Fluid trajectory tracking method based on physical heuristic neural network

Abstract

The invention relates to a fluid trajectory tracking method based on a physical heuristic neural network, and the method specifically comprises the steps: building a first full-connection network, and obtaining a particle trajectory through the prediction of the first full-connection network; a second full-connection network is established, and the flow field speed and the flow field pressure are obtained through prediction of the second full-connection network based on the particle trajectory; connecting the first full-connection network and the second full-connection network in series, and training to obtain a prediction network; and performing fluid trajectory tracking through the prediction network. According to the method, the accuracy and efficiency of prediction are improved while the physical consistency is ensured.

Description

Technical Field

[0001] The present invention relates to the technical field of fluid flow quantification, and in particular to a fluid trajectory tracking method based on a physics-inspired neural network. Background Art

[0002] With the rapid development of computing hardware and big data, artificial intelligence has provided a powerful tool for building data-driven models. In the field of fluid mechanics, using a large amount of experimental observation and numerical simulation data to train artificial intelligence algorithms has become a new way to solve fluid flow problems. Artificial intelligence methods learn the positional patterns in the data by building models. These models usually contain unknown parameters to capture the relationship between the data. Through optimization processes such as gradient descent, the parameters of the model are adjusted to minimize the difference between the predicted and actual data. The parameters are gradually refined through repeated iterations until the model can accurately reflect the patterns in the data.

[0003] However, as the number of tracked particles increases, the required computing resources also increase accordingly, which greatly affects the feasibility and efficiency of numerical simulations. The increase in the number of particles means that more computing memory and processing time are required, especially for large-scale problems. At the same time, in unstructured grids, Lagrangian particle tracking is slow in calculation, which greatly limits the number of particles that can be actually tracked and the flow state that can be simulated.

[0004] Experimental techniques such as PIV perform well in obtaining velocity distribution in flow fields and can provide intuitive and accurate data about fluid motion. However, since PIV requires the use of high-quality and uniform-density particles as tracking markers, it is not suitable for some low-density or special gas situations. At the same time, as an experimental method for obtaining the velocity distribution of flow fields, PIV cannot measure the flow pressure field due to its single measurement target, requiring additional experimental setup and complex data processing, which increases the complexity and cost of the experiment. Although the flow data obtained by other experimental methods such as drifters are accurate and efficient, the spatial domain that can be measured is much smaller than the size required to study mesoscale flows. The spatial domain covered by the data is often insufficient for comprehensive fluid analysis. For many practical problems, the data obtained through experiments are relatively sparse.

[0005] Traditional AI models often require a large amount of data to obtain effective prediction models. When data is scarce, the performance of these models will drop significantly. In addition, due to their black box characteristics, the interpretability and generalization capabilities of traditional AI models are often questioned. These limitations are particularly important in fields such as fluid mechanics that require high accuracy and strong interpretability. Lack of transparency may hinder the deployment of these models in safety-critical and mission-critical applications. Summary of the invention

[0006] The present invention provides a fluid trajectory tracking method based on a physics-inspired neural network to solve the defects of the prior art.

[0007] The present invention provides a fluid trajectory tracking method based on a physics-inspired neural network, comprising:

[0008] S1: establishing a first fully connected network, and obtaining particle trajectories through prediction of the first fully connected network;

[0009] S2: establishing a second fully connected network, and based on the particle trajectory, obtaining the flow field velocity and the flow field pressure through the second fully connected network prediction;

[0010] S3: Connecting the first fully connected network and the second fully connected network in series and training them to obtain a prediction network;

[0011] S4: Tracking fluid trajectories through the prediction network.

[0012] According to a fluid trajectory tracking method based on a physics-inspired neural network provided by the present invention, step S1 further comprises:

[0013] S11: Establishing a first fully connected network;

[0014] S12: inputting the initial information of the particles into the first fully connected network to obtain the mapped particle displacement;

[0015] S13: Calculate and obtain the particle trajectory according to the particle displacement and the particle initial information.

[0016] According to a fluid trajectory tracking method based on a physics-inspired neural network provided by the present invention, the initial information of the majority of particles in step S12 includes the initial position of the particles, the release time of the particles and the first movement time, wherein the first movement time is the particle movement time under Lagrangian description.

[0017] According to a fluid trajectory tracking method based on a physics-inspired neural network provided by the present invention, the expression of the particle displacement in step S12 is:

[0018]

[0019] in, is the mapped particle displacement, x0 is the initial position of the particle, t0 is the particle release time, τ is the particle motion time under Lagrangian description, and θ is the trainable parameter of the first fully connected network;

[0020] The expression of the particle trajectory in step S13 is:

[0021]

[0022] Among them, x q is the predicted particle trajectory.

[0023] According to a fluid trajectory tracking method based on a physics-inspired neural network provided by the present invention, step S2 further comprises:

[0024] S21: Establishing a second fully connected network;

[0025] S22: Inputting the second motion time and the particle trajectory into the second fully connected network to predict the flow field velocity and the flow field pressure; wherein the second motion time is the particle motion time described by Euler.

[0026] According to a fluid trajectory tracking method based on a physics-inspired neural network provided by the present invention, the expression of the second motion time in step S22 is:

[0027] t=t0⊕τ;

[0028] Among them, t is the particle motion time under Euler description, t0 is the particle release time, and τ is the particle motion time under Lagrangian description.

[0029] According to a fluid trajectory tracking method based on a physics-inspired neural network provided by the present invention, the expression of the flow field velocity in step S22 is:

[0030]

[0031] Among them, u is the predicted fluid velocity, u0 is the fluid velocity in the previous state, x0 is the initial position of the particle, t0 is the particle release time, and τ is the particle motion time described by Lagrangian. is the trainable parameter of the second fully connected network, and θ is the trainable parameter of the first fully connected network;

[0032] The expression of the flow field pressure in step S22 is:

[0033]

[0034] Among them, p is the predicted fluid pressure, and p0 is the fluid pressure in the previous state.

[0035] According to a fluid trajectory tracking method based on a physics-inspired neural network provided by the present invention, the expression of the training loss of the prediction network in step S3 is:

[0036]

[0037] in, To predict the overall training loss of the network, θ is the trainable parameter of the first fully connected network, are the trainable parameters of the second fully connected network, is the loss evaluated at the data point, is the loss evaluated at the collocation point, For the first data loss, For the second data loss, is the first residual physical loss, is the second residual physical loss, λ1 is the first weight parameter, λ2 is the second weight parameter, and λ3 is the third weight parameter.

[0038] According to a fluid trajectory tracking method based on a physics-inspired neural network provided by the present invention, step S4 further includes:

[0039] S41: performing a first automatic differentiation through the prediction network to obtain a derivative of a particle position and a first motion time, wherein the derivative is used to balance the training of the first fully connected network and the second fully connected network;

[0040] S42: Performing a second automatic differentiation through the prediction network to obtain a functional relationship between the flow field velocity, flow field pressure, particle position, and particle movement time.

[0041] According to a fluid trajectory tracking method based on a physics-inspired neural network provided by the present invention, the expression of the functional relationship in step S42 is:

[0042]

[0043] Among them, u is the flow field velocity, t is the particle movement time, is the gradient operator, ρ is the fluid density, p is the flow field pressure, and μ is the fluid dynamic viscosity.

[0044] The present invention provides a fluid trajectory tracking method based on a physics-inspired neural network, and proposes a neural network architecture design called TrajectoryNSNet, which consists of two fully connected networks in series, so that the artificial neural network prediction is more consistent with the laws of physics, thereby providing a more comprehensive understanding of the physical problem under study, and can predict the entire flow field information given only the initial position and motion time, and by combining physical residuals, the connectivity and optimization speed of the two networks are improved. In addition, the two networks in series constrain each other and ultimately reach an optimal solution. The network architecture proposed in the present invention can efficiently process sparse trajectory data and achieve accurate tracking of flow and particle trajectories. The network proposed in the present invention combines the flexibility of data-driven learning with the constraints of the physics-based Navier-Stokes equations, thereby improving the accuracy and efficiency of prediction while ensuring physical consistency, so that the model can adapt to complex flow patterns, and accurately predict the trajectory of particles in different flow scenarios, expanding the scope of application of existing technologies. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0046] Figure 1 A schematic flow chart of a fluid trajectory tracking method based on a physics-inspired neural network provided in an embodiment of the present invention;

[0047] Figure 2 A schematic diagram of a process for predicting particle trajectories through a first fully connected network provided by an embodiment of the present invention;

[0048] Figure 3 A schematic diagram of a flow chart for predicting flow field velocity and flow field pressure through a second fully connected network provided in an embodiment of the present invention;

[0049] Figure 4 A schematic diagram of the performance of the present invention in predicting particle flow trajectories in a simulation example of top cover driven square cavity flow provided by an embodiment of the present invention;

[0050] Figure 5 A schematic diagram of comparison between predicted values ​​and actual values ​​of the present invention in a simulation example of top cover driven square cavity flow provided by an embodiment of the present invention;

[0051] Figure 6 A schematic diagram of the performance of the present invention in predicting particle flow trajectories in a simulation example of complex pipeline flow provided by an embodiment of the present invention;

[0052] Figure 7 A schematic diagram showing a comparison between predicted values ​​and actual values ​​of the present invention in a calculation example of simulating complex pipeline flow provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0053] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings in the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments, and they should not be understood as limitations on the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. In the description of the present invention, it should be understood that the terms used are only for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0054] In order to better understand the embodiments of the present invention, the background of the present invention is first described below.

[0055] Tracking and quantifying fluid flow plays an important role in many natural and engineering applications, such as meteorology, oceanography, ecology, pharmacokinetics, etc. However, the inherent complexity of the Navier-Stokes equations describing fluid flow states makes direct solutions very difficult.

[0056] Numerical methods track passive particles in the fluid and characterize the flow state by solving discrete partial differential equations. Among them, Lagrangian particle tracking based on flow characteristics obtained from fluid dynamics models is an important tool for quantifying fluid transport. By tracking the trajectories of Lagrangian particles representing fluid elements, this method can achieve a comprehensive analysis of fluid motion and an understanding of complex flow phenomena, becoming a valuable tool for studying particle behavior and transport properties in fluid systems.

[0057] Experimental techniques, such as particle image velocimetry (PIV) and floaters, have proven to be effective and accurate in capturing flow information of small-scale and mesoscale fluid dynamics. Particle image velocimetry is a measurement technique developed in the 1980s that can obtain velocity information of the entire flow field in a fraction of a second. PIV has a wide range of applications, from basic turbulence, combustion, two-phase pipe flow, etc. In recent years, advances in positioning and data transmission technology have greatly enhanced the practicality of floaters as experimental tools for measuring mesoscale eddies. Each float can be regarded as a particle moving with the water flow, able to track the sea surface currents and provide key ocean current information including position, velocity and pressure.

[0058] Combine the following Figures 1 to 7 Embodiments of the present invention are described.

[0059] like Figure 1 As shown, the present invention provides a fluid trajectory tracking method based on a physics-inspired neural network, comprising:

[0060] S1: Establish a first fully connected network, and obtain particle trajectories through prediction of the first fully connected network.

[0061] In step S1, the first ANN is controlled by the trainable parameter θ, which maps the particle's initial position, release time, and motion time x0,t0,τ under Lagrangian description to its displacement Then, by adding the particle displacement to the initial position of the particle, we can get the particle trajectory x q .

[0062] like Figure 2 As shown, step S1 further includes:

[0063] S11: Establishing a first fully connected network.

[0064] S12: Inputting the initial particle information into the first fully connected network to obtain the mapped particle displacement.

[0065] Among them, the initial information of most particles in step S12 includes the initial position of the particles, the release time of the particles and the first movement time, wherein the first movement time is the particle movement time under Lagrangian description.

[0066] Wherein, the expression of the particle displacement in step S12 is:

[0067]

[0068] in, is the mapped particle displacement, x0 is the initial position of the particle, t0 is the particle release time, τ is the particle motion time described by Lagrangian, and θ is the trainable parameter of the first fully connected network.

[0069] Furthermore, in step S12, the initial information of the particle is first provided as input data to the fully connected network established previously. The network processes the input data through forward propagation and outputs the displacement of the particle, that is, the relative movement of the particle over a period of time, or the absolute position of the particle at a certain moment. The output displacement data is obtained based on the nonlinear mapping ability of the network to the input data. The mapping ability is achieved through the weights and biases learned during the training process, that is, the trainable parameters θ of the first fully connected network.

[0070] S13: Calculate and obtain the particle trajectory according to the particle displacement and the particle initial information.

[0071] Wherein, the expression of the particle trajectory in step S13 is:

[0072]

[0073] Among them, x q is the predicted particle trajectory.

[0074] In step S13, the particle displacement information obtained from the fully connected network and the initial information of the particle (such as the initial position) are used to calculate the trajectory of the particle, that is, the displacement is added to the initial position to obtain the position coordinates of the particle at different time points. The final particle trajectory is used as input for subsequent calculations or simulations.

[0075] S2: Establish a second fully connected network, and based on the particle trajectory, obtain the flow field velocity and flow field pressure through the second fully connected network prediction.

[0076] In step S2, the second ANN consists of trainable parameters Control, taking the particle trajectory predicted by the first ANN and the motion time t described by Euler as input, learns the mapping between flow field velocity u and pressure p.

[0077] like Figure 3 As shown, step S2 further includes:

[0078] S21: Establish a second fully connected network.

[0079] S22: Inputting the second motion time and the particle trajectory into the second fully connected network to predict the flow field velocity and the flow field pressure; wherein the second motion time is the particle motion time described by Euler.

[0080] The expression of the second motion time in step S22 is:

[0081] t=t0⊕τ;

[0082] Among them, t is the particle motion time under Euler description, t0 is the particle release time, and τ is the particle motion time under Lagrangian description.

[0083] Wherein, the expression of the flow field velocity in step S22 is:

[0084]

[0085] Among them, u is the predicted fluid velocity, u0 is the fluid velocity in the previous state, x0 is the initial position of the particle, t0 is the particle release time, and τ is the particle motion time described by Lagrangian. are the trainable parameters of the second fully connected network.

[0086] Wherein, the expression of the flow field pressure in step S22 is:

[0087]

[0088] Among them, p is the predicted fluid pressure, and p0 is the fluid pressure in the previous state.

[0089] In step S12, the particle motion time and particle trajectory information described by Euler are provided as input data to the second fully connected network established previously. The network processes these input data through forward propagation and outputs the predicted flow field velocity and pressure. The output flow field velocity and pressure are obtained based on the nonlinear mapping ability of the network to the input data. The mapping ability is obtained through the weights and biases learned during the training process, that is, the trainable parameters of the second fully connected network. To achieve.

[0090] S3: Connecting the first fully connected network and the second fully connected network in series and performing training to obtain a prediction network.

[0091] The expression of the training loss of the prediction network in step S4 is:

[0092]

[0093] in, To predict the overall training loss of the network, θ is the trainable parameter of the first fully connected network, are the trainable parameters of the second fully connected network, is the loss evaluated at the data point, is the loss evaluated at the collocation point, For the first data loss, For the second data loss, is the first residual physical loss, is the second residual physical loss, λ1 is the first weight parameter, λ2 is the second weight parameter, and λ3 is the third weight parameter.

[0094] Furthermore, optimizing the above total loss function can obtain the overall ANN, which can not only predict the trajectory of passive particles, but also reveal the flow state of the fluid field. It should be noted that the total loss function has an implicit complex form, which makes the direct solution of the optimization problem very challenging. In order to solve this problem, the present invention adopts a pre-training method. Initially, two fully connected networks are trained separately while keeping the training data unchanged. After this pre-training stage, the network will continue to be trained as a whole.

[0095] S4: Tracking fluid trajectories through the prediction network.

[0096] Wherein, step S4 also includes:

[0097] S41: performing a first automatic differentiation through the prediction network to obtain a derivative of a particle position and a first motion time, wherein the derivative is used to balance the training of the first fully connected network and the second fully connected network;

[0098] S42: Performing a second automatic differentiation through the prediction network to obtain a functional relationship between the flow field velocity, flow field pressure, particle position, and particle movement time.

[0099] The expression of the functional relationship in step S42 is:

[0100]

[0101] Among them, u is the flow field velocity, t is the particle movement time, is the gradient operator, ρ is the fluid density, p is the flow field pressure, and μ is the fluid dynamic viscosity.

[0102] It is important to note that since the measurement data already reflect specific initial / boundary conditions I / BC, these I / BC are either known a priori or obtained through measurement, so there is no need to include them explicitly.

[0103] In addition, the neural network provided by the present invention essentially acts as a function approximator to represent the mapping relationship of each part, so in step S4, using automatic differentiation, we calculate the particle position x q The derivative with respect to the motion time τ The residual between this derivative and the network-predicted velocity is used to further balance the training of the two networks at machine precision. In addition, automatic differentiation constructs the relationship between flow field velocity and pressure and position and motion time.

[0104] Furthermore, a fluid trajectory tracking method based on a physics-inspired neural network and an algorithm theory based on the corresponding neural network provided by the present invention are described below.

[0105] The passive particles under the Lagrangian description studied in this invention represent fluid microcapsules composed of microscopic particles. The size of the fluid microcapsule is large enough on a macroscopic scale to retain the average meaning, and small enough on a microscopic scale to be effectively regarded as a point. Assuming that the process starts from a reference configuration and is mapped to its deformed configuration, it is mathematically represented as a mapping from reference coordinates to Euler coordinates.

[0106]

[0107] Among them, x = X (ξ, t) is the Euler coordinate space position of the fluid microcapsule ξ at time t. This mapping is one-to-one, continuous and differentiable, so the fluid microcapsule ξ can also be expressed as ξ = ξ (x, t) ∶ = X -1 (x,t), where It is a mapping from the Euler coordinates back to the reference coordinates. The present invention uses x as the mapping X to simplify the notation and regards the change from the Euler coordinates to the Lagrange coordinates as a variable change.

[0108] x=x(ξ,τ),t=τ#(1)

[0109] For trajectories, identification is obvious because the position of the fluid microcapsule is known at any time. We propose to identify each fluid microcapsule by referring to its initial position x0 and initial motion time t0, that is:

[0110] x=x(ξ,τ)=x(x0,τ0,τ)=x(x0,t0,t)#(2)

[0111] The above expression is an Euler vector field and will be handled directly in the Euler model.

[0112] In order to express the physical laws composed of partial derivatives, they need to be converted to the Lagrangian coordinate system (x(ξ,τ),τ). According to the chain rule, we can get:

[0113]

[0114] in is the gradient operator with respect to x, u is the particle velocity, and f t is the time derivative of the function x and t, where the derivative with respect to the τ variable is expressed as:

[0115]

[0116] The Navier-Stokes equations without considering external forces can be expressed as:

[0117]

[0118] This equation characterizes the motion of a fluid, incorporating the effects of inertia, pressure, and viscosity.

[0119] The goal of the present invention is to relate the initial position of a particle to its trajectory by analyzing the measured particle motion trajectory, velocity and pressure, while using these data to predict the velocity and pressure changes throughout the flow field. In the real world, when the data capture cost is high or the data itself is limited, the data is often incomplete, sparse and noisy.

[0120] The present invention regards all passive particles as fluid microcapsules, which means that they can be regarded as part of the fluid. These passive particles can be released at any position and time in the fluid domain. The initial position x0 and the initial time t0 distinguish each particle. Therefore, the trajectory x of the passive particle can be calculated using the above formula 2. According to the particle trajectory, the fluid velocity u and pressure p along the trajectory can be calculated using the above formula 6 and formula 7:

[0121] u=u(x,t)#(6)

[0122] p=p(x,t)#(7)

[0123] It is important to note that the state variables in these calculations must satisfy corresponding relationships. Specifically, the time derivative of the particle trajectory x must be equal to the velocity at that position, that is,

[0124]

[0125] In addition, the predicted flow velocity and pressure must satisfy the above formula 5.

[0126] The following describes a fluid trajectory tracking method based on a physics-inspired neural network and the performance of the corresponding neural network provided by the present invention in conjunction with specific embodiments.

[0127] The top cover driven square cavity flow is a classic problem in the field of fluid dynamics, which covers a variety of complex phenomena, such as boundary layer separation, intracavity vortex and self-sustaining oscillation. We used FLUENT software to create a square cavity model with a side length of 1, in which the left, right and bottom walls are fixed and the top wall is used as a moving boundary. Initially, the top cover moves to the right at a speed u0 = 1, and the Reynolds number calculated based on this speed is 100. The computational domain is discretized into a uniform grid of 100×100. Driven by the moving cover, a large vortex is formed near the geometric center of the cavity, while the flow velocity at the bottom and side edges is slowed down.

[0128] At t = 3 seconds, we randomly distributed 200 particles in the cavity, such as Figure 4 As shown in the figure, these particles are used to capture the trajectory, velocity and pressure values ​​at their respective positions. Subsequently, we randomly selected 50 particles for training and 100 non-repeated particles for testing. The entire simulation process lasted 30 seconds. In order to enhance the randomness of particle distribution, we focused on training and predicting the characteristics of passive particles from the 22nd to the 30th second.

[0129] Specifically, Figure 4 (a) is the comparison between the true value (red line) and the network prediction value (blue line) in the test set. Figure 4(b) is a separate comparison between the true values ​​(red dots) and the network predicted values ​​(blue dots) of some particles in the selected test set.

[0130] Figure 5 It is a comparison between the x-direction velocity, y-direction velocity, and pressure value predicted by the present invention when t=25s in the simulation example of the top cover driven square cavity flow and the actual value (left column), and the error range is given (right column).

[0131] The particle trajectories in the test set are as follows Figure 4 As shown, the relative x and y directions The errors are reduced to 3.20×10 3 and 2.72×10 3 , the prediction accuracy is high. The predicted velocity field and pressure field at t = 25s are as follows Figure 5 As shown in the test set, the relative x and y directions of the velocity The errors are 5.18×10 2 and 7.41×10 2 . Relative pressure The error is 2.58×10 1 , indicating that the network has strong predictive ability.

[0132] In addition, we introduce a complex pipe flow example to verify the network's ability to handle non-closed boundary problems. This example aims to simplify and express a series of complex fluid dynamics phenomena, including but not limited to the transport and distribution of drugs in blood vessels, the mechanism of thrombosis, and the evolution of vascular malformations.

[0133] By simulating complex pipe flows, we can deeply study the flow characteristics of fluids in complex pipes, including flow velocity, distribution, pressure changes, and the interaction between fluids and walls. In this study, we used FLUENT software to construct an incompressible fluid flow data set containing passive particles passing through a complex pipe. The pipe is uniquely designed with one inlet and two outlets. The inlet coordinates are located at (0,125) and the diameter is 50mm; the two outlet coordinates are (382,500) and (0,500), respectively, with corresponding diameters of 49.11mm and 42mm, respectively. The maximum diameter of the pipe is about 105mm and the minimum diameter is about 38mm.

[0134] In the simulation, we set the flow velocity of the fluid at the inlet in the x direction to a constant value of 1m / s and the flow velocity in the y direction to 0m / s. The density of the fluid is 1kg / m3 and the viscosity is 10 -2Pa·s, the pressure at the outlet is set to 0Pa, and a no-slip boundary condition is adopted. All passive particles are released from the pipeline inlet, and their trajectories and velocities are tracked and recorded in real time. Under the influence of the inlet, the passive particles flow along the pipeline and are finally discharged from the two outlet directions.

[0135] In particular, at t = 1s, we randomly spread 300 particles in the pipe cavity and recorded their movement trajectories, velocities, and pressure values. For the needs of training and testing, we randomly selected 200 particles for training and another set of 100 non-repeating particles for testing. The entire movement process lasted 5 seconds, but in order to increase the randomness of particle distribution, we only trained and predicted the characteristics of passive particles from the 3rd to the 5th second.

[0136] Figure 6 (a) is the comparison between the true value (red point) and the network prediction value (blue point) in the test set. Figure 6 (b) is a separate comparison between the true values ​​(red dots) and the network predicted values ​​(blue dots) of some particles in the selected test set.

[0137] Figure 7 This is a comparison of the x-direction velocity, y-direction velocity, and pressure values ​​(middle column) predicted by the present invention when t=4s in a simulation example of complex pipeline flow with the actual values ​​(left column), and an error range is given (right column).

[0138] The particle trajectories in the test set are as follows Figure 6 As shown, the relative x and y directions The errors are reduced to 4.29×10 3 and 8.51×10 3 , with high prediction accuracy. The predicted velocity field and pressure field at t = 4s are as follows Figure 5 As shown in the test set, the relative x and y directions of the velocity The errors are 3.43×10 2 and 8.86×10 2 . Relative pressure The error is 2.60×10 1 , indicating that the network has strong predictive ability. We have successfully achieved accurate tracking and inversion of particle trajectories and flow field information in complex pipeline flows, thus verifying the excellent performance of the physical-driven deep neural network of the present invention in dealing with such complex fluid dynamics problems.

[0139] Specific implementation cases where the present invention can be applied include, in the medical field, tracking the transport trajectory of drugs in the body, helping to accurately locate the location of drugs acting on diseased cells, improving the effectiveness of drug treatment, and reducing side effects. In terms of ocean dynamics, accurately predicting the path of pollutants on the ocean surface, weather forecasts, maritime search and rescue operations, and iceberg tracking, etc., obtaining the real-time movement trajectory of the target and the flow information of the sea area under the premise of only knowing the initial position of the target, can help effectively deal with emergencies and improve rescue efficiency.

[0140] Traditional numerical methods have limitations when dealing with particle-carrying flow simulations, but the physical information-based deep neural network of the present invention can effectively integrate a large amount of experimental observation and numerical simulation data, providing a new solution. This method not only improves the accuracy of the simulation, but also can handle the motion solution of more than one million particles, overcoming the shortcomings of traditional methods in data sparsity.

[0141] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A fluid trajectory tracking method based on a physics-inspired neural network, characterized in that: include: S1: establishing a first fully connected network, and obtaining particle trajectories through prediction of the first fully connected network; S2: establishing a second fully connected network, and based on the particle trajectory, obtaining the flow field velocity and the flow field pressure through the second fully connected network prediction; S3: Connecting the first fully connected network and the second fully connected network in series and training them to obtain a prediction network; S4: Tracking fluid trajectories through the prediction network.

2. The fluid trajectory tracking method based on physics-inspired neural network according to claim 1 is characterized in that: Step S1 further comprises: S11: Establishing a first fully connected network; S12: inputting the initial information of the particles into the first fully connected network to obtain the mapped particle displacement; S13: Calculate and obtain the particle trajectory according to the particle displacement and the particle initial information.

3. The fluid trajectory tracking method based on physics-inspired neural network according to claim 2 is characterized in that: In step S12, the initial information of most particles includes the initial position of the particles, the release time of the particles and the first movement time, wherein the first movement time is the particle movement time under the Lagrangian description.

4. The fluid trajectory tracking method based on physics-inspired neural network according to claim 3 is characterized in that: The expression of the particle displacement in step S12 is: in, is the mapped particle displacement, x0 is the initial position of the particle, t0 is the particle release time, τ is the particle motion time under Lagrangian description, and θ is the trainable parameter of the first fully connected network; The expression of the particle trajectory in step S13 is: Among them, x q is the predicted particle trajectory.

5. The fluid trajectory tracking method based on physics-inspired neural network according to claim 1, characterized in that: Step S2 further comprises: S21: Establishing a second fully connected network; S22: Inputting the second motion time and the particle trajectory into the second fully connected network to predict the flow field velocity and the flow field pressure; wherein the second motion time is the particle motion time described by Euler.

6. The fluid trajectory tracking method based on physics-inspired neural network according to claim 5, characterized in that: The expression of the second motion time in step S22 is: Among them, t is the particle motion time under Euler description, t0 is the particle release time, and τ is the particle motion time under Lagrangian description.

7. The fluid trajectory tracking method based on physics-inspired neural network according to claim 5, characterized in that: The expression of the flow field velocity in step S22 is: u=u0(x0,t0,τ;θ,θ); Where u is the predicted fluid velocity, u0 is the fluid velocity in the previous state, x0 is the initial position of the particle, t0 is the particle release time, τ is the particle motion time described by Lagrangian, θ is the trainable parameter of the second fully connected network, and θ is the trainable parameter of the first fully connected network; The expression of the flow field pressure in step S22 is: p=p0(x0,t0,τ;θ,θ); Among them, p is the predicted fluid pressure, and p0 is the fluid pressure in the previous state.

8. The fluid trajectory tracking method based on physics-inspired neural network according to claim 1, characterized in that: The expression of the training loss of the prediction network in step S3 is: in, To predict the overall training loss of the network, θ is the trainable parameter of the first fully connected network, θ is the trainable parameter of the second fully connected network, is the loss evaluated at the data point, is the loss evaluated at the collocation point, For the first data loss, For the second data loss, is the first residual physical loss, is the second residual physical loss, λ1 is the first weight parameter, λ2 is the second weight parameter, and λ3 is the third weight parameter.

9. The fluid trajectory tracking method based on physics-inspired neural network according to claim 1, characterized in that: Step S4 also includes: S41: performing a first automatic differentiation through the prediction network to obtain a derivative of a particle position and a first motion time, wherein the derivative is used to balance the training of the first fully connected network and the second fully connected network; S42: Performing a second automatic differentiation through the prediction network to obtain a functional relationship between the flow field velocity, flow field pressure, particle position, and particle movement time.

10. The fluid trajectory tracking method based on physics-inspired neural network according to claim 1, characterized in that: The expression of the functional relationship in step S42 is: Among them, μ is the flow field velocity, t is the particle movement time, is the gradient operator, ρ is the fluid density, p is the flow field pressure, and μ is the fluid dynamic viscosity.

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