A complex geometry flow field prediction method and system
By introducing weak formal constraints based on the divergence theorem and multi-scale control volume sampling into the prediction of complex geometric flow fields, and combining a two-stage training strategy, the problems of time-consuming mesh generation and high computational cost in complex geometric structures of traditional methods are solved, and high-precision, physically conserved flow field prediction is achieved.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SHANDONG UNIV
- Filing Date
- 2026-03-05
- Publication Date
- 2026-05-08
AI Technical Summary
Traditional computational fluid dynamics methods suffer from time-consuming and computationally expensive mesh generation when dealing with complex geometries. Existing improved methods struggle to effectively handle complex industrial geometries without a mesh framework, leading to gradient instability, violation of mass conservation, and convergence difficulties.
We employ the integral conservation law based on the divergence theorem as a weak formal constraint, combined with a multi-scale control volume sampling strategy, to construct a weak formal loss function that conserves mass and momentum. We then optimize the neural network through a two-stage training strategy to generate flow field prediction results.
It achieves high-precision, physically conserved flow field prediction in complex geometries, significantly improving the convergence and accuracy of flow field prediction. Compared with existing technologies, it reduces the relative error by up to 93% while maintaining the physical consistency of the flow field.
Smart Images
Figure CN121766159B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the interdisciplinary field of computational fluid dynamics and deep learning, and specifically relates to a method and system for predicting complex geometric flow fields. 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] In aerospace, automotive, and chemical energy industries, components such as heat exchangers often contain complex geometries, such as Triply Periodic Minimal Surfaces (TPMS) structures. Traditional computational fluid dynamics (CFD) methods are time-consuming and computationally expensive to handle such complex geometries.
[0004] In recent years, Physical-Informed Neural Networks (PINNs) have attracted widespread attention as a meshless method. However, standard PINN methods primarily rely on point-by-point minimization of residuals from strongly-form Partial Differential Equations (PDEs). In regions with complex geometries and tortuous flow channels (such as the internal flow channels of heat exchangers), such local point-by-point constraints struggle to effectively propagate global physical information, leading to gradient instability, violation of mass conservation, and convergence difficulties. Existing improved methods, such as region-based sampling or traditional weakly-form methods, often require mesh-based integration or cumbersome region decomposition, making it difficult to handle complex industrial geometries within a truly meshless framework. Summary of the Invention
[0005] To address the aforementioned problems, this invention proposes a method and system for predicting complex geometric flow fields. This invention employs the integral conservation law based on the divergence theorem as a weak formal constraint and combines it with a multi-scale control volume sampling strategy to achieve high-precision, physically conserved prediction of the flow field in complex geometric structures.
[0006] According to some embodiments, the present invention adopts the following technical solution:
[0007] A method for predicting complex geometric flow fields includes the following steps:
[0008] Obtain fluid domains with complex geometries, and sample the fluid domain interior and boundaries to construct strong formal physical constraints and boundary condition constraints.
[0009] Spherical control volumes of different scales are generated within the fluid domain, including large-scale subdomains for long-range coupling, medium-scale subdomains distributed along the flow channel skeleton, and small-scale subdomains for local correction.
[0010] Based on the steady-state incompressible Navier-Stokes equations, the volume integral within the control volume is transformed into the flux integral on the boundary using the divergence theorem, thus constructing a weak form loss function that conserves mass and momentum.
[0011] The flow field variables are approximated using a neural network model. A total loss function is constructed by combining strong formal physical constraints, boundary condition constraints, and the weak formal loss function. A two-stage training strategy is used to optimize the network and generate the final flow field prediction results.
[0012] As an alternative implementation, obtaining a fluid domain with a complex geometry and sampling within and at the boundaries of the fluid domain to construct strong formal physical constraints and boundary condition constraints includes: for a given complex geometry, defining the fluid domain Ω and its boundaries. Ω, randomly sampled points within the fluid domain It is used to calculate the pointwise residuals of the standard steady-state incompressible Navier-Stokes equations, while sampling at the boundaries. To apply boundary conditions.
[0013] As an alternative implementation, the process of generating spherical control volumes of different scales within the fluid domain includes: sampling and retaining the center point located within the fluid domain within the geometric bounding box, generating a control volume covering a large area, and obtaining a large-scale subdomain for capturing long-range physical correlations;
[0014] Extract the topological skeleton of the fluid domain, distribute the control volume along the skeleton path to obtain the mesoscale subdomain, and make it cover the main fluid transport channels to ensure that physical information is effectively propagated along complex flow channels.
[0015] Uniform sampling within the fluid domain generates a small-radius control volume, resulting in a small-scale subdomain used to capture fine local geometric features and correct local errors.
[0016] As a further defined implementation, during the generation of the mesoscale subdomain, an average curvature algorithm is used to extract the geometric skeleton, and the control volume center is ensured to be located on the topological centerline of the flow channel.
[0017] As an alternative implementation, the process of constructing a weakly form loss function that conserves mass and momentum includes: for any control volume Using the divergence theorem to constrain volume integrals Transform into surface integral constraints ,in:
[0018] The mass-conserved weak-form residual is obtained by calculating the velocity flux integral across the control volume boundary:
[0019]
[0020] The weak form of momentum conservation residuals is calculated by integrating the momentum flux through the control volume boundary and the resultant force of pressure and viscous forces:
[0021] ;
[0022] in, For speed, For pressure, For the surface normal vector, It is the Reynolds number.
[0023] As an alternative implementation, in the process of transforming the volume integral within the control volume into the flux integral on the boundary using the divergence theorem, the surface flux integral is calculated using a meshless Monte Carlo sampling method, which divides the control volume boundary into a spherical part and a truncated geometric boundary part, and samples and weights sums them separately.
[0024] As an alternative implementation method, the process of optimizing the network using a two-stage training strategy includes: the first stage is the pre-training stage, in which only the strong form loss, boundary loss and weak form mass conservation loss are activated to quickly suppress large-scale mass leakage and establish global flow field continuity.
[0025] The second stage is the refinement stage. Based on the first stage, the weak form of momentum conservation loss is activated, the flow field details are corrected, and a fine solution with physical consistency is achieved.
[0026] As an alternative implementation, the neural network model employs a Fourier feature embedding layer to map spatial coordinates into high-dimensional features, thereby mitigating spectral bias and capturing multi-scale flow field features.
[0027] A complex geometric flow field prediction system, comprising:
[0028] The fluid computational domain construction module is configured to acquire fluid domains with complex geometries, and to sample within and at the boundaries of the fluid domains to construct strong formal physical constraints and boundary condition constraints.
[0029] The multi-scale integral subdomain construction module is configured to generate spherical control volumes of different scales within the fluid domain, including large-scale subdomains for long-range coupling, medium-scale subdomains distributed along the flow channel skeleton, and small-scale subdomains for local correction.
[0030] The weak form conservation loss construction module is configured to be based on the steady-state incompressible Navier-Stokes equations, using the divergence theorem to transform the volume integral within the control volume into the flux integral on the boundary, and constructing a weak form loss function that conserves mass and momentum.
[0031] The two-stage joint optimization module is configured to approximate the flow field variables using a neural network model, combine strong formal physical constraints, boundary condition constraints and the weak formal loss function to construct a total loss function, and use a two-stage training strategy to optimize the network to generate the final flow field prediction result.
[0032] An electronic device includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the steps in the method described above.
[0033] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0034] This invention overcomes the limitations of standard PINN in complex geometries by introducing weak formal constraints based on integral forms, thus overcoming the deficiency of traditional point-by-point residuals in propagating global information in complex topologies and significantly improving the convergence and accuracy of flow field prediction.
[0035] The multi-scale strategy provided by this invention enhances physical consistency. By combining large-scale (long-range coupling), medium-scale (skeleton perception), and small-scale (local correction) control volumes, it effectively solves the mass conservation problem in slender and curved flow channels, reducing the relative error by up to 93% compared to existing technologies.
[0036] This invention achieves a meshless and efficient solution by using Monte Carlo integration to calculate flux without generating complex volume meshes, thus retaining the meshless advantage of the PINN method. At the same time, it improves the stability and efficiency of training through a two-stage training strategy.
[0037] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description
[0038] 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.
[0039] Figure 1 This is an overall process architecture diagram of one embodiment, illustrating the complete process from geometric multi-scale sampling to two-stage training of the neural network;
[0040] Figure 2This is a schematic diagram of an integral control volume (intersection of a sphere and a fluid domain) according to one embodiment;
[0041] Figure 3 This is a schematic diagram illustrating the distribution of mesoscale subdomains along the flow channel skeleton in one embodiment.
[0042] Figure 4 This paper compares the streamline diagram generated in a complex flow channel of an industrial-grade liquid-cooled plate with CFD and baseline methods in one embodiment, demonstrating the advantages of the present method in maintaining streamline continuity. (a) is the result generated by the method provided in this embodiment, (b) is the result generated by CFD, and (c) is the result generated by the baseline method.
[0043] Figure 5 This is a diagram demonstrating the conservation of mass flow rate along the flow direction in a Gyroid structure, proving that the method can effectively prevent mass leakage. Detailed Implementation
[0044] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0045] It should be noted that the following detailed description is illustrative and intended to provide further explanation 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.
[0046] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.
[0047] Where there is no conflict, the embodiments and features described in this application may be combined with each other.
[0048] Example 1
[0049] A method for predicting complex geometric flow fields, such as Figure 1 As shown, it includes the following steps:
[0050] Constructing the fluid computation domain and strong formal sampling: Obtaining a fluid domain with complex geometry, and sampling inside and at the boundaries of the fluid domain to construct strong formal physical constraints and boundary condition constraints;
[0051] Constructing multi-scale integral subdomains: Generating spherical control volumes of different scales within the fluid domain, including large-scale subdomains for long-range coupling, medium-scale subdomains distributed along the flow channel skeleton, and small-scale subdomains for local correction.
[0052] Constructing a weak form of conservation loss: Based on the steady-state incompressible Navier-Stokes equations, the volume integral within the control volume is transformed into the flux integral on the boundary using the divergence theorem, thus constructing a weak form of loss function that conserves mass and momentum.
[0053] Two-stage joint optimization training: The network is optimized by using a neural network to approximate the flow field variables (velocity and pressure) and combining strong form loss, boundary loss and multi-scale weak form loss to generate the final flow field prediction results.
[0054] In this embodiment, the process of constructing the multi-scale integral subdomain includes:
[0055] Large-scale subdomains: Sample and retain the center point located within the fluid domain within the geometric bounding box to generate a control volume covering a large area, used to capture long-range physical correlations;
[0056] Mesoscale subdomain: Extract the topological skeleton of the fluid domain, distribute the control volume along the skeleton path to cover the main fluid transport channels, and ensure that physical information is effectively propagated along complex flow channels;
[0057] Small-scale subdomains: Uniform sampling within the fluid domain generates small-radius control volumes, which are used to capture fine local geometric features and correct local errors.
[0058] In this embodiment, the generation of the mesoscale subdomain uses an average curvature algorithm to extract the geometric skeleton, ensuring that the control volume center is located on the topological centerline of the flow channel.
[0059] In this embodiment, the process of constructing the weakly form conserved loss includes: for any control volume Using the divergence theorem to constrain volume integrals Transform into surface integral constraints Specifically, this includes:
[0060] Weak form residuals with mass conservation: Calculate the velocity flux integral across the control volume boundary:
[0061]
[0062] Weak form residual of momentum conservation: Calculate the momentum flux and the resultant force integral of pressure and viscous forces passing through the control volume boundary.
[0063] ;
[0064] in, For speed, For pressure, For the surface normal vector, It is the Reynolds number.
[0065] In this embodiment, the surface flux integral is calculated using a meshless Monte Carlo sampling method, which divides the control volume boundary into a spherical part and a truncated geometric boundary part, and samples and weights sums them separately.
[0066] In this embodiment, the two-stage joint optimization training process includes:
[0067] Phase 1 (Pre-training): Only strong form loss, boundary loss and weak form mass conservation loss are activated to quickly suppress large-scale mass leakage and establish global flow field continuity;
[0068] The second stage (refinement): Based on the first stage, the weak form of momentum conservation loss is activated to further refine the flow field details and achieve a fine solution with physical consistency.
[0069] In this embodiment, the neural network model employs a Fourier feature embedding layer to map spatial coordinates into high-dimensional features, thereby mitigating spectral bias and capturing multi-scale flow field features.
[0070] Example 2
[0071] A method for predicting complex geometric flow fields, such as Figure 1 As shown, the main core steps include the following:
[0072] Step (1): Geometric preprocessing and strong form sampling
[0073] First, for a given complex geometry (such as the flow channel of a TPMS heat exchanger), define the fluid domain Ω and its boundary. Ω (including inlet) ,exit and wall Randomly sampled placement points within the fluid domain. This is used to calculate the standard strong-form PDE residuals (i.e., the pointwise residuals of the steady-state incompressible Navier-Stokes equations). Simultaneously, sampling is performed at the boundaries. Apply boundary conditions (inlet velocity, outlet pressure, no wall slip).
[0074] Step (2): Construction of multi-scale integral subdomains
[0075] To overcome the locality of point supervision, this embodiment constructs three sets of spherical control volumes of different scales, such as... Figure 2 As shown:
[0076] ;
[0077] Large-scale subdomains :radius It is relatively large, with the center sampling across the entire domain. It is used to establish long-range physical coupling across regions and prevent large-scale flow field drift.
[0078] Medium-scale subdomain :like Figure 3 As shown, this is a key innovation. The geometric skeleton of the flow channel is extracted using the average curvature flow algorithm, and the subdomain center is set on the skeleton with a radius... Adapts to flow channel width. This "skeleton-aware" distribution ensures that constraints can be continuously covered along the main path of fluid transport, making it particularly suitable for slender and curved pipes.
[0079] Small-scale subdomains :radius Smaller size, uniformly distributed throughout the entire area, used for fine-tuning of local flow field details.
[0080] Step (3): Calculation of weak formal conservation constraints
[0081] For each control volume, this invention does not calculate the volume integral, but instead uses the divergence theorem to transform it into a flux integral on the boundary, thereby achieving meshless computation.
[0082] Continuity equation (mass conservation): Transform into That is, the net flow rate out of the control volume should be zero.
[0083] Momentum equation: Write the momentum equation in divergence form And transform it into a boundary integral. The integral calculation employs the Monte Carlo method, focusing on the spherical portion of the control volume. and the boundary portion that is geometrically truncated The samples were taken separately and then weighted and summed.
[0084] Step (4): Neural Network Construction and Two-Stage Training Construct a fully connected neural network with spatial coordinates as input. After Fourier feature mapping, the output speed is... and pressure The loss function is defined as:
[0085] ;
[0086] in and The specific calculation process for the weak form losses of mass and momentum on the above multi-scale subdomains is as follows:
[0087] ;
[0088] ;
[0089] in, These represent large-scale, medium-scale, and small-scale subdomains, respectively. Representing scale The set of sphere centers controlling the volume below, The number of centers of the spheres in this set; This refers to the control volume radius at the corresponding scale; and These are the weighted hyperparameters for the weak form losses of mass conservation and momentum conservation at the corresponding scales; and These are the weak form residuals of mass conservation and momentum conservation on the corresponding control volumes, respectively. and The specific calculation process is as follows:
[0090] Boundary condition constraint loss Calculation:
[0091] Set of boundary sampling points Divided into entry point set Export point collection and non-slip wall point set For different boundary conditions, calculate the mean squared error loss relative to the true boundary distribution:
[0092] (1) Inlet velocity loss :
[0093] ;
[0094] in, Given the inlet velocity distribution;
[0095] (2) Losses due to export pressure :
[0096] ;
[0097] in, Given the export pressure;
[0098] (3) No slippage loss on the wall surface :
[0099] ;
[0100] The overall boundary condition loss function is obtained by integration.
[0101] ;
[0102] in, , and These are the weighted hyperparameters corresponding to the inlet, outlet, and wall loss, respectively.
[0103] Strong formal physical constraint loss Calculation:
[0104] The set of sampling points within the fluid domain Above, pointwise residuals of the continuity equation are calculated based on the steady-state incompressible Navier-Stokes equations. Point-by-point residuals of the momentum equation :
[0105] ;
[0106] ;
[0107] in, and The neural network model predicts the points... Speed and pressure at the point, It is the Reynolds number.
[0108] Then calculate the strong form loss function. :
[0109] ;
[0110] in, and The preset weight hyperparameters, Represents the internal sampling point set The number of points.
[0111] The training employs a two-stage strategy, by control:
[0112] Phase 1: It optimizes only the strong form and the weak form with mass conservation. This allows the network to quickly learn the global mass conservation properties and avoid getting trapped in local minima.
[0113] Phase Two: We then incorporate a weak form of momentum conservation to make final physical constraint corrections to the flow field.
[0114] Experimental results show that, in complex three-period minimal surface TPMS structures such as Gyroid and Diamond, compared with existing methods such as Standard PINN and ROPINN, [the following methods are used]. Figure 4 , Figure 5 As shown, the method provided in this embodiment significantly reduces the relative L2 error of the velocity field and maintains strict mass conservation on the flow channel cross-section, successfully solving the problem of flow field prediction in complex flow channels.
[0115] Example 3
[0116] A complex geometric flow field prediction system, comprising:
[0117] The fluid computational domain construction module is configured to acquire fluid domains with complex geometries, and to sample within and at the boundaries of the fluid domains to construct strong formal physical constraints and boundary condition constraints.
[0118] The multi-scale integral subdomain construction module is configured to generate spherical control volumes of different scales within the fluid domain, including large-scale subdomains for long-range coupling, medium-scale subdomains distributed along the flow channel skeleton, and small-scale subdomains for local correction.
[0119] The weak form conservation loss construction module is configured to be based on the steady-state incompressible Navier-Stokes equations, using the divergence theorem to transform the volume integral within the control volume into the flux integral on the boundary, and constructing a weak form loss function that conserves mass and momentum.
[0120] The two-stage joint optimization module is configured to approximate the flow field variables using a neural network model, combine strong formal physical constraints, boundary condition constraints and the weak formal loss function to construct a total loss function, and use a two-stage training strategy to optimize the network to generate the final flow field prediction result.
[0121] Example 4
[0122] An electronic device includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, wherein the computer instructions, when executed by the processor, perform the steps in the method of Embodiment 1 or Embodiment 2.
[0123] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of one or more computer-usable storage media (including, but not limited to, disk storage, etc.) containing computer-usable program code. CD - ROM It takes the form of a computer program product implemented on (such as optical memory, etc.).
[0124] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0125] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0126] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0127] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made by those skilled in the art without creative effort within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for predicting the flow field of a complex geometric heat exchanger channel, characterized in that, Includes the following steps: The fluid domain of a complex geometric heat exchanger flow channel structure is obtained, and sampling is performed inside and at the boundary of the fluid domain to construct strong formal physical constraints and boundary condition constraints. Spherical control volumes of different scales are generated within the fluid domain, including large-scale subdomains for long-range coupling, medium-scale subdomains distributed along the flow channel skeleton, and small-scale subdomains for local correction. Based on the steady-state incompressible Navier-Stokes equations, the volume integral within the control volume is transformed into the flux integral on the boundary using the divergence theorem, thus constructing a weak form loss function that conserves mass and momentum. The flow field variables are approximated using a neural network model. A total loss function is constructed by combining strong formal physical constraints, boundary condition constraints, and the weak formal loss function. A two-stage training strategy is used to optimize the network and generate the final flow field prediction results. The process of generating spherical control volumes of different scales within a fluid domain includes: sampling and retaining the center point located within the fluid domain within the geometric bounding box, generating control volumes covering a large area, and obtaining large-scale subdomains for capturing long-range physical correlations; Extract the topological skeleton of the fluid domain, distribute the control volume along the skeleton path to obtain the mesoscale subdomain, and make it cover the main fluid transport channels to ensure that physical information is effectively propagated along complex flow channels. Uniform sampling within the fluid domain generates a small-radius control volume, resulting in a small-scale subdomain used to capture fine local geometric features and correct local errors. The process of constructing a weak form loss function that conserves mass and momentum includes: for any control volume Using the divergence theorem to constrain volume integrals Transformed into surface integral constraints ,in: The mass-conserved weak-form residual is obtained by calculating the velocity flux integral across the control volume boundary: The weak form of momentum conservation residuals is calculated by integrating the momentum flux through the control volume boundary and the resultant force of pressure and viscous forces: ； in, For speed, For pressure, For the surface normal vector, It is the Reynolds number.
2. The method for predicting the flow field of a complex geometric heat exchanger channel as described in claim 1, characterized in that, The process of obtaining a fluid domain with a complex geometry and sampling within and at the boundaries of that domain to construct strong formal physical constraints and boundary condition constraints includes: for a given complex geometry, defining the fluid domain Ω and its boundaries. Ω, randomly sampled points within the fluid domain It is used to calculate the pointwise residuals of the standard steady-state incompressible Navier-Stokes equations, while sampling at the boundaries. To apply boundary conditions.
3. The method for predicting the flow field of a complex geometric heat exchanger channel as described in claim 1, characterized in that, During the generation of the mesoscale subdomain, the average curvature algorithm is used to extract the geometric skeleton and ensure that the control volume center is located on the topological centerline of the flow channel.
4. The method for predicting the flow field of a complex geometric heat exchanger channel as described in claim 1, characterized in that, In the process of transforming the volume integral within the control volume into the flux integral on the boundary using the divergence theorem, the surface flux integral is calculated using a meshless Monte Carlo sampling method. The control volume boundary is divided into a spherical part and a truncated geometric boundary part, and sampling and weighted summation are performed separately.
5. The method for predicting the flow field of a complex geometric heat exchanger channel as described in claim 1, characterized in that, The process of optimizing the network using a two-stage training strategy includes: the first stage is the pre-training stage, in which only the strong form loss, boundary loss and weak form mass conservation loss are activated to quickly suppress large-scale mass leakage and establish global flow field continuity. The second stage is the refinement stage. Based on the first stage, the weak form of momentum conservation loss is activated, the flow field details are corrected, and a fine solution with physical consistency is achieved.
6. The method for predicting the flow field of a complex geometric heat exchanger channel as described in claim 1, characterized in that, The neural network model employs a Fourier feature embedding layer to map spatial coordinates into high-dimensional features, thereby mitigating spectral bias and capturing multi-scale flow field features.
7. A flow field prediction system for complex geometric heat exchanger channels, employing the method described in claim 1, characterized in that, include: The fluid computational domain construction module is configured to acquire the fluid domain of complex geometric heat exchanger channel structures, and to sample the fluid domain and its boundaries to construct strong formal physical constraints and boundary condition constraints. The multi-scale integral subdomain construction module is configured to generate spherical control volumes of different scales within the fluid domain, including large-scale subdomains for long-range coupling, medium-scale subdomains distributed along the flow channel skeleton, and small-scale subdomains for local correction. The weak form conservation loss construction module is configured to be based on the steady-state incompressible Navier-Stokes equations, using the divergence theorem to transform the volume integral within the control volume into the flux integral on the boundary, and constructing a weak form loss function that conserves mass and momentum. The two-stage joint optimization module is configured to approximate the flow field variables using a neural network model, combine strong formal physical constraints, boundary condition constraints and the weak formal loss function to construct a total loss function, and use a two-stage training strategy to optimize the network to generate the final flow field prediction result.
8. An electronic device, characterized in that, It includes a memory and a processor, as well as computer instructions stored in the memory and running on the processor, which, when executed by the processor, perform the steps of the method according to any one of claims 1-6.