFD-DEM simulation model through mesh independence verification, and generating a particle flow simulation dataset through multi-condition simulation, wherein the multi-condition includes different stirring speeds and solid contents.

[0011] Furthermore, the physical constraints of the physical information neural network model are described by partial differential equations, and during the training process, the residuals of the physical equations are embedded into the physical constraint loss function through an automatic differentiation method, thereby forcing the output of the physical information neural network model to conform to the laws of fluid mechanics and particle dynamics.

[0012] Furthermore, during the training of the established physical information neural network model, the effective viscosity of the fluid and the particle drag coefficient are corrected for high solids content scenarios to accurately reflect the influence of interparticle interaction and fluid resistance.

[0013] Furthermore, the effective viscosity of the fluid is corrected using the Krieger-Dougherty model, and the particle drag coefficient is corrected based on the Reynolds number and solids content intervals.

[0014] Furthermore, the training of the physical information neural network model employs the Adam optimizer and an early stopping strategy to prevent overfitting.

[0015] A second aspect of the present invention provides a PINN-based system for predicting particle flow parameters in a stirred tank.

[0016] A PINN-based particle flow parameter prediction system for stirred tanks includes: The bidirectional coupling simulation module is configured to: simulate the two-phase flow process of solid and liquid in a stirred tank based on the bidirectional coupling simulation model, generate a particle flow simulation dataset, and divide the particle flow simulation dataset into a training set and a test set. The model training module is configured to: construct a physical information neural network model, embed constraints based on the fundamental physical laws of particle motion into the constructed physical information neural network model; define a total loss function including data fitting loss and physical constraint loss based on the constraints; and train the constructed physical information neural network model using the training set. The parameter prediction module is configured to: use the trained physical information neural network model to perform time-series prediction of particle flow parameters in the stirred tank and real-time prediction of particle flow parameters under high solids content conditions; evaluate the prediction results through the test set to verify the prediction accuracy of the physical information neural network model under different conditions, and output the particle flow parameters through a visualization tool. A third aspect of the present invention provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps in the PINN-based method for predicting particle flow parameters in a stirred tank as described in the first aspect of the present invention.

[0017] The fourth aspect of the present invention provides an electronic device, including a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in the PINN-based method for predicting particle flow parameters in a stirred tank as described in the first aspect of the present invention.

[0018] The above one or more technical solutions have the following beneficial effects: (1) This invention first simulates the two-phase flow process of solid and liquid in a stirred tank using a two-way coupled simulation model, then constructs a physical information neural network model and embeds constraints based on the fundamental physical laws of particle motion into it; finally, based on the constructed physical information neural network model, it performs time-series prediction of particle flow parameters in the stirred tank and real-time prediction of particle flow parameters under high solid content conditions. This invention, by constructing a prediction framework that integrates two-way coupled simulation and physical information neural network (PINN), can efficiently generate particle flow parameter prediction models covering multiple working conditions based on limited simulation data. This method eliminates the dependence on densely deployed physical sensors, and can quickly simulate particle behavior under different stirring conditions and solid content in digital space, significantly reducing experimental costs and cycle time, and providing effective data support for real-time perception and rapid control optimization of particle flow in industrial settings.

[0019] (2) The physical information neural network introduced in this invention constructs a lightweight proxy model driven by both data and physical mechanisms by embedding physical constraints describing the motion laws of particles. While maintaining the key physical mechanisms, this model avoids the cumbersome iterative calculation process of CFD-DEM in real-time prediction, thereby enabling the rapid output of particle motion parameter prediction results that conform to physical laws at a lower computational cost, thus improving the response speed to dynamic working conditions. Compared with existing technologies, it is more suitable for the real-time requirements in industrial scenarios.

[0020] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0021] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0022] Figure 1 This is a flowchart of the particle flow parameter prediction method in a stirred tank based on PINN in Embodiment 1 of the present invention.

[0023] Figure 2 This is a flowchart of the CFD-DEM bidirectional coupling algorithm in Embodiment 1 of the present invention.

[0024] Figure 3 This is a flowchart of the neural network optimization algorithm based on genetic algorithm in Embodiment 1 of the present invention.

[0025] Figure 4 This is a flowchart of particle motion timing prediction in Embodiment 1 of the present invention. Detailed Implementation

[0026] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0027] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations of the present invention.

[0028] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0029] The overall approach proposed in this invention is as follows: This invention provides a method for predicting particle flow parameters in a stirred tank based on PINN. This method integrates a CFD-DEM bidirectional coupling model with the PINN algorithm. Specifically: First, a solid-liquid stirred tank is numerically simulated using a bidirectional coupling method, and the simulation dataset is divided into training and testing sets to establish a neural network structure. Then, physical constraints are embedded in the neural network to make the data-driven approach more consistent with physical laws. Finally, the constructed PINN neural network is used for time-series and real-time prediction of particle motion parameters, and the prediction effect is evaluated.

[0030] Example 1 This embodiment discloses a method for predicting particle flow parameters in a stirred tank based on PINN.

[0031] like Figure 1 As shown, the method for predicting particle flow parameters in a stirred tank based on PINN includes: Step S1: Based on the two-way coupled simulation model, simulate the two-phase flow process of solid and liquid in the stirred tank, generate a particle flow simulation dataset, and divide the particle flow simulation dataset into a training set and a test set. Step S2: Construct a physical information neural network model and embed constraints based on the fundamental physical laws of particle motion into the constructed physical information neural network model; define a total loss function that includes data fitting loss and physical constraint loss based on the constraints, and train the constructed physical information neural network model using the training set; Step S3: Using the trained physical information neural network model, perform time-series prediction of particle flow parameters in the stirred tank and real-time prediction of particle flow parameters under high solids content conditions; evaluate the prediction results through the test set to verify the prediction accuracy of the physical information neural network model under different conditions, and output the particle flow parameters through visualization tools.

[0032] Based on the above process, this invention can quickly and accurately reproduce the complex flow of particles under high solids content, improve the accuracy of predicting particle flow parameters in a stirred tank, and provide effective data support for the control of the stirred tank. To facilitate understanding of the technical solution of this invention, the specific implementation methods of this invention will be further explained and described below.

[0033] In step S1, based on the CFD-DEM bidirectional coupling simulation model, the two-phase flow process of solid and liquid in the stirred tank is simulated to generate a particle flow simulation dataset, which is then divided into a training set and a test set.

[0034] The core of CFD-DEM bidirectional coupling is to realize the simulation of fluid-particle interaction and information transmission coordination, which is mainly divided into four parts, including: The first part involves the independent simulation initialization of two basic models: the CFD model and the DEM model. The CFD model undergoes fluid initialization settings: based on continuum mechanics, the fluid phase is treated as a continuous medium, and the fluid flow characteristics are simulated using the finite element method. A motion-related setting, such as a slip mesh, is used to pre-determine the computational mesh for the fluid domain. The DEM model undergoes particle initialization settings: each particle is treated as an independent discrete entity, and the particles are initialized based on a discrete particle model, with pre-defined interaction rules between particles.

[0035] The second part sequentially transmits the fluid's force on the particles using a CFD model and a DEM model. First, on the CFD side, the fluid dynamics of the fluid on each particle are calculated based on the fluid flow state, and the fluid force is transmitted to the DEM side. Subsequently, the DEM side receives these fluid forces and, combined with the interaction forces between particles and between particles and boundaries, updates the particle motion state.

[0036] The third part describes the transmission of particle reaction forces on the fluid through CFD and DEM models. First, the DEM model calculates the disturbance feedback of the particles on the surrounding fluid based on the particle's motion state and transmits this reaction force back to the CFD side. After receiving this reaction force, the CFD uses it as the source term of the fluid flow, corrects the fluid flow equation, and updates the changes in velocity and pressure field caused by particle obstruction.

[0037] Part Four: Motion State Coordination and Geometric Sharing. When data transmission involves changes in the particle or fluid domain, the CFD defines motion parameters through a sliding mesh. These parameters are automatically converted into motion frames in the DEM to ensure consistency between the motion reference frames of the fluid domain and the particles. When importing CAS files, the CFD and DEM share the geometric model, and the mesh motion in the CFD is automatically synchronized with the particle motion-related parameters in the DEM, ensuring consistency of motion state during continuous motion.

[0038] The specific implementation process of numerical simulation based on the CFD-DEM two-way coupled simulation model involves simulating particle flow in a stirred tank using an Eulerian-Lagrangian solid-liquid two-phase model. In the two-way coupled simulation model, CFD is used to simulate fluid flow characteristics, while DEM is used to track the trajectory of solid particles under the influence of the fluid. In CFD, to accurately capture solid-liquid mixing behavior, the fluid is treated as a continuous phase, and the turbulence model adopts the standard Reynolds-averaged System (RANS) framework. k -epsilon (Standard) k-ε The Standard model is based on the Boussinesq eddy viscosity assumption. This assumption correlates Reynolds stress with the mean velocity gradient through eddy viscosity, effectively predicting turbulent characteristics. k-ε The model is widely adopted due to its combination of economy, stability, and high computational accuracy. Furthermore, in the DEM, to reduce computational load and simplify particle modeling, the solid phase is treated as a discrete phase, and the rock solid is simplified to spherical particles. Their trajectories are tracked according to Newton's second law, considering both inter-particle and particle-boundary collisions, and parameters are set according to actual working conditions. In the inter-particle interactions, drag and lift jointly determine the particle phase's trajectory and velocity distribution. Since the solid-liquid two-phase system involves changes in particle concentration, the drag calculation uses the Huilin-Gidaspow model. This model, by switching formulas, can adapt to both sparse and dense flow regimes, avoiding computational biases when single models experience concentration changes. The lift calculation uses the Saffman model, which calculates the shear-induced lift experienced by particles when a velocity gradient exists in the fluid. Both models can be selected in the DEM solid phase. After obtaining the numerical simulation dataset (i.e., the particle flow simulation dataset), the training and test sets are divided in an 8:2 ratio.

[0039] Furthermore, the simulation of the two-phase flow process of solid and liquid in the stirred tank based on the two-way coupled simulation model also includes: optimizing the CFD-DEM simulation model through mesh independence verification, and generating a particle flow simulation dataset through multi-condition simulation, wherein the multi-condition includes different stirring speeds and solid contents. In this embodiment, by calculating the motion characteristics of particles in the solid-liquid stirred tank as the stirring speed and solid contents increase respectively, 4500 sets of simulation data are finally generated as a dataset.

[0040] like Figure 2As shown, in the CFD-DEM bidirectional coupled simulation model, the fluid flow characteristics are simulated using traditional continuum mechanics methods. This method can accurately calculate the hydrodynamic forces acting on individual particles. The particle trajectory and motion are tracked using a discrete particle model. The bidirectional coupled simulation model treats each particle as an independent entity, considering factors such as particle interactions, fluid forces, and gravity. By combining the continuous fluid model and the discrete particle model, the CFD-DEM model comprehensively simulates the interaction between fluid and particles, providing a powerful tool for a deeper understanding and optimization of multiphase flow systems. In the DEM-CFD bidirectional coupled simulation, particles, as part of the fluid flow, influence the fluid through bidirectional interactions. That is, the particle motion is affected by interactions with other particles and the surrounding fluid, while the fluid flow state is also altered by the presence of particles. In the DEM, the fluid flow exerts forces such as pressure gradient forces, drag, and virtual mass forces on the particles. In the CFD, the reaction forces acting on the particles act on the fluid phase. A sliding mesh is enabled on the CFD side to achieve shared model motion. These settings are automatically converted into DEM motion frames when the CAS file is imported, and the motion settings in the CFD are also automatically converted into new motion frames in the DEM. In this way, it is possible to ensure that the motion of shared geometry remains consistent between the two programs.

[0041] In step S2, a physical information neural network model is constructed, and constraints based on the fundamental physical laws of particle motion are embedded in the constructed physical information neural network model. Based on the constraints, a total loss function including data fitting loss and physical constraint loss is defined, and the constructed physical information neural network model is trained using a training set.

[0042] The Physical Information Neural Network (PINN) model relies partly on training data and partly on the physical processes described by partial differential equations (PDEs). According to the PINN algorithm, firstly, the neural network training performs a nonlinear mapping from input variables to output variables by minimizing the loss function. Then, automatic differentiation during backpropagation is used to represent all differential operators in the PDE; the PINN loss function includes the adaptation of state variables or boundary conditions (BC) and initial conditions (IC) given the data. PINN's physical constraint function is based on the core assumption that the total net force on particles is zero in steady state. By accurately constructing the force equilibrium relationship of particles, it adapts to the needs of particle motion prediction in high solid content scenarios. Its goal is to solve the problem that existing neural networks, lacking physical constraints, easily produce prediction results that violate mechanical laws when particle collisions and fluid resistance are significant in high solid content scenarios, thus achieving accurate prediction driven by both data fitting and physical constraints. In specific implementation, physical constraints are implemented by embedding the loss function. During model training, the calculation residuals of the physical formulas are introduced into the loss function, which, together with the data fitting loss, constitutes the total loss function. By balancing the weights of data loss and physical loss, the model can learn the patterns in the data while being forced to follow physical laws, ultimately outputting prediction results that conform to the principles of mechanics.

[0043] In this embodiment, the implementation process of the PINN algorithm is as follows: Figure 3 As shown, the particle flow simulation dataset generated by CFD-DEM bidirectional coupling simulation is used for data preprocessing, and the input features and output values ​​are normalized. An MLP is used as the basic framework, with the number of neurons in the output layer as the input feature dimension. Four hidden layers are set, with 256 neurons per layer. The tanh function is used as the activation function, which can effectively fit positive and negative physical quantities and has stable gradient characteristics. The number of neurons in the output layer is used as the output target dimension. Then, the physical laws of particle motion are transformed into mathematical constraints, forcing the neural network output to satisfy the basic physical equations to ensure the physical rationality of the prediction results. Next, the physical equations are rewritten in residual form, and the total loss function is set as a weighted sum of the data fitting loss and the physical constraint loss. Training parameters are configured during model training, and the decreasing trend of the residuals is monitored in real time. An early stopping strategy is used to avoid overfitting. Finally, new input features are input into the trained PINN model, and the output prediction results are restored to the actual physical quantities through inverse normalization. The root mean square error (RMSE) and coefficient of determination (CRM) are used to measure the results. The error and accuracy of the prediction results are evaluated. Through the above steps, the PINN algorithm can achieve efficient and physically consistent prediction of particle motion parameters with the support of a small amount of labeled data, combined with physical laws, providing data support for the real-time control of complex flow fields such as stirred tanks.

[0044] In step S3, the trained physical information neural network model is used to perform time-series prediction of particle flow parameters in the stirred tank and real-time prediction of particle flow parameters under high solids content conditions. The prediction results are evaluated using a test set to verify the accuracy of the physical information neural network model under different conditions, and the particle flow parameters are output through a visualization tool.

[0045] This paper utilizes a trained physical information neural network model to predict the time-series flow parameters of particles in a stirred tank. This includes using the PINN algorithm to predict future time-step particle motion characteristics driven by physical constraints and data fusion. First, various libraries required for prediction are imported, including NumPy for numerical computation, Pandas for data processing, and TensorFlow for deep learning. A random seed is set to ensure consistent random numbers generated in each run, guaranteeing repeatability. Then, a multilayer perceptron (MLP) network is defined, using the hyperbolic tangent (tanh) function as the activation function to predict particle velocities at different positions and times. Physical constraints are defined based on fluid dynamics principles, calculating the drag, gravity, and buoyancy acting on the particles, and establishing their relationship with acceleration according to Newton's second law. A total loss function is constructed by combining the data fitting loss and the physical constraint loss, and the Adam optimizer is used to minimize the loss function. Finally, the PINN structure is defined, including the number of nodes in the output layer, hidden layers, and output layer. Physical parameters such as particle mass, diameter, and density are set. Model instances are created and trained, with loss values ​​printed periodically during training. Predictions were made using the test set, and the prediction results were inversely normalized to the original data range. The RMSE of the particle velocity component was then calculated. Measure the accuracy of model predictions.

[0046] Using a trained physical information neural network model, real-time prediction of particle flow parameters under high solids content conditions is performed. This includes setting up the PINN model structure as described above, but because it's necessary to predict the particle velocity at specific moments under high solids content conditions, its physical constraints need to be adjusted accordingly to the flow characteristics of this scenario to ensure prediction accuracy. The physical constraints in this scenario are based on a steady-state assumption, with the core principle being that the total net force on the particles is zero. The total net force includes drag, particle collision force, gravity, and buoyancy. Drag, as the main force acting on particles during fluid motion, increases significantly with increasing solids content. Since drag is calculated based on the definition of the drag coefficient, corrections to the effective viscosity and drag coefficient are necessary. At high solids content, the effective viscosity is much higher than the baseline viscosity due to inter-particle compression hindering fluid flow. The code uses the Krieger-Dougherty model to calculate the effective viscosity. Regarding the drag coefficient, high solids content exacerbates inter-particle interference. The code uses the Reynolds number (…) ReThe drag coefficient is adjusted by dividing the solids content into intervals to match the actual drag characteristics under different flow conditions.

[0047] like Figure 4 As shown, the entire process of predicting particle motion parameters can be summarized as follows: First, a CFD-DEM coupled model is established, and mesh generation and mesh independence verification are performed. Under the verified mesh system, governing equations are set based on Newton's second law, the Navier-Stokes equations, etc., and the particle motion-related physical quantities involved in the equations are defined, including drag, gravity, buoyancy, etc. Considering the high solids content of the target scenario, the Krieger-Dougherty model is used to correct the effective viscosity, and based on... Re The drag coefficient is calculated in intervals based on the solid content, and physical constraints are embedded based on the steady-state assumption. Hyperparameters required for model training are set, including learning rate, number of iterations, number of hidden layer neurons, and physical constraint weights. The trained model is used to predict particle motion parameters, and the results are presented using visualization tools. RMSE and R-squared values ​​are used. 2 Evaluation indicators are used to verify the accuracy of predictions, and predictions under multiple operating conditions (such as different rotation speeds and solid contents) are also carried out to support the intelligent control of the mixing tank.

[0048] The prediction results are evaluated using a test set to verify the accuracy of the physical information neural network model under different operating conditions. Particle flow parameters are output through visualization tools. Specifically, Paraview is used to generate a particle velocity vector map, visually representing the flow path within the stirred tank from impeller propulsion to radial diffusion and axial circulation, identifying any local dead zones or vortices. Matplotlib is used to plot time-series curves of particle concentration to analyze the stability of the solids content distribution. Furthermore, a comparison curve between predicted and measured particle velocity values ​​can be output, allowing for a direct observation of the prediction accuracy and stability. These visualization results, combined with quantitative indicators, not only verify the model's reliability but also provide direct reference for intelligent control measures such as stirred tank speed adjustment and impeller structure improvement.

[0049] Based on the above process, this invention achieves the following significant advancements: 1) It overcomes the shortcomings of existing experimental methods, such as long experimental cycles and high costs. Specifically, by combining CFD-DEM bidirectional coupling with the PINN algorithm, it achieves efficient prediction of particle flow parameters, enabling real-time prediction of dynamic working conditions and reducing research costs; 2) It reduces the demand for computing resources. Specifically, under high solids content, the large number of particles leads to high computational load in numerical simulation. PINN, based on data-driven and physical constraints, can quickly and accurately output particle motion parameters, making it more suitable for the rapid response needs of industrial scenarios; 3) It overcomes the shortcomings of existing machine learning models that rely solely on data fitting and are prone to violating physical laws. Specifically, by integrating the principles of fluid mechanics and particle dynamics into the loss function, it can force the model to output results that conform to mechanical laws, significantly improving the rationality and generalization ability of predictions.

[0050] Example 2 This embodiment discloses a PINN-based system for predicting particle flow parameters in a stirred tank.

[0051] A PINN-based particle flow parameter prediction system for stirred tanks includes: The bidirectional coupling simulation module is configured to: simulate the two-phase flow process of solid and liquid in a stirred tank based on the bidirectional coupling simulation model, generate a particle flow simulation dataset, and divide the particle flow simulation dataset into a training set and a test set. The model training module is configured to: construct a physical information neural network model, embed constraints based on the fundamental physical laws of particle motion into the constructed physical information neural network model; define a total loss function including data fitting loss and physical constraint loss based on the constraints; and train the constructed physical information neural network model using the training set. The parameter prediction module is configured to: use the trained physical information neural network model to perform time-series prediction of particle flow parameters in the stirred tank and real-time prediction of particle flow parameters under high solids content conditions; evaluate the prediction results through the test set to verify the prediction accuracy of the physical information neural network model under different conditions, and output the particle flow parameters through a visualization tool. Example 3 The purpose of this embodiment is to provide a computer-readable storage medium.

[0052] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the steps in the PINN-based method for predicting particle flow parameters in a stirred tank as described in Embodiment 1 of this disclosure.

[0053] Example 4 The purpose of this embodiment is to provide an electronic device.

[0054] An electronic device includes a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in the PINN-based method for predicting particle flow parameters in a stirred tank as described in Embodiment 1 of this disclosure.

[0055] The steps and methods involved in the apparatuses of Embodiments 2, 3, and 4 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0056] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0057] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A method for predicting parameters of particle flow in a stirred tank based on PINN, characterized in that, The method comprises the following steps: Based on the two-way coupling simulation model, the two-phase flow process of solid-liquid in the stirring tank is simulated, the particle flow simulation data set is generated, and the particle flow simulation data set is divided into a training set and a test set; A physical information neural network model is constructed, and a constraint condition based on the basic physical law of particle motion is embedded in the constructed physical information neural network model; a total loss function including data fitting loss and physical constraint loss is defined based on the constraint condition, and the constructed physical information neural network model is trained through the training set; The trained physical information neural network model is used to perform time series prediction of particle flow parameters in the stirring tank and real-time prediction of particle flow parameters under high solid content conditions; the prediction results are evaluated through the test set to verify the prediction accuracy of the physical information neural network model under different conditions, and the particle flow parameters are output through a visualization tool.

2. The PINN-based in-pit agitator flow parameter prediction method of claim 1, wherein, The two-way coupling simulation model is used to simulate the two-phase flow process of solid-liquid in the stirring tank, which comprises the following steps: firstly, the CFD model and the DEM model are simulated and initialized respectively; then, the force transmission from fluid to particles is sequentially performed through the CFD model and the DEM model; then, the force transmission from particles to fluid is sequentially performed through the DEM model and the CFD model; finally, the geometry sharing is performed through the CFD model and the DEM model to realize the coordination of the motion state.

3. The PINN-based in-pit flow parameter prediction method of claim 2, wherein, The two-way coupling simulation model is used to simulate the two-phase flow process of solid-liquid in the stirring tank, which further comprises the following steps: the CFD-DEM simulation model is optimized through grid independence verification, and the particle flow simulation data set is generated through multi-condition simulation, wherein the multi-condition includes different stirring speeds and solid contents.

4. The PINN-based in-pit agitator flow parameter prediction method of claim 1, wherein, The physical constraint condition of the physical information neural network model is described by a partial differential equation, and the physical equation residual is embedded into the physical constraint loss function through an automatic differentiation method during the training process, so as to force the physical information neural network model to output in accordance with the fluid mechanics and particle dynamics law.

5. The PINN-based in-pit agitator flow parameter prediction method of claim 1, wherein, During the training process of the constructed physical information neural network model, the effective viscosity of fluid and the drag coefficient of particles are corrected for the high solid content scenario, so as to accurately reflect the influence of particle interaction and fluid resistance.

6. The PINN-based in-pit flow parameter prediction method of claim 5, wherein, The correction of the effective viscosity of fluid adopts the Krieger-Dougherty model, and the correction of the drag coefficient of particles is based on the Reynolds number and the solid content partition interval.

7. The PINN-based in-pit agitator flow parameter prediction method of claim 1, wherein, The training of the physical information neural network model adopts the Adam optimizer and adopts the early stopping strategy to prevent overfitting.

8. A PINN-based system for predicting parameters of particle flow in a stirred tank, characterized in that, The method comprises the following steps: A two-way coupling simulation module is configured to simulate the two-phase flow process of solid-liquid in the stirring tank based on a two-way coupling simulation model, generate a particle flow simulation data set, and divide the particle flow simulation data set into a training set and a test set; A model training module is configured to construct a physical information neural network model, embed a constraint condition based on the basic physical law of particle motion in the constructed physical information neural network model, define a total loss function including data fitting loss and physical constraint loss based on the constraint condition, and train the constructed physical information neural network model through the training set; The parameter prediction module is configured to: use the trained physical information neural network model to respectively perform time series prediction of the particle flow parameters in the stirring tank and real-time prediction of the particle flow parameters under high solid content conditions; evaluate the prediction results by using the test set, verify the prediction accuracy of the physical information neural network model under different conditions, and output the particle flow parameters through a visualization tool.

9. A computer-readable storage medium having stored thereon a program, characterized in that, The program is executed by the processor to implement the steps in the PINN-based particle flow parameter prediction method in the stirring tank according to any one of claims 1-7.

10. An electronic device comprising a memory, a processor, and a program stored in the memory and capable of running on the processor, characterized by The processor executes the program to implement the steps in the PINN-based particle flow parameter prediction method in the stirring tank according to any one of claims 1-7.

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