Embedded manifold microchannel heat sink heat flow characteristic simulation method and device based on parameterized physical information neural network

Abstract

The application provides a simulation method and device for thermal flow characteristics of an embedded manifold micro-channel radiator based on a parameterized physical information neural network, and relates to the technical field of chip heat dissipation simulation. The method uses geometric parameters and spatial coordinates as network inputs, and introduces geometric embedding features to keep the spatial relationship of sampling points relative to the boundary of the sub-region consistent in the embedding space under different geometric parameters; a composite loss function is formed by using control equation residuals and boundary condition residuals for physical constraint training, so that a single neural network covers a continuous geometric design space. After training, for any target geometric parameter combination, only one forward propagation is required to obtain the prediction results of the velocity field, pressure field and temperature field, realizing fast simulation. The application solves the technical problems of high calculation cost and weak cross-geometric generalization ability of traditional numerical simulation methods in the geometric design space, and can be used for customized design and rapid optimization iteration of chip radiators.

Description

Technical Field

[0001] This application relates to the field of chip heat dissipation simulation technology, and in particular to a method and device for simulating the thermal flow characteristics of an embedded manifold microchannel heat sink based on a parameterized physical information neural network. Background Technology

[0002] As the power density of integrated circuits continues to rise, the heat flux density of microprocessors and wide-bandgap power devices such as silicon carbide and gallium nitride has far exceeded the capabilities of conventional air cooling. Insufficient heat dissipation will directly lead to increased junction temperature, performance degradation, and shortened lifespan. Embedded microfluidic cooling technology reduces thermal resistance by etching microchannels on the back of the chip, allowing the coolant to be as close as possible to the heat-generating area. Among them, the embedded manifold microchannel (EMMC) configuration can significantly enhance heat transfer while maintaining a low voltage drop.

[0003] Currently, the industry primarily uses commercial software based on the finite element method (FEM) for three-dimensional conjugate heat transfer simulation of EMMC radiators. This method requires independent model building, mesh generation, and solving of the governing equations for each geometric design. When geometric parameters change, the previously calculated mesh and solution cannot be reused, necessitating a complete re-execution of the modeling and solving process. For design spaces containing multiple geometric parameters, extensive calculations involving parameter combinations are required. Furthermore, methods based on physical information neural networks have been explored to accelerate physical field simulations. Existing solutions, when applied to radiator designs with variable geometric parameters, typically use the geometric parameters as additional inputs to the network, allowing a single network to attempt to cover multiple geometric configurations.

[0004] However, the above-mentioned solutions still face many difficulties when applied to the parametric simulation of EMMC heat sinks. On the one hand, EMMC heat sinks involve fluid-solid coupled heat transfer and operate under convection-dominated conditions, resulting in a significant difference in thermal conductivity between the fluid and solid domains, making numerical solutions extremely difficult. On the other hand, changes in geometric parameters alter the spatial topology of the simulation object, and effectively adapting the simulation model to these geometric changes is a pressing technical challenge. Therefore, a method for rapidly simulating EMMC heat sinks within their geometric design space is urgently needed to support customized heat sink designs for specific application scenarios. Summary of the Invention

[0005] In view of the above problems, this application provides a method and device for simulating the thermal flow characteristics of an embedded manifold microchannel heat sink based on a parameterized physical information neural network, so as to overcome the above problems or at least partially solve the above problems.

[0006] A first aspect of this application discloses a method for simulating the heat flow characteristics of an embedded manifold microchannel heat sink based on a parameterized physical information neural network, the method comprising: Obtain the geometric parameters and spatial coordinates of the sampling points of the embedded manifold microchannel heat sink to be simulated; Based on the geometric parameters and the spatial coordinates, the parameterized sub-region to which the sampling point belongs is determined, and the normalized local coordinates of the sampling point within the parameterized sub-region are calculated. The normalized local coordinates are transformed by a smooth saturated monotonic mapping function to generate geometric embedding features, which are used to characterize the relative position of the sampling point with respect to the boundary of the parameterized sub-region. The geometric embedding features are concatenated with the normalized geometric parameters and the spatial coordinates to form an enhanced input vector; The enhanced input vector is input into the physical information neural network to obtain the physical field prediction value of the sampling point, which includes the velocity field, pressure field and temperature field. The residuals of the governing equations and boundary conditions are calculated based on the predicted physical field values ​​to form a composite loss function, and the physical information neural network is trained based on the composite loss function. The target geometric parameters and spatial coordinates of the target sampling points of the embedded manifold microchannel heat sink are obtained and constructed as the target enhancement input vector. The vector is then input into the trained physical information neural network to obtain the predicted results of the heat flow characteristics.

[0007] Optionally, based on the geometric parameters and the spatial coordinates, the parameterized sub-region to which the sampling point belongs is determined, and the normalized local coordinates of the sampling point within the parameterized sub-region are calculated, including: Based on the geometric parameters, determine the boundary positions of each parameterized sub-region; Based on the spatial coordinates of the sampling point and the boundary positions of each parameterized sub-region, the parameterized sub-region to which the sampling point belongs is determined; Obtain the minimum boundary values ​​of the parameterized sub-region to which the sampling point belongs in each coordinate direction. and boundary maximum value The normalized local coordinates of the sampling points are calculated using the following formula: , in, For the sampling point at the th Coordinate values ​​in each coordinate direction, For the sampling point at the th Normalized local coordinates in each coordinate direction.

[0008] Optionally, the smooth saturated monotonic mapping function is a sigmoid function, and the geometric embedding features are calculated as follows: , in, For the sigmoid function, For scale parameters, The geometric embedding feature of the sampling point in the i-th coordinate direction, For the sampling point at the th Normalized local coordinates in each coordinate direction.

[0009] Optionally, the residuals of the governing equations and boundary conditions are calculated based on the predicted physical field values ​​to form a composite loss function, including: Acquire internal sampling points in the fluid and solid domains of the embedded manifold microchannel heat sink, as well as boundary sampling points on the boundary; Based on the predicted physical field values ​​of the internal sampling points, the residuals of the governing equations are calculated. The residuals of the governing equations include: the residuals of the continuity equation, momentum equation, and fluid energy equation in the fluid domain, and the residuals of the solid thermal conductivity equation in the solid domain. Based on the predicted physical field values ​​of the boundary sampling points, the boundary condition residuals are calculated. The boundary condition residuals include: inlet boundary residual, outlet boundary residual, heated bottom surface boundary residual, adiabatic top surface boundary residual, symmetry surface boundary residual, no-slip condition residual on the fluid-solid interface, temperature continuity condition residual on the fluid-solid interface, and heat flow continuity condition residual on the fluid-solid interface. The weighted summation of the residuals of the governing equations and the residuals of the boundary conditions constitutes the composite loss function.

[0010] Optionally, during the training of the physical information neural network based on the composite loss function, a course learning strategy is adopted: Get current training steps According to the current training steps Determine the continuation factor The continuation factor With training steps The increase is from the initial value to the target value; According to the continuation factor The physical parameters in the composite loss function are adjusted so that they gradually transition from easily trained values ​​to target physical values; wherein the physical parameters include Prandtl number in the fluid energy equation and / or thermal conductivity ratio in the fluid-solid interface heat flow continuity condition.

[0011] Optionally, the continuation factor Determine using the following formula: , in, This represents the current number of training steps. The preset number of preheating steps; The Prandt number transitions from the easily trainable value to the target physical value according to the following formula: , in, This represents the effective Prandtl number for the current number of training steps. For Prandtl numbers, which are easy-to-train values, For the target Prandtl number; The thermal conductivity ratio transitions from the easily trained value to the target physical value according to the following formula: , in, This is the ratio of effective thermal conductivity at the current number of training steps. The target thermal conductivity ratio.

[0012] Optionally, when training the physical information neural network using a course learning strategy, the entry boundary residuals in the composite loss function are assembled in the following manner: The entrance boundary residual According to the continuation factor Assemble according to the following formula: , in, For the inlet scalar constraint loss term, For the inlet flux constraint loss term, This is the inlet auxiliary temperature constraint loss term; The heating bottom surface boundary residual According to the continuation factor Assemble according to the following formula: , in, This is the temperature constraint loss term for the solid side of the heating bottom surface. This is the fluid-side coupling loss term for the heated bottom surface.

[0013] Optionally, the sampling points are generated in real time on the graphics processor, including: The fluid domain and solid domain of the embedded manifold microchannel heat sink are decomposed into multiple parameterized bounding boxes, and the boundary positions of the parameterized bounding boxes are determined by the geometric parameters. Sample internal points within each of the parameterized bounding boxes; Sample boundary points on the parameterized boundary surface; Sampling points with a higher density than those in the internal area are arranged at the fluid-solid wall, microchannel gaps, and inlet and outlet boundaries.

[0014] Optionally, during the training of the physical information neural network based on the composite loss function, a matrix preconditioning optimizer is used to update the parameters of the physical information neural network, and a dynamic gradient normalization strategy is used to adjust the weights of each loss component in the composite loss function.

[0015] A second aspect of this application discloses an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the simulation method for the thermal flow characteristics of an embedded manifold microchannel heat sink based on a parameterized physical information neural network as described in the first aspect of this application.

[0016] The embodiments of this application have the following advantages: In this embodiment, by incorporating geometric parameters as part of the network input and introducing geometric embedding features to characterize the relative position of sampling points with respect to the boundary of their respective sub-regions, the physical information neural network can cover a continuous geometric design space composed of multiple geometric parameters after a single training iteration. After training, for any combination of target geometric parameters, a single forward propagation is sufficient to obtain the predicted thermal flow characteristics, eliminating the need for remodeling or solving governing equations, thus improving simulation efficiency.

[0017] Furthermore, by calculating the normalized local coordinates of the sampling points within their respective parameterized sub-regions and transforming them using a smooth, saturated, monotonic mapping function to generate geometric embedding features, the relative positions of the sampling points with respect to the sub-region boundaries are stably represented in the embedding space. Regardless of changes in geometric parameters, key relative positions such as boundaries and centers are mapped to consistent embedding values. The network can stably distinguish different regions and their boundaries during continuous changes in geometric configuration, overcoming the learning difficulties caused by geometric changes and ensuring prediction accuracy on unseen combinations of geometric parameters.

[0018] By concatenating geometric embedding features with normalized geometric parameters and spatial coordinates, an enhanced input vector is formed and fed into the physical information neural network. The network output directly includes the velocity, pressure, and temperature fields. This eliminates the need for step-by-step iterative solutions to the flow and energy equations, avoiding the staged error accumulation inherent in traditional numerical methods, resulting in a concise and efficient inference process. Furthermore, the physical information neural network is trained using a composite loss function composed of the residuals of the control equations and boundary conditions as the optimization objective, without relying on labeled data such as finite element simulation results. During the learning process, the network is forced to satisfy the conservation of mass, momentum, and energy, as well as various boundary conditions, ensuring that the prediction results naturally conform to physical laws while reducing dependence on training samples. Attached Figure Description

[0019] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a flowchart illustrating the steps of a method for simulating the thermal flow characteristics of an embedded manifold microchannel radiator based on a parameterized physical information neural network, as provided in this application embodiment. Figure 2 This is a schematic cross-sectional view of a symmetrical computing unit with an embedded manifold microchannel heat sink provided in an embodiment of this application. Figure 3 This is a schematic diagram illustrating the principle of geometric embedding feature mapping provided in an embodiment of this application; Figure 4 This application provides an embodiment of the overall architecture and data flow diagram of a physical information neural network; Figure 5 This is a training process and course learning diagram provided in an embodiment of this application; Figure 6 This is a schematic diagram of the structure of an embedded manifold microchannel heat sink heat flow characteristic simulation device based on a parameterized physical information neural network provided in this application embodiment; Figure 7 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0021] To make the above-mentioned objectives, features, and advantages of this application more apparent and understandable, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0022] This application addresses the technical problems of high simulation cost and weak cross-geometric generalization ability of embedded manifold microchannel heat sinks within the geometric design space. It proposes a simulation method for the thermal flux characteristics of embedded manifold microchannel heat sinks based on a parametric physical information neural network. The technical concept is as follows: geometric parameters and spatial coordinates are used as network inputs. By calculating the normalized local coordinates of sampling points within their respective parametric sub-regions and transforming them through a smooth, saturated, monotonic mapping function, geometric embedding features that characterize the relative positions of sampling points with respect to the sub-region boundaries are generated. This ensures that boundary positions are mapped to consistent embedding values ​​under different geometric parameters, thus overcoming the learning difficulties caused by geometric variations. Physical constraint training is performed using a composite loss function composed of the control equation residuals and boundary condition residuals as the optimization objective, without relying on labeled data. After training, for any combination of target geometric parameters, the predicted results of the three-dimensional velocity field, pressure field, and temperature field can be obtained with only one forward propagation.

[0023] Reference Figure 1 As shown, Figure 1 This is a flowchart illustrating the steps of a simulation method for the thermal flow characteristics of an embedded manifold microchannel heat sink based on a parameterized physical information neural network, as provided in an embodiment of this application. Figure 1 As shown, the method may include steps S110 to S170: Step S110: Obtain the geometric parameters and spatial coordinates of the sampling points of the embedded manifold microchannel heat sink to be simulated.

[0024] In this embodiment, the simulation object is an embedded manifold microchannel heat sink, which belongs to a three-dimensional conjugate heat transfer system composed of a solid domain and a fluid domain. To reduce computational costs, the entire system is simplified into a single microchannel symmetrical computational unit by utilizing the structural periodicity and symmetry, and symmetrical boundary conditions are applied on the corresponding plane. Figure 2 As shown, the computing unit is divided into three layers from bottom to top along the height direction: a silicon substrate layer ( Solid domain, its bottom surface Isothermal heating of the bottom surface), microchannel fluid layer ( ], fluid domain, which can use water as coolant), manifold solid layer ( (Solid domain, silicon can be extracted); the jet inlet groove and jet outlet groove are located within the manifold layer, respectively located in and The coolant flows vertically downwards from the top surface to the top of the microchannel layer. The coolant enters vertically downwards from the jet inlet, impacts the bottom of the microchannel, then turns and flows along the microchannel before flowing vertically upwards through the jet outlet. The upper surface of the manifold layer between the slots is an insulated top surface, with the left and right sides being symmetrical surfaces passing through the inlet center and the outlet center, respectively.

[0025] Geometric parameters are adjustable parameters used to describe the geometry of an embedded manifold microchannel heatsink, including but not limited to microchannel width, microchannel height, jet inlet width, and jet outlet width. The value range of these geometric parameters can be predetermined according to actual design requirements and manufacturing process constraints, forming a multi-dimensional continuous geometric design space. A sampling point refers to a spatial location point selected within the fluid and / or solid domain of the heatsink to be simulated, defined by its spatial coordinates. The sampling points are uniquely determined. The selection method can be uniform grid sampling, random sampling, or importance sampling, and the number of samples can be set according to accuracy and efficiency requirements.

[0026] Step S120: Based on the geometric parameters and the spatial coordinates, determine the parameterized sub-region to which the sampling point belongs, and calculate the normalized local coordinates of the sampling point within the parameterized sub-region.

[0027] In this embodiment, a parameterized sub-region refers to decomposing the computational domain of the heat sink into several regularly shaped sub-regions according to its geometric structure. The fluid domain can be decomposed into inlet groove region, microchannel region, and outlet groove region, etc.; the solid domain can be decomposed into silicon substrate layer region and manifold layer region, etc. The boundary position of each parameterized sub-region is determined analytically by the geometric parameters obtained in step S110. Therefore, as the geometric parameters change, the spatial range of each sub-region also changes.

[0028] For any given sampling point, its spatial coordinates are first compared with the boundary positions of each parameterized sub-region to determine its sub-region affiliation. Then, the minimum and maximum boundary values ​​of that sub-region in each coordinate direction are obtained, and the normalized local coordinates of the sampling point within its sub-region are calculated. It is understandable that the normalized local coordinates reflect the relative position of the sampling point within its sub-region (e.g., near the center or boundary), and its range is always [value range missing]. The range does not change with variations in geometric parameters.

[0029] Step S130: The normalized local coordinates are transformed by a smooth saturated monotonic mapping function to generate geometric embedding features, which are used to characterize the relative position of the sampling point with respect to the boundary of the parameterized sub-region.

[0030] In this embodiment, a smooth saturated monotonically mapping function refers to a class of functions that are smooth (i.e., differentiable), monotonically increasing, and whose function values ​​approach two different saturation values ​​as the independent variable approaches 0 and 1, respectively. These include, but are not limited to, the sigmoid function, the tanh function (which has been translated and scaled to adapt its domain and range), and other sigmoid saturated functions. After normalized local coordinates are transformed by this mapping function, when the sampling point is located at the boundary of the sub-region, it is mapped to the vicinity of the saturation value; when located near the center, it is mapped to the vicinity of the intermediate value.

[0031] It's important to note that regardless of changes in geometric parameters, the boundary and center of a sub-region always correspond to the same position in the embedding space. This property stems from the calculation method of normalized local coordinates: normalization is performed based on the boundary range of the sub-region itself, ensuring that the boundary always corresponds to 0 or 1, and the center always corresponds to 0.5. The smooth saturated monotonic mapping function introduces saturation characteristics on this basis, causing the embedding values ​​near the boundary to stably approach the saturation value. This avoids the fluctuations in embedding values ​​near the boundary caused by small changes in geometric parameters, thus ensuring the stability and convergence of the neural network training process. Through this method, the network can clearly identify the spatial positional relationship of sampling points relative to the sub-region boundary.

[0032] Step S140: Concatenate the geometric embedding features with the normalized geometric parameters and the spatial coordinates to form an enhanced input vector.

[0033] In this embodiment, the geometric parameters and spatial coordinates obtained in step S110 are normalized to ensure that all dimensions are within the same numerical range, which facilitates network training convergence. Subsequently, the normalized geometric parameters, spatial coordinates, and the geometric embedding features generated in step S130 are concatenated along the vector dimension to form an enhanced input vector. This enhanced input vector simultaneously contains the absolute spatial location information of the sampling points, geometric configuration parameter information, and the relative position information of the sampling points within their respective sub-regions.

[0034] Step S150: Input the enhanced input vector into the physical information neural network to obtain the physical field prediction value of the sampling point. The physical field prediction value includes the velocity field, pressure field and temperature field.

[0035] In this embodiment, the Physics-Informed Neural Network (PINN) takes the enhanced input vector obtained in step S140 as input, undergoes nonlinear transformation by a multi-layer neural network, and outputs the predicted physical field value for the corresponding sampling point. For sampling points within the fluid domain, the network outputs the velocity field. The network outputs a pressure field (p) and a temperature field (T); for sampling points within the solid domain, the network outputs the temperature (T). The structure of the physical information neural network can employ a multilayer perceptron, residual network, or other differentiable architectures; this embodiment does not specifically limit this.

[0036] Step S160: Calculate the control equation residuals and boundary condition residuals based on the predicted physical field values ​​to form a composite loss function, and train the physical information neural network based on the composite loss function.

[0037] In this embodiment, the governing equations include the continuity, momentum, and energy equations for the fluid domain, and the heat conduction equation for the solid domain, all used in dimensionless form. The governing equation residual refers to the difference between the left and right sides of the equation after substituting the predicted physical field values ​​at the sampling points into the governing equation; the boundary condition residual refers to the difference after substituting the predicted values ​​into various boundary condition equations. These residuals are weighted and summed to form a composite loss function. The network parameters are updated through backpropagation with the goal of minimizing this loss function. The training process does not require finite element simulation results or experimental measurement data as labeled samples, belonging to a physics-driven training paradigm.

[0038] Step S170: Obtain the target geometric parameters and spatial coordinates of the target sampling point of the target embedded manifold microchannel heat sink, construct them as the target enhancement input vector, input them into the trained physical information neural network, and obtain the heat flow characteristic prediction result.

[0039] In this embodiment, steps S110 to S160 are the training phase, the purpose of which is to train a physical information neural network capable of accurate prediction throughout the entire geometric design space. Step S170 is the inference phase. During inference, for any target geometric parameters and the spatial coordinates of any target sampling point, a target enhancement input vector is constructed following the same process as in the training phase. This vector is then input into the trained network to perform a forward propagation, thereby obtaining the predicted thermal flux characteristics (i.e., the predicted values ​​of velocity, pressure, and temperature at the sampling point). Repeating the above process for multiple target sampling points yields the three-dimensional thermal flux field distribution across the entire computational domain.

[0040] The technical solution adopted in this embodiment uses geometric parameters as part of the network input, enabling a single physical information neural network to cover a continuous geometric design space. After training, only a single forward propagation is needed to obtain the prediction result, improving simulation efficiency. Furthermore, by calculating normalized local coordinates and generating geometric embedding features through a smooth, saturated, monotonic mapping function, key relative positions such as boundaries and centers are mapped to consistent values ​​in the embedding space. The network can stably distinguish different regions and their boundaries during continuous changes in geometric configuration, ensuring prediction accuracy even with unknown combinations of geometric parameters. The network is trained using a composite loss function composed of the residuals of the control equations and boundary conditions as the optimization objective, without relying on labeled data, and the prediction results naturally conform to physical laws. The network output directly includes the velocity field, pressure field, and temperature field, eliminating the need for step-by-step iterative solutions and avoiding the accumulation of staged errors in traditional numerical methods.

[0041] As an optional implementation, the sampling points are generated in real time on the graphics processor, which may specifically include steps B1 to B4: Step B1: Decompose the fluid domain and solid domain of the embedded manifold microchannel heat sink into multiple parameterized bounding boxes, the boundary positions of which are determined by the geometric parameters.

[0042] In this embodiment, a parameterized bounding box refers to decomposing the computational domain into several cuboid-shaped sub-regions according to its geometric structure. The boundary position of each bounding box in each coordinate direction is uniquely determined by the analytical function of the geometric parameters. Specifically, the fluid domain can be decomposed into the jet inlet slot region (within the manifold layer, where fluid flows vertically downwards from the top), the microchannel mainstream region (within the microchannel layer, where fluid flows horizontally), and the jet outlet slot region (within the manifold layer, where fluid flows upwards), etc.; the solid domain can be decomposed into the silicon substrate layer region and the manifold layer solid region, etc. Given any set of geometric parameters, the spatial extent of all bounding boxes can be directly calculated without the need for mesh generation tools or geometric modeling software.

[0043] Step B2: Sample interior points within each of the parameterized bounding boxes.

[0044] In this embodiment, interior points refer to sampling points located inside the bounding box, excluding points falling on the boundary surface. For each parameterized bounding box, sampling points in three-dimensional space are formed by independently generating and combining random coordinate values ​​or grid coordinate values ​​in each of its x, y, and z directions. The number of samples in each direction can be independently set according to the scale ratio of each direction and the drastic change of the physical field. The purpose of sampling interior points within each parameterized bounding box is to provide sampling points for the calculation of the residuals of the governing equations, so as to meet the constraint requirements of the continuity equation, momentum equation, and energy equation within the fluid and solid domains.

[0045] Step B3: Sample boundary points on the parameterized boundary surface.

[0046] In this embodiment, the parameterized boundary surface refers to the boundary surface in the computational domain that requires the application of boundary condition constraints, and its location is also determined analytically by geometric parameters. The boundary surfaces sampled for boundary points include: the jet inlet boundary surface (top surface of the inlet slot, with inlet boundary conditions applied), the jet outlet boundary surface (top surface of the outlet slot, with outlet boundary conditions applied), the heating bottom surface (bottom surface of the silicon substrate, with heating temperature boundary conditions applied), the adiabatic top surface (top surface of the manifold layer, with adiabatic boundary conditions applied), the symmetry surface (two symmetrical sides of the computational unit, with symmetry boundary conditions applied), and the fluid-structure interaction interface (between the microchannel layer and the substrate layer, and between the microchannel layer and the manifold layer, with interface coupling conditions applied). On each parameterized boundary surface, random coordinate values ​​or grid coordinate values ​​are independently generated in two coordinate directions within the surface and combined to form boundary sampling points. The purpose of boundary point sampling is to provide sampling points for boundary condition residual calculation, ensuring the sufficient application of boundary constraints.

[0047] Step B4: Arrange sampling points at a higher density than in the internal area at the fluid-solid wall, microchannel gap, and inlet and outlet boundaries.

[0048] In this embodiment, for regions with drastic changes in the physical field, a region-aware importance sampling strategy is employed to deploy a higher density of sampling points. The fluid-solid wall is the coupling interface between the fluid and solid domains, where the velocity rapidly transitions from the fluid domain's flow state to the wall's no-slip condition, resulting in a significant velocity gradient. Simultaneously, temperature and heat flow continuity must be satisfied on both sides of the interface. Increased sampling density helps the network learn the near-wall flow and heat transfer characteristics more accurately. The microchannel gap refers to the narrow space along the width direction of the microchannel, typically only on the order of tens of micrometers. The spatial rate of change of the velocity and temperature fields is high. Increasing the number of sampling points along the width direction ensures sufficient sampling points in this narrow dimension to analyze the physical field distribution. The inlet and outlet boundaries are where the jet impact effect and flow acceleration effect are most significant. Increased sampling density helps the network learn the flow and heat transfer characteristics near these boundaries more accurately.

[0049] Thus, by decomposing the computational domain into parameterized bounding boxes and generating sampling points in real time on the GPU, the spatial position of the sampling points can be dynamically adjusted according to the geometric parameters, always accurately adapting to the current geometric configuration, avoiding the problem of offline pre-generated sampling points failing when geometric parameters change. Through a region-aware importance sampling strategy, higher density sampling points are deployed in areas with drastic physical field changes, such as fluid-solid walls, microchannel gaps, and inlet / outlet boundaries, enhancing the constraint strength of the network in these critical areas and improving prediction accuracy and training efficiency. The GPU real-time generation method eliminates the data transfer overhead between the CPU and GPU during training, further improving overall training efficiency.

[0050] As an optional implementation, step S120 above, "determining the parameterized sub-region to which the sampling point belongs based on the geometric parameters and the spatial coordinates, and calculating the normalized local coordinates of the sampling point within the parameterized sub-region to which it belongs," may include steps S120-1 to S120-3: Step S120-1: Determine the boundary positions of each parameterized sub-region based on the geometric parameters.

[0051] In this embodiment, the computational domain of the embedded manifold microchannel heat sink is decomposed into several parameterized sub-regions, such as the jet inlet groove region, microchannel mainstream region, and jet outlet groove region in the fluid domain, and the silicon substrate layer region and manifold layer region in the solid domain. There is a definite analytical relationship between the boundary position of each sub-region and the geometric parameters. Therefore, once the geometric parameters are determined, the boundary position of each sub-region can be directly calculated.

[0052] Step S120-2: Determine the parameterized sub-region to which the sampling point belongs based on the spatial coordinates of the sampling point and the boundary position of each parameterized sub-region.

[0053] In this embodiment, after determining the boundary positions of each sub-region, for each sampling point, its spatial coordinates are compared with the boundary positions of each sub-region. If the coordinates of a sampling point simultaneously satisfy the boundary range conditions of a sub-region in all directions, then the sampling point is determined to belong to the parameterized sub-region. If the sampling point is located on the interface of the sub-regions, it can be assigned to any one of the adjacent sub-regions, or simultaneously to two sub-regions, according to preset rules.

[0054] Step S120-3: Obtain the minimum boundary value of the parameterized sub-region to which the sampling point belongs in each coordinate direction. and boundary maximum value The normalized local coordinates of the sampling points are calculated using the following formula: , in, For the sampling point at the th Coordinate values ​​in each coordinate direction, For the sampling point at the th Normalized local coordinates in each coordinate direction.

[0055] The essence of this formula is to perform linear normalization on the sampling points within their respective sub-regions. Regardless of the absolute size of the sub-region, the sampling points within the sub-region are all mapped to... The corresponding position within the interval. The sub-region boundary corresponds to normalized coordinates 0 or 1, and the geometric center corresponds to 0.5, enabling the network to perceive the relative position of the sampling point within its sub-region.

[0056] The technical solution of this embodiment decomposes the computational domain into multiple parameterized sub-regions and determines the boundary positions of each sub-region analytically based on geometric parameters, thereby achieving rapid determination of the region affiliation of sampling points and efficient calculation of normalized local coordinates. Since there is an analytical relationship between the boundary positions and geometric parameters, the normalized local coordinates change continuously with the geometric parameters, providing an accurate and differentiable positional encoding basis for the subsequent generation of geometric embedding features.

[0057] As an optional implementation, the smooth saturated monotonic mapping function in step S130 above is a sigmoid function, and the geometric embedding features are calculated as follows: , in, For the sigmoid function, For scale parameters, The geometric embedding feature of the sampling point in the i-th coordinate direction, For the sampling point at the th Normalized local coordinates in each coordinate direction.

[0058] In this embodiment, the expression for the sigmoid function is: Its function value monotonically increases with the independent variable, approaching 1 and 0 respectively as the independent variable approaches positive and negative infinity, and is differentiable throughout its entire domain. The above formula first normalizes the local coordinates... Shift by -0.5, so that its range is from Become Then divide by the scale parameter Control the steepness of the transition. For positive values, smaller values ​​indicate faster saturation near the boundary, while larger values ​​result in a smoother transition region. After this transformation, the geometric center of the sub-region ( The corresponding embedding value is 0.5, and the boundary ( or The corresponding embedded value is close to 0 or 1, which is independent of the specific value of the geometric parameter.

[0059] like Figure 3 As shown, Figure 3 This is a schematic diagram of the principle of geometric embedding feature mapping provided in an embodiment of this application. Figure 3 Part (a) illustrates the mapping between the physical distance from the sampling point to the wall and the geometric embedding features under different design parameters. Taking Design ① (solid line) and Design ② (dashed line) as examples, the two designs have different geometric parameters (e.g., jet inlet width). They are respectively and Since the physical dimensions of the sub-regions differ, the absolute physical distance from the sampling points to the walls also varies. However, due to the combined effect of normalized local coordinates and smooth saturated monotonic mapping, sampling points located at the geometric center of the sub-regions in both designs are mapped to an embedding value of 0.5, while sampling points located at the boundaries are mapped to saturation values ​​approaching 0 or 1. Figure 3 Part (b) further illustrates the complete calculation process from sampling points to geometric embedding features: For a given sampling point, firstly, the boundary values ​​of its sub-region in each coordinate direction are determined according to the current geometric parameters, the normalized local coordinates are calculated, and then the geometric embedding features are obtained through smooth saturated monotonic mapping.

[0060] The technical solution of this embodiment employs the sigmoid function as a smooth, saturated, monotonic mapping function, ensuring that the boundaries and centers of sub-regions are mapped to consistent and stable embedding values ​​under different geometric parameters. This allows the network to stably identify the relative positions of region boundaries and interiors under different geometric configurations. The smoothness of the sigmoid function guarantees the continuous differentiability of the gradient, which is beneficial for stable network training.

[0061] As an optional implementation, step S160 above, "calculating the control equation residuals and boundary condition residuals based on the predicted physical field values ​​to form a composite loss function," may include steps S160-1 to S160-4: Step S160-1: Obtain the internal sampling points in the fluid domain and solid domain of the embedded manifold microchannel heat sink, as well as the boundary sampling points on the boundary.

[0062] In this embodiment, based on their location within the computational domain, sampling points can be categorized into two types: internal sampling points and boundary sampling points. Internal sampling points are located within the fluid or solid domain and are used to calculate the residuals of the governing equations; boundary sampling points are located on various boundary surfaces and are used to calculate the residuals of boundary conditions.

[0063] Step S160-2: Calculate the residuals of the governing equations based on the predicted physical field values ​​of the internal sampling points. The residuals of the governing equations include: the residuals of the continuity equation, momentum equation, and fluid energy equation in the fluid domain, and the residuals of the solid thermal conductivity equation in the solid domain.

[0064] In this embodiment, the physical processes of the embedded manifold microchannel heat sink involve fluid flow and heat transfer. The governing equations include two parts: governing equations in the fluid domain and governing equations in the solid domain. The governing equations are used in dimensionless form, and each residual is the mean square value of the equation residuals at the corresponding sampling point.

[0065] Specifically, for the fluid domain, the governing equations include: (1) the continuity equation (mass conservation). Continuous residual Within the fluid domain The mean value is used to constrain the velocity field predicted by the network to satisfy mass conservation. (2) Momentum equation (Navier-Stokes equation) Momentum residual Within the fluid domain The mean of the sum of squares of each component is used to constrain the velocity and pressure fields predicted by the network to satisfy momentum conservation. is the Reynolds number, a dimensionless parameter characterizing the flow state. (3) Fluid energy equation: Fluid energy residual Within the fluid domain The mean of is used to constrain the fluid temperature field predicted by the network to satisfy energy conservation. is the Prandtl number, a dimensionless parameter characterizing the relative importance of momentum diffusion and thermal diffusion in fluids.

[0066] For the solid domain, the governing equation is the solid heat conduction equation: Solid energy residual Within the solid domain The mean value is used to constrain the solid temperature field predicted by the network to satisfy the heat conduction equation.

[0067] In practical implementation, calculating the residuals of the above governing equations requires the use of automatic differentiation techniques to calculate the first-order partial derivatives of the network output with respect to spatial coordinates (e.g., , , , ) and second-order partial derivatives (such as , , , ).

[0068] Step S160-3: Calculate the boundary condition residuals based on the predicted physical field values ​​of the boundary sampling points. The boundary condition residuals include: inlet boundary residual, outlet boundary residual, heating bottom surface boundary residual, adiabatic top surface boundary residual, symmetry surface boundary residual, no-slip condition residual on the fluid-solid interface, temperature continuity condition residual on the fluid-solid interface, and heat flow continuity condition residual on the fluid-solid interface.

[0069] In this embodiment, the simulation of the embedded manifold microchannel heat sink requires the application of various boundary conditions. The sampling points on different types of boundaries undertake different boundary constraint tasks, and the residuals of various boundary conditions are the mean square values ​​of the corresponding constraint equation residuals on the boundary sampling points.

[0070] Specifically, the inlet boundary residual is used to constrain the flow and temperature conditions at the inlet, including inlet scalar constraints. (Such as inlet pressure, tangential velocity constraints) and inlet flux constraints (e.g., inflow thermal balance constraint). Among these, the inlet scalar constraint... For the entrance surface The mean value is used to specify the inlet pressure and make the tangential velocity zero; inlet flux constraint. For the entrance surface The mean value is used to constrain the inflow heat balance condition.

[0071] Export boundary residual For export The mean value is used to constrain the outlet pressure, tangential velocity, and temperature normal gradient to zero.

[0072] Heating bottom boundary residual On a solid base The mean, of which Predicted bottom solid temperature Given a heating temperature value; the heating bottom boundary residual is used to constrain the temperature conditions of the heated wall surface.

[0073] Insulation top surface boundary residual solid top surface The average value is used to constrain the thermal insulation conditions of the top surface.

[0074] The boundary residuals of the symmetry plane include velocity constraints. and scalar constraints , On the plane of symmetry The mean value is used to constrain the velocity conditions on the plane of symmetry (normal velocity is zero, tangential velocity is free). On the plane of symmetry The mean, of which This is used to constrain the normal gradient of the scalar field on the plane of symmetry to be zero.

[0075] No-slip conditional residuals at fluid-solid interfaces For fluid-solid interface The mean value is used to constrain the fluid velocity at the interface to zero.

[0076] Temperature continuity residual at the fluid-solid interface For the interface The average value is used to constrain the temperature on both sides of the interface to be equal.

[0077] Thermal flux continuity condition residual at the fluid-solid interface For the interface The mean value is used to constrain the continuity of heat flux density on both sides of the interface. It is the ratio of the thermal conductivity of the solid to the thermal conductivity of the fluid.

[0078] Step S160-4: The residuals of the governing equations and the residuals of the boundary conditions are weighted and summed to form the composite loss function.

[0079] In this embodiment, all the control equation residuals calculated in step S160-2 and all the boundary condition residuals calculated in step S160-3 are weighted and summed according to their respective preset weight coefficients to obtain a scalar value, which is the composite loss function.

[0080] For example, the composite loss function can be expressed as:

[0081] in, This represents the k-th loss term (including residuals from various governing equations and boundary conditions). This represents the weighting coefficient of the k-th loss term, used to adjust the relative importance of each loss term in the total loss.

[0082] In each training iteration, after calculating the composite loss function value, the gradient of the loss function with respect to the network parameters is calculated using the backpropagation algorithm. The network parameters are then updated using the optimizer, causing the loss function value to gradually decrease. As the training iterations proceed, the physical field predicted by the network gradually approximates the physical solution that satisfies the governing equations and boundary conditions.

[0083] The technical solution adopted in this embodiment transforms training into a problem of minimizing a composite loss function. During the learning process, the network is forced to satisfy mass conservation, momentum conservation, energy conservation, and various boundary conditions, without relying on a large amount of labeled data. It also includes fluid domain, solid domain, and fluid-solid interface conditions, effectively handling conjugate heat transfer problems.

[0084] As an optional implementation, during the training of the physical information neural network based on the composite loss function, a matrix preconditioning optimizer is used to update the parameters of the physical information neural network, and a dynamic gradient normalization strategy is used to adjust the weights of each loss component in the composite loss function.

[0085] In this embodiment, a matrix preconditioning optimizer (such as a SOAP optimizer) performs a linear transformation on the gradient direction using a preconditioning matrix, making the update direction closer to the natural gradient direction. For the problem of different curvatures in the parameter gradients corresponding to each loss component in a composite loss function, the preconditioning matrix can adaptively scale gradients in different directions, effectively alleviating the common problem of loss stagnation or convergence to incorrect solution branches in rigid multiphysics PINN training. The dynamic gradient normalization strategy calculates the gradient norm of each loss component with respect to the network parameters in each training step and dynamically adjusts the weights of each loss component based on the statistics of the gradient norm. Components with larger gradient norms have their weights appropriately reduced, while those with smaller gradient norms have their weights appropriately increased, ensuring balanced optimization of each physical constraint during training.

[0086] Thus, by combining the matrix preconditioner with dynamic gradient normalization, the problem of significant differences in the magnitude of each loss component and ill-conditioned gradient conditions in the composite loss function is effectively addressed, improving the convergence speed and stability of training and avoiding the tedious manual parameter tuning.

[0087] As an optional implementation, in step S160 above, during the training of the physical information neural network based on the composite loss function, a course learning strategy is adopted, specifically including steps A1 to A2: Step A1: Get the current training steps According to the current training steps Determine the continuation factor The continuation factor With training steps The increase is from the initial value to the target value.

[0088] In this embodiment, the core idea of ​​the course learning strategy is to gradually transition the network from easier physics problems to the target physics problem during training. To quantitatively control this transition process, a continuation factor is introduced. It is the number of training steps. It is a monotonically increasing function. Specifically, the continuation factor... Starting from an initial value (usually 0), as the number of training steps increases... The value increases gradually until it reaches the target value (usually 1).

[0089] In one implementation, the continuation factor Determine using the following formula: , in, This represents the current number of training steps. The preset number of warm-up steps, i.e., before training. Within a single step, the continuation factor increases linearly from 0 to 1; when the number of training steps exceeds... Afterwards, the continuation factor remains at 1. The value can be set according to the specific problem. For example, in one implementation, it can be set to half of the total number of training steps (e.g., when the total number of steps is 200,000). step).

[0090] Step A2: Based on the continuation factor The physical parameters in the composite loss function are adjusted so that they gradually transition from easily trained values ​​to target physical values; wherein the physical parameters include Prandtl number in the fluid energy equation and / or thermal conductivity ratio in the fluid-solid interface heat flow continuity condition.

[0091] In this embodiment, after the continuation factor is determined, it is used to adjust the parameters related to physical difficulty in the composite loss function. Specifically, one physical parameter that needs to be adjusted is the Prandtl number in the fluid energy equation. The Prandtl number is the ratio of a fluid's momentum diffusivity to its thermal diffusivity, characterizing the relative strength of convective and conductive heat transfer in a flow. Target Prandtl number. This is determined by the physical properties of the coolant. However, directly using a large Prandtl number in the early stages of training will cause the energy equation to exhibit strong convection-dominated characteristics, resulting in strong numerical rigidity, difficulty in gradient propagation, and difficulty in network convergence. Therefore, a smaller, easier-to-train value is used in the early stages of training. (For example At this point, the energy equation is diffusion-dominated, exhibiting good numerical stability and ease of optimization. As the continuation factor increases, the effective Prandtl number gradually decreases from [a certain value, likely a magnitude] to [another value, likely a magnitude]. Transition to target physical value .

[0092] In one implementation, the Prandtl number transitions from the easily trainable value to the target physical value according to the following formula: , in, This represents the effective Prandtl number for the current number of training steps. These are the easy-to-train values ​​(initial values) for the Prandtl number. For the target Prandtl number. When hour, ;when hour, .

[0093] Another physical parameter that needs to be adjusted is the thermal conductivity ratio under the fluid-solid interface heat flow continuity condition. The thermal conductivity ratio is defined as the ratio of the thermal conductivity of a solid to its thermal conductivity. With fluid thermal conductivity The ratio, that is If the target thermal conductivity ratio is used directly in the early stages of training, the network will find it difficult to simultaneously satisfy the heat flow continuity condition on both sides of the interface. Therefore, a small, easily trainable value is used in the early stages of training (e.g., starting from 1, i.e., matching thermal conductivity on both sides) to make the interface coupling condition easier to satisfy; as the continuity factor increases, the effective thermal conductivity ratio gradually transitions to the target physical value.

[0094] In one implementation, the thermal conductivity ratio transitions from the easily trained value to the target physical value according to the following formula: , in, This is the ratio of effective thermal conductivity at the current number of training steps. The target thermal conductivity ratio. When hour, ;when hour, .

[0095] By adopting the technical solution of this embodiment, Prandtl number and thermal conductivity ratio are gradually adjusted by the continuation factor, so that the training can smoothly transition from an easily optimized state dominated by diffusion and with interface thermal conductivity matching to a target state dominated by convection and with strong thermal conductivity contrast. This effectively avoids the numerical rigidity and convergence difficulties caused by convection terms and interface coupling terms during direct training.

[0096] As an optional implementation, when training the physical information neural network using a course learning strategy, the entry boundary residuals in the composite loss function are assembled in the following manner.

[0097] In this embodiment, the continuation factor It is also used to control the gradual activation of some boundary conditions. This mechanism can be seen as an extension of the course learning strategy at the boundary condition level. That is, the network first learns to satisfy simplified boundary constraints in the early stage of training, and then gradually transitions to complete physical boundary conditions as training progresses. Specifically, the inlet boundary residual and the heating bottom boundary residual are dynamically assembled with the continuation factor in the following manner.

[0098] (1) The inlet boundary residual According to the continuation factor Assemble according to the following formula: , in, For the inlet scalar constraint loss term, For the inlet flux constraint loss term, This is the inlet auxiliary temperature constraint loss term.

[0099] Specifically, the entry scalar constraint loss term The pressure and tangential velocity conditions used to constrain the inlet are maintained with fixed weights throughout training and do not change with the continuity factor. Inlet flux constraint loss term. Used to constrain the inflow heat balance condition, its weight is determined by the continuation factor. Control. Inlet auxiliary temperature constraint loss term. This is used to provide a simple anchor point constraint for the temperature field near the inlet in the early stages of training, and its weights are determined by... control.

[0100] In the early stages of training ( In the inlet boundary residual, the auxiliary temperature constraint term has a larger weight, while the flux constraint term has a smaller weight. This means that the network initially learns to satisfy a simplified inlet temperature condition (e.g., the inlet fluid temperature is close to one reference value, and the inlet solid temperature is close to another reference value). As training progresses... Gradually increase the weight of the auxiliary temperature constraint term. The weight of the flux constraint term is gradually reduced to zero. Gradually increasing to 1, the inlet boundary condition smoothly transitions from a simplified temperature anchor constraint to a complete inflow thermal balance constraint. When training ends ( The auxiliary temperature constraint term has a weight of zero, and the inlet boundary residual is restored to the complete physical boundary conditions. .

[0101] (2) The residual at the boundary of the heated bottom surface According to the continuation factor Assemble according to the following formula: , in, This is the temperature constraint loss term for the solid side of the heating bottom surface. This is the fluid-side coupling loss term for the heated bottom surface.

[0102] Specifically, the temperature constraint loss term on the solid side of the heated bottom surface This term, used to constrain the solid temperature at the bottom surface to a given heating temperature (isothermal heating condition), maintains a fixed weight throughout training. (Bottom surface fluid-side coupling loss term) The temperature conditions used to constrain the fluid side of the bottom surface (i.e., on the fluid side of the heated bottom surface, the temperature should also satisfy corresponding boundary conditions, such as symmetry conditions or temperature continuity conditions) are weighted by the continuation factor. control.

[0103] In the early stages of training ( The weight of the fluid-side coupling loss term in the boundary residual of the heated bottom surface is zero, and the network only needs to satisfy the temperature constraint of the solid bottom surface. As training progresses ( As the weight of the fluid-side coupling loss term gradually increases, the network gradually learns to satisfy the temperature conditions on the fluid side near the bottom surface. When training ends (…), The residuals at the bottom boundary are restored to complete physical boundary conditions by heating. .

[0104] By integrating physical parameter continuation and auxiliary boundary loss fading, the course learning strategy comprises three parallel transition processes: physical parameter continuation (Prändt number and thermal conductivity ratio transitioning from easily trained values ​​to target values), inlet auxiliary temperature constraint fading, and bottom surface fluid-side coupling gradual activation. All three share the same continuation factor. α(t) enables unified scheduling.

[0105] The technical solution adopted in this embodiment gradually activates the network through inlet auxiliary temperature constraint decay and bottom surface fluid-side coupling, eliminating the need for overly complex boundary constraints in the early training stages and reducing early learning difficulty. As training progresses, complex boundary constraints are gradually introduced, allowing the network to gradually adapt to complete physical boundary conditions based on its already relatively accurate predictions. The auxiliary term weights eventually decay to zero, without changing the physical correctness of the final boundary conditions.

[0106] The following is combined with Figure 4 The overall technical solution of the embodiments of this application will be described. Figure 4 This is an embodiment of a physical information neural network provided in this application, showing its overall architecture and data flow diagram. For example... Figure 4 As shown, the entire architecture starts with the original input and goes through geometric feature embedding (i.e., geometric ansatz embedding), feature concatenation, Fourier feature embedding, PirateNet backbone network, linear output scaling and other processing steps in sequence. Finally, the network training is completed through a composite loss function and optimizer, forming a complete closed loop of "input-feature extraction-network mapping-physical constraints-parameter update".

[0107] Specifically, the original input is a 7-dimensional vector, including the spatial coordinates of the sampling points. and four geometric parameters (jet inlet width) Jet outlet width Microchannel width Microchannel height The original input, after normalization, enters two parallel paths: one is directly used for subsequent concatenation, and the other enters the geometric feature embedding module to generate 8-dimensional geometric embedding features. These two paths are then concatenated to form a 15-dimensional enhanced input vector. After being mapped by a Fourier feature embedding layer (256 embedding dimensions), the data is input into the PirateNet backbone network (4 residual blocks × 256 hidden units, supplemented by random weight decomposition). The network ends with a linear output scaling layer, outputting 6-dimensional physics predictions, including a 3D velocity field. Pressure field ( ), fluid temperature field ( ) and solid temperature field ( ).

[0108] The network outputs predicted physical fields, which are then fed into two computational branches: the PDE residual loss branch (containing continuity, momentum, fluid energy, and solid thermal conductivity residuals) and the boundary and interface loss branch (containing inlet, outlet, heated bottom surface, adiabatic top surface, symmetry plane, and fluid-solid interface constraint residuals). All loss components are weighted and summed after dynamic gradient normalization to form a composite loss function. With the goal of minimization, gradients are calculated via backpropagation, and network parameters are updated by the SOAP optimizer (a schedule-free variant). After training, for any combination of target geometric parameters, the prediction result can be obtained by constructing the augmented input vector and performing a single forward propagation, following the same process.

[0109] Thus, through the synergistic cooperation of geometric feature embedding, Fourier feature embedding, and the PirateNet backbone, the physical information neural network can stably learn the physical field mapping relationship across geometric parameters within a continuous geometric design space. Geometric feature embedding solves the problem of distinguishing between the boundary and internal regions under varying geometric parameters. The composite constraint of PDE residuals and boundary condition residuals allows the network to learn solutions that satisfy physical laws without labeled data. The combination of dynamic gradient normalization and the SOAP optimizer ensures stable convergence of multi-physics coupled training. These modules work together to achieve end-to-end direct mapping from geometric parameters and spatial coordinates to a complete three-dimensional thermal flow field, providing reliable technical support for the efficient simulation and design optimization of EMMC heat sinks.

[0110] See Figure 5 , Figure 5 This is a schematic diagram illustrating a training process and course learning provided in an embodiment of this application. For example... Figure 5 As shown, the entire training cycle consists of four main stages: Step 1 involves online GPU sampling. The sampling program decomposes the fluid and solid domains into multiple parameterized bounding boxes based on the current geometric parameters. Internal points are sampled within each bounding box, and boundary points are sampled on the parameterized boundary surfaces. The sampling point density is increased at the fluid-solid walls, microchannel gaps, and inlet and outlet boundaries. Sampling is entirely performed on the GPU, avoiding CPU-GPU data transfer overhead.

[0111] Step ② involves forward propagation and automatic differentiation in the forward mode. After the spatial coordinates and geometric parameters of the sampling points are concatenated and normalized, they are sequentially processed through geometric feature embedding, Fourier feature embedding, and the PirateNet backbone network to obtain the predicted physical field values. Subsequently, the automatic differentiation in the forward mode is used to calculate the first and second derivatives of the network output with respect to the spatial coordinates, which are then used for calculating the residuals of the subsequent governing equations. The forward mode is suitable for the low input dimension and high output dimension characteristics of this application, significantly reducing the computational cost of coordinate derivatives compared to the reverse mode.

[0112] Step ③ involves weighted summation of the composite loss and scheduling of course learning. Based on the predicted physics field values ​​and their derivatives, various PDE residuals and boundary condition residuals are calculated, and then weighted summed to form the composite loss function. Course learning is conducted through a continuation factor. Perform scheduling: such as Figure 5 As shown in the illustration, the continuation factor Press according to the number of training steps t The coefficient increases linearly from 0 to 1. This is achieved by adjusting physical parameters (Prändt number, thermal conductivity ratio) on one hand, and controlling the gradual reduction of inlet auxiliary temperature constraints and the gradual activation of bottom surface fluid-side coupling on the other. Simultaneously, dynamic gradient normalization is used to balance the various loss components.

[0113] Step 4 involves updating the SOAP optimizer parameters. The gradient of the composite loss function with respect to the network parameters is calculated via backpropagation. The parameters are then updated using a schedule-free variant of the SOAP optimizer, with the base learning rate... The first 5000 steps are a linear warm-up, and this remains constant during the main training phase. Repeat steps ① to ④ until the preset number of training steps is reached.

[0114] Thus, by combining GPU online sampling, forward-mode automatic differentiation, curriculum learning scheduling, and the SOAP optimizer, a complete and efficient training loop is formed. The curriculum learning strategy guides the network from easy to difficult learning from two dimensions: the continuation of physical parameters and the gradual reduction of boundary conditions. This solves the technical obstacles of PINN training instability and difficulty in convergence in the three-dimensional convection-dominated conjugate heat transfer problem, ensuring the network's prediction accuracy and generalization ability under the target physical conditions.

[0115] To verify the necessity and synergistic effect of the key components of this application, the applicant conducted ablation experiments under the same experimental conditions. The experiments used finite element ultrafine mesh solutions generated by COMSOL Multiphysics 6.3 (approximately [number missing] per calculation example). Using the unit as a reference, a full factorial scan was performed in the 4-parameter design space (each parameter taking 5 values, for a total of...). The prediction accuracy of each variant was evaluated on a group design.

[0116] The ablation experiment setup is as follows: (1) Remove geometric feature embedding: Input the normalized local coordinates directly into the network without smooth saturation monotonic mapping function transformation; (2) Eliminate course learning: The target Prandtl number and target thermal conductivity ratio are used directly throughout the training process; (3) Remove the SOAP optimizer: Replace the matrix preconditioning optimizer with the Adam optimizer; (4) Remove the schedule-free strategy: Replace the schedule-free variant with a regular learning rate decay plan.

[0117] The prediction errors for each ablation variant are shown in the table below:

[0118] Experimental results show that after removing the geometric feature embeddings, the training loss stagnates at approximately [value missing]. The magnitude and speed error increased to This indicates that geometric feature embedding is a prerequisite for the network to effectively distinguish between boundaries and interior regions under varying geometric parameters; removing it prevents the network from learning effective mappings across geometric parameters. After removing the learning process, the temperature error... Rise to This indicates that directly training on physics problems dominated by convection and with strong thermal conductivity contrast leads to a significant degradation in temperature field prediction accuracy. The course learning strategy plays an irreplaceable role in ensuring the network's prediction accuracy under the target physical conditions. After removing the SOAP optimizer, the velocity error is reduced from... Rise to Temperature error is caused by Rise to This indicates that the matrix preconditioning optimizer plays a crucial role in the stable convergence of the rigid multiphysics loss. Removing the schedule-free strategy or the auxiliary loss both resulted in significant instability during training, further demonstrating the synergistic dependency among the key components of this application.

[0119] In summary, the ablation experiments demonstrate that the geometric feature embedding, curriculum learning strategy, matrix preconditioning optimizer, and schedule-free strategy in this application are all indispensable key technical features. These components work together to ensure the stable training and high-precision prediction of the physical information neural network on the three-dimensional convection-dominated conjugate heat transfer problem.

[0120] This application also provides an embedded manifold microchannel radiator heat flow characteristic simulation device based on a parametric physical information neural network, referring to... Figure 6 As shown, Figure 6 This is a schematic diagram of a simulation device for the thermal flux characteristics of an embedded manifold microchannel radiator based on a parametric physical information neural network, provided in an embodiment of this application. The device includes: The acquisition module 610 is used to acquire the geometric parameters and spatial coordinates of the sampling points of the embedded manifold microchannel heat sink to be simulated. The determining module 620 is used to determine the parameterized sub-region to which the sampling point belongs based on the geometric parameters and the spatial coordinates, and to calculate the normalized local coordinates of the sampling point within the parameterized sub-region to which it belongs; The transformation module 630 is used to transform the normalized local coordinates through a smooth saturated monotonic mapping function to generate geometric embedding features, which are used to characterize the relative position of the sampling point with respect to the boundary of the parameterized sub-region. The splicing module 640 is used to splice the geometric embedding features with the normalized geometric parameters and the spatial coordinates to form an enhanced input vector; Prediction module 650 is used to input the enhanced input vector into the physical information neural network to obtain the physical field prediction value of the sampling point, the physical field prediction value including velocity field, pressure field and temperature field; The training module 660 is used to calculate the control equation residuals and boundary condition residuals based on the predicted physical field values, form a composite loss function, and train the physical information neural network based on the composite loss function. The inference module 670 is used to obtain the target geometric parameters and spatial coordinates of the target sampling point of the target embedded manifold microchannel heat sink, and construct them as the target enhancement input vector. The vector is then input into the trained physical information neural network to obtain the thermal flow characteristic prediction result.

[0121] The specific implementation methods of each of the above modules can be found in the description of the corresponding steps in the aforementioned method embodiments, and will not be repeated here.

[0122] This application also provides an electronic device, which is described in reference to... Figure 7 , Figure 7 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Figure 7 As shown, the electronic device 700 includes a memory 710 and a processor 720. The memory 710 and the processor 720 are connected via a bus for communication. The memory 710 stores a computer program that can run on the processor 720 to implement the steps of the embedded manifold microchannel heat sink thermal flow characteristic simulation method based on parameterized physical information neural network described in the embodiments of this application.

[0123] This application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the method for simulating the thermal flow characteristics of an embedded manifold microchannel radiator based on a parameterized physical information neural network as described in this application.

[0124] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the embedded manifold microchannel heat sink thermal flow characteristic simulation method based on a parameterized physical information neural network described in this application.

[0125] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0126] This application describes embodiments of methods and apparatus according to flowchart illustrations and / or block diagrams. It should 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 terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, 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.

[0127] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate 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.

[0128] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal equipment, causing a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal 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.

[0129] Although preferred embodiments of the present application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present application.

[0130] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0131] The above provides a detailed description of the simulation method and device for the thermal flow characteristics of an embedded manifold microchannel heat sink based on a parametric physical information neural network. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A simulation method for the thermal flux characteristics of an embedded manifold microchannel radiator based on a parametric physical information neural network, characterized in that, include: Obtain the geometric parameters and spatial coordinates of the sampling points of the embedded manifold microchannel heat sink to be simulated; Based on the geometric parameters and the spatial coordinates, the parameterized sub-region to which the sampling point belongs is determined, and the normalized local coordinates of the sampling point within the parameterized sub-region are calculated. The normalized local coordinates are transformed by a smooth saturated monotonic mapping function to generate geometric embedding features, which are used to characterize the relative position of the sampling point with respect to the boundary of the parameterized sub-region. The geometric embedding features are concatenated with the normalized geometric parameters and the spatial coordinates to form an enhanced input vector; The enhanced input vector is input into the physical information neural network to obtain the physical field prediction value of the sampling point, which includes the velocity field, pressure field and temperature field. The residuals of the governing equations and boundary conditions are calculated based on the predicted physical field values ​​to form a composite loss function, and the physical information neural network is trained based on the composite loss function. The target geometric parameters and spatial coordinates of the target sampling points of the embedded manifold microchannel heat sink are obtained and constructed as the target enhancement input vector. The vector is then input into the trained physical information neural network to obtain the predicted results of the heat flow characteristics.

2. The method according to claim 1, characterized in that, Based on the geometric parameters and the spatial coordinates, the parameterized sub-region to which the sampling point belongs is determined, and the normalized local coordinates of the sampling point within the parameterized sub-region are calculated, including: Based on the geometric parameters, determine the boundary positions of each parameterized sub-region; Based on the spatial coordinates of the sampling point and the boundary positions of each parameterized sub-region, the parameterized sub-region to which the sampling point belongs is determined; Obtain the minimum boundary values ​​of the parameterized sub-region to which the sampling point belongs in each coordinate direction. and boundary maximum value The normalized local coordinates of the sampling points are calculated using the following formula: , in, For the sampling point at the th Coordinate values ​​in each coordinate direction, For the sampling point at the th Normalized local coordinates in each coordinate direction.

3. The method according to claim 2, characterized in that, The smooth, saturated, monotonic mapping function is the sigmoid function, and the geometric embedding features are calculated as follows: , in, For the sigmoid function, For scale parameters, The geometric embedding feature of the sampling point in the i-th coordinate direction, For the sampling point at the th Normalized local coordinates in each coordinate direction.

4. The method according to claim 1, characterized in that, Based on the predicted physical field values, the residuals of the governing equations and boundary conditions are calculated to form a composite loss function, including: Acquire internal sampling points in the fluid and solid domains of the embedded manifold microchannel heat sink, as well as boundary sampling points on the boundary; Based on the predicted physical field values ​​of the internal sampling points, the residuals of the governing equations are calculated. The residuals of the governing equations include: the residuals of the continuity equation, momentum equation, and fluid energy equation in the fluid domain, and the residuals of the solid thermal conductivity equation in the solid domain. Based on the predicted physical field values ​​of the boundary sampling points, the boundary condition residuals are calculated. The boundary condition residuals include: inlet boundary residual, outlet boundary residual, heated bottom surface boundary residual, adiabatic top surface boundary residual, symmetry surface boundary residual, no-slip condition residual on the fluid-solid interface, temperature continuity condition residual on the fluid-solid interface, and heat flow continuity condition residual on the fluid-solid interface. The weighted summation of the residuals of the governing equations and the residuals of the boundary conditions constitutes the composite loss function.

5. The method according to claim 4, characterized in that, During the training of the physical information neural network based on the aforementioned composite loss function, a course-based learning strategy is employed: Get current training steps According to the current training steps Determine the continuation factor The continuation factor With training steps The increase is from the initial value to the target value; According to the continuation factor The physical parameters in the composite loss function are adjusted so that they gradually transition from easily trained values ​​to target physical values; wherein the physical parameters include Prandtl number in the fluid energy equation and / or thermal conductivity ratio in the fluid-solid interface heat flow continuity condition.

6. The method according to claim 5, characterized in that, The continuation factor Determine using the following formula: , in, This represents the current number of training steps. The preset number of preheating steps; The Prandt number transitions from the easily trainable value to the target physical value according to the following formula: , in, This represents the effective Prandtl number for the current number of training steps. For Prandtl numbers, which are easy-to-train values, For the target Prandtl number; The thermal conductivity ratio transitions from the easily trained value to the target physical value according to the following formula: , in, This is the ratio of effective thermal conductivity at the current number of training steps. The target thermal conductivity ratio.

7. The method according to claim 5, characterized in that, When training the physical information neural network using a course-based learning strategy, the entry boundary residuals in the composite loss function are assembled in the following manner: The entrance boundary residual According to the continuation factor Assemble according to the following formula: , in, For the inlet scalar constraint loss term, For the inlet flux constraint loss term, This is the inlet auxiliary temperature constraint loss term; The heating bottom surface boundary residual According to the continuation factor Assemble according to the following formula: , in, This is the temperature constraint loss term for the solid side of the heating bottom surface. This is the fluid-side coupling loss term for the heated bottom surface.

8. The method according to claim 1, characterized in that, Sampling points are generated in real time on the graphics processor, including: The fluid domain and solid domain of the embedded manifold microchannel heat sink are decomposed into multiple parameterized bounding boxes, and the boundary positions of the parameterized bounding boxes are determined by the geometric parameters. Sample internal points within each of the parameterized bounding boxes; Sample boundary points on the parameterized boundary surface; Sampling points with a higher density than those in the internal area are arranged at the fluid-solid wall, microchannel gaps, and inlet and outlet boundaries.

9. The method according to claim 1, characterized in that, During the training of the physical information neural network based on the composite loss function, a matrix preconditioning optimizer is used to update the parameters of the physical information neural network, and a dynamic gradient normalization strategy is used to adjust the weights of each loss component in the composite loss function.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the simulation method for the thermal flow characteristics of an embedded manifold microchannel heat sink based on a parameterized physical information neural network as described in any one of claims 1-0.

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