Rapid heat transfer simulation method and device based on neural network

Abstract

The invention discloses a rapid heat transfer simulation method and device based on a neural network, and relates to the technical field of physical simulation. The method comprises the steps that a hybrid neural network model is trained, the model learns operator mapping from an input function to a temperature or heat flow field, and meanwhile physical constraints such as a heat conduction partial differential equation are coded into a loss function; for a new simulation task, single forward inference is carried out by using the operator mapping, and an initial prediction result is rapidly generated; then, according to physical constraints of coding, calculating a physical residual error of initial prediction, and when the residual error exceeds a preset threshold value, executing a small amount of optimization iteration by taking the prediction as an initial value to carry out rapid local correction; the problems that a traditional numerical method is long in calculation time and an existing neural network method is insufficient in physical fidelity are solved, and high efficiency and high precision of heat transfer simulation are achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of physical simulation, in particular to a fast heat transfer simulation method and device based on a neural network. BACKGROUND

[0002] Heat transfer simulation is an indispensable core technology in many key engineering and scientific fields such as aerospace, energy power, electronic device heat dissipation, advanced manufacturing (such as welding, additive manufacturing), etc. It predicts the temperature field, heat flux density distribution and their evolution law with time under the action of complex boundary conditions and heat sources by numerically solving heat conduction partial differential equations (PDEs), providing key theoretical guidance for product design, performance optimization and process control.

[0003] The numerical simulation of heat transfer problems mainly relies on classical mesh-based numerical methods such as finite element method (FEM), finite difference method (FDM) or finite volume method (FVM). These methods can obtain high accuracy of physical solution by discretizing the solution domain into a large number of mesh elements and transforming the control equations into large algebraic equation systems for solving. However, these traditional methods have inherent limitations: first, the computational cost is extremely high. For complex three-dimensional geometry, multi-scale structure or long-time transient problems, generating high-quality meshes is itself a challenge, and the solving process requires a large amount of computational resources and time, making it difficult to meet the needs of rapid iteration and real-time simulation in engineering design. Second, for problems involving moving heat sources, phase change or fluid-structure coupling, complex adaptive mesh reconstruction techniques are required, which further increases the complexity and computational overhead of the algorithm. Finally, when conducting parameterized research or optimization design, whenever the input parameters such as boundary conditions, material properties or heat source functions change, the traditional method usually needs to start from scratch and perform a complete and time-consuming simulation calculation, which is inefficient.

[0004] In recent years, artificial intelligence technology represented by deep learning has provided a new solution to accelerating physical simulation. One approach is to build a purely data-driven surrogate model, which learns the mapping relationship between input parameters and output physical fields by training neural networks on a large number of data sets generated by traditional simulation software. Once the model is trained, its online inference speed is extremely fast. However, its main defect lies in that the model only learns the statistical correlation in the data, and its prediction results may violate basic physical laws such as energy conservation, leading to insufficient physical authenticity, and its generalization ability is heavily dependent on the quality and coverage of the training data, making it difficult to guarantee the prediction accuracy for conditions outside the training set.

[0005] Another emerging method is the Physics-Informed Neural Networks (PINNs). It directly imposes the constraints of physical laws during the training process of neural networks by taking the residual of partial differential equations as a loss function, thereby reducing the dependence on massive labeled data and ensuring the physical consistency of the solution. However, the standard PINN method also has challenges. It is usually designed for solving a specific instance (i.e., a set of fixed boundary conditions, initial conditions, and source terms), and when these conditions as function inputs change, the network needs to be completely retrained, and the optimization process itself can be very time-consuming, making it difficult to serve as a general solver that can quickly respond to arbitrary input functions.

[0006] In summary, the existing technology still faces significant technical challenges in achieving fast, accurate, and universal simulation of heat transfer problems. Traditional numerical methods are too time-consuming, while existing deep learning methods either lack physical fidelity or cannot efficiently handle changing input conditions, making it difficult to meet the comprehensive requirements of speed, accuracy, and flexibility in engineering applications. SUMMARY

[0007] The present application provides a neural network-based fast heat transfer simulation method and device, which solves the problems of time-consuming calculation of traditional numerical methods and insufficient physical fidelity of pure data-driven models in the prior art.

[0008] In a first aspect, the embodiments of the present application provide a neural network-based fast heat transfer simulation method, which comprises: training a hybrid neural network model based on historical simulation data or physical equation constraints, the hybrid neural network model being configured to learn an operator mapping from input functions to output temperature fields or heat flow fields, and encoding heat conduction partial differential equations, initial conditions, boundary conditions, and / or multi-layer material interface continuity conditions as loss function constraints; receiving new simulation task parameters, and performing a single forward inference using the learned operator mapping in the hybrid neural network model to generate an initial temperature field or heat flow field prediction result; calculating the physical residual of the prediction result according to the physical information constraints encoded in the hybrid neural network model, and determining whether the physical residual exceeds a preset error threshold; if it does, performing optimization iterations of a preset number of steps with the prediction result as the initial value to minimize the physical residual, thereby quickly locally correcting the prediction result.

[0009] Preferably, the step of training a hybrid neural network model based on historical simulation data or physical equation constraints comprises: a norm error between the predicted output of the operator mapping and the true solution as a data-driven loss term, and a physical residual calculated according to the physical information constraint as a physics-driven loss term; a hybrid loss function is constructed by weighted sum of the data-driven loss term and the physics-driven loss term; and, an adaptive weight adjustment strategy is adopted to dynamically balance the contribution of the data-driven loss term and the physics-driven loss term in the training process.

[0010] Preferably, the step of training a hybrid neural network model adopts a multi-domain physical information neural network architecture, assigns an independent sub neural network for each material domain, and additionally includes an interface loss term in the hybrid loss function, the interface loss term is used to constrain the temperature values predicted by the respective sub neural networks to satisfy continuity and heat flux conservation on the interface of adjacent material domains.

[0011] Preferably, the step of training a hybrid neural network model further comprises: a multi-grid training strategy is adopted to accelerate the learning convergence of the operator mapping, the multi-grid training strategy includes firstly pre-training the hybrid neural network model on a low-resolution coarse grid, and then migrating the model parameters obtained by pre-training to a high-resolution fine grid to continue training as initial values.

[0012] Preferably, the step of training a hybrid neural network model further comprises learning an operator mapping from a temperature field at a current time to a time derivative of the temperature field at the current time; the step of performing a single forward inference using the learned operator mapping in the hybrid neural network model comprises: inputting the temperature field at the current time into the hybrid neural network model to obtain the time derivative thereof; and, a numerical time integration format is adopted to iteratively advance using the time derivative, thereby realizing stable evolution in a long time domain.

[0013] Preferably, when learning the operator mapping from the temperature field at a current time to the time derivative of the temperature field at the current time, a dual-output structure is adopted to simultaneously output a reconstructed field of the temperature field at the current time and a predicted time derivative; the hybrid loss function further includes a consistency loss term, the consistency loss term is used to minimize the difference between the predicted time derivative and a time derivative obtained by automatic differentiation on the reconstructed field.

[0014] Preferably, the step of learning the operator mapping from the temperature field at a current time to the time derivative of the temperature field at the current time adopts a pseudo-differential neural operator architecture, the pseudo-differential neural operator architecture parameterizes the sign of the pseudo-differential operator through a time-varying sign network, the sign network takes frequency and time as input and outputs a sign that depends on both space and frequency, thereby learning the evolution operator in continuous time.

[0015] Preferably, the method further comprises: obtaining a time or space function by parameterizing the position and trajectory of the moving heat source, and incorporating the time or space function into a source term of the heat conduction partial differential equation to handle the time-varying source term in the loss function constraint and the physical residual calculation.

[0016] Preferably, the step of learning the operator mapping from the input function to the output temperature field or heat flow field adopts a lifting product Fourier neural operator architecture, and the implementation of the lifting product Fourier neural operator architecture comprises: processing a boundary function defined on a low-dimensional boundary by using two parallel low-dimensional Fourier neural operators to generate two independent low-dimensional feature representations; combining the two independent low-dimensional feature representations into a feature field on a high-dimensional domain through a lifting product layer, wherein the lifting product layer performs an outer product operation on each feature channel; and projecting the high-dimensional feature field to the solution space to obtain the final global solution.

[0017] In a second aspect, an embodiment of the present application provides a fast heat transfer simulation device based on a neural network, the device comprising: a model training unit configured to train a hybrid neural network model based on historical simulation data or physical equation constraints, the hybrid neural network model being configured to learn an operator mapping from an input function to an output temperature field or heat flow field, and to encode a heat conduction partial differential equation, an initial condition, a boundary condition, and / or a multi-layer material interface continuity condition into a loss function constraint; an online inference unit configured to receive new simulation task parameters, and to perform a single forward inference by using the learned operator mapping in the hybrid neural network model to generate an initial temperature field or heat flow field prediction result; an adaptive correction unit configured to calculate a physical residual of the prediction result according to the physical information constraint encoded in the hybrid neural network model, to determine whether the physical residual exceeds a preset error threshold, and to perform an optimization iteration of a preset number of steps to minimize the physical residual when the physical residual exceeds the error threshold, so as to quickly locally correct the prediction result.

[0018] In a third aspect, an embodiment of the present application provides an electronic device, the electronic device comprising: at least one processor; and a memory connected to the at least one processor in communication; wherein The memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the method according to the first aspect of the present application.

[0019] The fourth aspect of the embodiment of the present application provides a computer readable storage medium, which stores a computer program, and the program is executed by a processor to realize the method according to the first aspect of the embodiment of the present application.

[0020] Beneficial effects: The present application provides a neural network-based fast heat transfer simulation method, aiming to solve the contradiction between time-consuming calculation of traditional numerical methods and insufficient physical fidelity of pure data-driven models in the prior art. By training a hybrid neural network model capable of learning the operator mapping from the input function to the solution, the present method can generate an initial prediction result through only one forward inference when processing a new simulation task, realizing near-real-time simulation speed. This greatly surpasses the traditional finite element method which needs to be completely recalculated for each new parameter, significantly improving the iteration efficiency of engineering design. An online adaptive correction mechanism is introduced. It uses the physical information constraints encoded in the model to evaluate the physical residual of the initial prediction, and only when the residual exceeds the preset threshold, a small number of optimization iterations are triggered for local correction. This fast prediction and on-demand correction strategy ensures that the final solution strictly follows the physical laws such as heat conduction partial differential equations, overcoming the defect that pure data-driven models may produce physically unreasonable results, and ensuring the high fidelity of the simulation. The present application combines the efficient inference capability of neural operator with the strong constraint capability of physical information neural network, realizing a magnitude improvement in simulation speed without sacrificing physical accuracy, providing a solution for complex heat transfer problems with speed, accuracy and versatility. BRIEF DESCRIPTION OF DRAWINGS

[0021] Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The accompanying drawings are included to provide a description of the preferred embodiments, and are not intended to limit the scope of the present application. Moreover, the same reference numerals are used throughout the several views to designate the same or similar parts. In the drawings: Figure 1 An electronic device structure schematic diagram of a hardware running environment related to the embodiment of the present application; Figure 2 A step flowchart of a neural network-based fast heat transfer simulation method provided by the embodiment of the present application; Figure 3 A functional unit schematic diagram of a neural network-based fast heat transfer simulation device provided by the embodiment of the present application. DETAILED DESCRIPTION

[0022] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the present application will be briefly introduced below in combination with the drawings and the description of the embodiments or the prior art. Obviously, the following description of the drawings is only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained from these drawings without creative labor. It should be noted that the description of these embodiments is used to help understand the present application, but does not constitute a limitation on the present application. The technical solutions of the present application will be further described below in combination with the drawings.

[0023] Referring to Figure 1 , the electronic device structure schematic diagram of the hardware running environment involved in the embodiments of the present application.

[0024] As Figure 1 shown, the electronic device can include a processor 1001, such as a central processing unit (CPU), a communication bus 1002, a user interface 1003, a network interface 1004, and a memory 1005. The communication bus 1002 is used to realize the connection and communication between these components. The user interface 1003 can include a display, an input unit such as a keyboard, and an optional user interface 1003 can also include a standard wired interface, a wireless interface. The network interface 1004 can optionally include a standard wired interface, a wireless interface (such as a wireless fidelity (WIreless-FIdelity, WI-FI) interface). The memory 1005 can be a high-speed random access memory (RAM) memory, or a stable non-volatile memory (Non-Volatile Memory, NVM), such as a magnetic disk memory. The memory 1005 can also be an independent storage device from the aforementioned processor 1001.

[0025] Those skilled in the art can understand that Figure 1 the structure shown in the above description does not constitute a limitation on the electronic device, and can include more or fewer components than the drawings, or combine certain components, or different component arrangements.

[0026] As Figure 1 shown, the memory 1005 as a storage medium can include an operating device, a data storage module, a network communication module, a user interface module, and an electronic program.

[0027] In Figure 1The network interface 1004 is mainly used for data communication with a network server; the user interface 1003 is mainly used for data interaction with a user; the processor 1001 and the memory 1005 in the electronic device of the present application can be arranged in the electronic device, and the electronic device calls the neural network-based fast heat transfer simulation device stored in the memory 1005 through the processor 1001, and executes the neural network-based fast heat transfer simulation method provided in the embodiment of the present application.

[0028] With reference to Figure 2 The embodiment provides a neural network-based fast heat transfer simulation method, which aims to realize near-real-time and high-fidelity simulation of complex heat transfer problems, especially scenes involving complex geometry, multi-layer materials, time-varying boundaries and moving heat sources, by combining the efficient inference capability of neural operators with the strong constraint capability of physical information neural networks. The core of the method is to build a hybrid workflow of "offline training-online inference-online adaptive correction", which greatly improves the simulation speed while ensuring engineering accuracy. The specific process of the method described in the embodiment includes the following steps S101 to S103: S101: Based on historical simulation data or physical equation constraints, a hybrid neural network model is trained, and the hybrid neural network model is configured to learn the operator mapping from the input function to the output temperature field or heat flow field, and encode the heat conduction partial differential equation, initial condition, boundary condition and / or multi-layer material interface continuity condition into a loss function constraint; This step is the offline stage of the present application, and the core goal is to build a deep learning model that can accurately and quickly predict the heat transfer process. The hybrid neural network model is a composite architecture that not only learns the rules from data, but also encodes physical laws as internal constraints to ensure the physical consistency of the prediction results.

[0029] Specifically, the hybrid neural network model is configured to have two core functions: Learning the operator mapping from the input function to the output temperature field or heat flow field: This function aims to learn a general mapping relationship The mapping can directly map a class of functions (such as initial condition functions, boundary condition functions or heat source parameter functions) to the corresponding solution functions (i.e. the temperature field or heat flow field in the entire space-time domain). The module implementing this function usually adopts a neural operator architecture, such as Fourier Neural Operator (FNO), DeepONet, etc. The advantage of the neural operator is that once the training is completed, for a new input function, only one forward propagation is required to obtain the entire solution field, which is extremely fast and has the ability to generalize between different grid resolutions.

[0030] Encoding the heat conduction partial differential equation (PDE), initial conditions, boundary conditions, and / or multi-layer material interface continuity conditions into loss function constraints: This function is realized through a physics-informed neural network (PINN) that directly embeds the physical laws governing the heat transfer process (i.e., the heat conduction PDE) and the definite conditions into the loss function of the neural network. By minimizing these physical residuals during training, the network is forced to output results that satisfy the physical conservation laws, thereby avoiding the prediction results that violate the physical laws that may be produced by purely data-driven models.

[0031] In one preferred embodiment of the present embodiment, further refinement and optimization of step S101 can include the following sub-steps S1011 to S1016: S1011: Construct a hybrid loss function and train with adaptive weights.

[0032] In order to realize the above two core functions at the same time, this step constructs a hybrid loss function (Hybrid Loss Function), which is the optimization objective of the entire model training.

[0033] First, define the hybrid neural network model as a unified architecture that contains both neural operator layers (for learning operator mapping) and can calculate physical residuals through automatic differentiation (AD). Automatic differentiation is a technology that can accurately calculate derivatives and is the basis for implementing PINN.

[0034] Then, construct a hybrid loss function which is usually composed of two parts: S10111: Define the data-driven loss term .

[0035] This loss term is used to measure the gap between the model prediction and the true solution. The true solution can come from a small amount of high-fidelity traditional numerical simulation (such as finite element method FEM) sample data or existing experimental data.

[0036] The norm error between the predicted output of the operator mapping and the true solution is taken as the data-driven loss term. Commonly used norm errors include L2 norm error, whose mathematical expression is:

[0037] where is the number of training data samples, represents the spatial and temporal coordinates corresponding to the i-th training sample, is the predicted value of the model at the spatiotemporal point is the corresponding true value.

[0038] S10112: Define the physics-driven loss term .

[0039] This loss term is used to quantify the degree of violation of the physical law by the model prediction results.

[0040] The physics residual calculated according to the physical information constraint is taken as the physics-driven loss term. For a typical nonlinear transient heat conduction problem, its control equation can be expressed as:

[0041] where, is the temperature field, is the density, is the specific heat capacity, is the thermal conductivity, is the heat source term, is the gradient operator.

[0042] Using automatic differentiation technology, the derivatives of the model prediction with respect to the time and spatial coordinates can be accurately calculated, thereby obtaining the physics residual . The physics-driven loss term is the mean square error of the residual calculated at the randomly sampled collocation points in the solution domain and the time domain:

[0043] where, is the total number of collocation points used to calculate the physics residual. In addition, the initial condition (IC) residual and the boundary condition (BC) residual should also be included. For example, for the Dirichlet boundary condition , its loss term is

[0044] where is the sampling point on the boundary, is the total number of boundary sampling points, is the target value of the pre-set Dirichlet condition at the boundary point.

[0045] ​​S10113: Construct the total loss function and perform adaptive weight adjustment.

[0046] By weighted sum of the data-driven loss term and the physics-driven loss term, the final hybrid loss function is constructed:

[0047] where, and are weight coefficients. In the training process, there may be a huge difference in the gradient size of different loss terms, leading to unstable training or convergence to local optimum. Therefore, preferably, an adaptive weight adjustment strategy is used to dynamically balance the contributions of the data-driven loss term and the physics-driven loss term during training. For example, methods such as GradNorm or gradient-based uncertainty weighting can be used to dynamically adjust and so that the learning process of different tasks (data fitting and physical constraint satisfaction) is kept in synchronization, thereby improving the stability of training and the accuracy of the final model.

[0048] S1012: For multi-layer material problems, a multi-domain physical information neural network architecture is used.

[0049] In many engineering applications, the heat transfer body is composed of multiple materials with different thermal properties. In order to accurately simulate the heat transfer behavior at the interface between different materials, the embodiment preferably uses a multi-domain physical information neural network (Multi-domain PINN, MD-PINN) architecture.

[0050] S10121: Construct sub-networks.

[0051] Divide the entire computational domain into multiple sub-domains, each corresponding to a material. Assign an independent sub-network to each material domain. For example, for a system composed of three materials, three independent neural networks are constructed, respectively responsible for predicting the temperature field in each material domain.

[0052] S10122: Add interface loss term.

[0053] At the interface between different materials, the temperature and heat flux must satisfy the continuity condition, i.e.: Temperature continuity:

[0054] Heat flux conservation:

[0055] where, is the material and material The interface It refers to the direction of the interface's normal vector. and These are the thermal conductivity of the two materials, respectively.

[0056] To enforce these physical constraints in the model, an interface loss term is additionally included in the hybrid loss function. This loss item is in the materials and materials interface Upsampling Calculated on a set of points, its form is:

[0057] in, This represents the total number of interface sampling points. Add this interface loss term to the total loss function:

[0058] in, These are the weighting coefficients used to adjust the contribution of the interface loss term. By minimizing the total loss function that includes the interface loss, it can be ensured that the trained model can accurately capture the complex physical phenomenon of heat crossing the interfaces of multiple material layers.

[0059] S1013: To accelerate training, a multi-grid training strategy is adopted.

[0060] Training deep neural networks, especially large models like FNO, is typically very time-consuming. To significantly reduce training time, this embodiment preferably employs a multi-grid training strategy, particularly the ideas proposed in Multi-grid Fourier Neural Operator (MgFNO).

[0061] The core idea of ​​this strategy combines the frequency principle (F-Principle, which states that networks tend to learn low-frequency information first and then high-frequency information) of deep neural networks with the advantages of traditional multigrid methods in handling error components of different frequencies.

[0062] S10131: Construct a multi-level mesh.

[0063] First, define a series of grids from coarse to fine for the computational domain. For example, a three-layer grid system may include a coarse grid (e.g., 64×64), a medium grid (e.g., 128×128), and a fine grid (e.g., 256×256).

[0064] S10132: Implement the V-cycle training strategy.

[0065] A "coarse-to-fine" transfer learning strategy is adopted, which is similar to the V-cycle in the multigrid method: Coarse grid pre-training: The hybrid neural network model (especially the FNO module therein) is first pre-trained on the coarsest grid with the lowest resolution. Since the grid resolution is low, the computational cost of each iteration is also low, and the model can quickly learn the low-frequency, global features of the solution.

[0066] Transfer to fine grid: The model parameters pre-trained on the coarse grid are transferred as initial values to continue training on a finer grid with higher resolution. Since the model already has good initial parameters (has grasped the macro structure of the problem), the training on the fine grid can converge faster and focus on learning higher-frequency detail information.

[0067] Repeat the process: This process can be repeated in a V-cycle, i.e., from the coarsest grid to the finest grid layer by layer.

[0068] Since FNO itself is resolution-invariant, there is no need for complex interpolation (Prolongation) or restriction (Restriction) operators when transferring model parameters between grids of different resolutions, which greatly simplifies the implementation of the multigrid strategy and reduces the errors that may be introduced. In this way, the learning convergence process of the operator mapping can be significantly accelerated, and the total training time can be greatly shortened.

[0069] S1014: For transient problems, a strategy combining time derivative learning and numerical integration is used to achieve long-time stable evolution.

[0070] For transient heat transfer problems, traditional autoregressive (Autoregressive) methods (i.e., predicting future states step by step) are prone to error accumulation and difficult to achieve stable prediction in long time domain. To overcome this bottleneck, the embodiment preferably adopts a strategy combining time derivative learning and classical numerical time integration, which is derived from the Physics-Informed Time-Integrated DeepONet (PITI-DeepONet).

[0071] S10141: Learning the time derivative operator.

[0072] In the training step, the learning goal of the model is changed from directly predicting the temperature field at the next time step to learning an operator mapping from the temperature field at the current time step to the time derivative of the temperature field at the current time step :​

[0073] To achieve this, preferably, a dual-output structure is adopted. The model receives the current state as input, and outputs two results simultaneously: the reconstructed field of the previous state .

[0074] the predicted time derivative .

[0075] Meanwhile, an additional consistency loss term is included in the hybrid loss function . This loss term is used to minimize the difference between the time derivative predicted directly by the model and the time derivative obtained by automatic differentiation on the reconstructed field : this loss term is used to minimize the L2 norm squared difference between the time derivative predicted directly by the model and the time derivative obtained by automatic differentiation on the reconstructed field :

[0076] This forces the time evolution rule learned by the model to be mathematically self-consistent, greatly enhancing the stability and physical consistency of the model.

[0077] S10142: Use pseudo-differential neural operator for continuous-time evolution learning.

[0078] As a more advanced implementation, the step of learning the operator mapping of the time derivative can use a pseudo-differential neural operator (PDNO) architecture. PDNO is an extension of FNO, and its inspiration comes from pseudo-differential operators (PDO).

[0079] This architecture parameterizes the symbol of the pseudo-differential operator through a time-dependent symbol network. This symbol network takes the frequency and time as input, and outputs a symbol that depends on both spatial and frequency : By learning this time-varying symbol, the model can directly learn the evolution operator in continuous time instead of discrete time step mapping. This allows the model to adapt to arbitrary time step size when reasoning and has better long-term stability.

[0080] S1015: Handle moving heat source problems. For welding, additive manufacturing, and other application scenarios, moving heat sources are key physical processes. The method of the embodiment can effectively handle such problems.

[0081] Specifically, the position and trajectory of the moving heat source are parameterized as a function of time or space. For example, the center position of a two-dimensional Gaussian heat source can be represented as The heat source term becomes:

[0082] where, is the maximum power or energy density of the heat source, is the effective radius representing the influence range of the heat source.

[0083] This explicit time-dependent function is incorporated into the source term of the heat conduction partial differential equation. During training, this time-varying source term is used for the calculation of the physical residual, that is:

[0084] By minimizing the physical loss containing this time-varying source term, the model can learn the complex transient temperature field evolution law driven by the moving heat source.

[0085] S1016: For boundary-driven problems, use the lifting product Fourier neural operator architecture.

[0086] For heat transfer problems driven by complex, time-varying boundary conditions, for example, controlling the internal temperature distribution through boundary cooling or heating, the embodiment preferably uses the lifting product Fourier neural operator (LP-FNO) architecture. This architecture is specifically designed to learn the mapping from low-dimensional boundary functions to high-dimensional global solutions.

[0087] S10161: Process boundary functions.

[0088] The implementation of the architecture includes: first, use two parallel Fourier neural operators operating in low-dimensional space (for example, for a two-dimensional problem, use one-dimensional FNO) to process the boundary function defined on the low-dimensional boundary (for example, one-dimensional line boundary) to generate two independent low-dimensional feature representations and .

[0089] S10162: Perform lifting product operation.

[0090] Next, the two independent low-dimensional feature representations are combined into a feature field on a high-dimensional domain (e.g., a two-dimensional planar domain) by a novel lifting product layer For lifting from one dimension to two dimensions, the operation performs an outer product operation on each feature channel:

[0091] This operation effectively "lifts" and extends the information on the one-dimensional boundary to the entire two-dimensional domain.

[0092] S10163: Project to solution space.

[0093] Finally, the high-dimensional feature field is projected to the solution space by a point-wise linear projection layer to obtain the final global solution .

[0094] This architecture avoids the huge computational cost of regenerating meshes or point clouds due to boundary changes, and is particularly suitable for geometric optimization and inverse problem design.

[0095] S102: Receive new simulation task parameters and perform single forward inference using the learned operator mapping in the hybrid neural network model to generate an initial temperature field or heat flow field prediction result.

[0096] This step is the first part of the online application stage of the present application, and its core is to use the offline trained model for fast prediction.

[0097] S1021: Input new task parameters.

[0098] A new simulation task is received, and its parameters can be a new initial condition function, a boundary condition function, a material property parameter, or a trajectory function of a moving heat source.

[0099] S1022: Perform single forward inference.

[0100] The new task parameters are input into the trained hybrid neural network model. Since the core of the model is a neural operator that directly learns the mapping from the input function to the solution function, only one forward pass of the network is required to instantly (near real-time) generate an initial temperature field or heat flow field prediction result for the entire spatiotemporal domain . This process does not involve any iterative solution and is extremely fast.

[0101] S1023: Time evolution (for transient problem) combined with numerical integration.

[0102] If the model is trained according to the strategy of step S1014 (i.e. learning the time derivative), the inference process here is a step-by-step evolution process: Starting from the initial condition .

[0103] At the th time step, the current temperature field is input into the model to obtain its time derivative .

[0104] A classic numerical time integration scheme, such as the Fourth-order Runge-Kutta (RK4), is used to calculate the temperature field at the next time using . Here, is the temperature field at the th time step, and is the temperature field at the th time step. The calculation steps of the RK4 method are as follows:

[0105]

[0106]

[0107]

[0108] Here, is the trained time derivative operator, is the time step size. are the four intermediate slopes (or stage derivatives) in the Runge-Kutta method.

[0109] This process is repeated until the desired total simulation time is reached.

[0110] Since each step only involves a few network forward inferences and simple algebraic operations, the entire evolution process is still very fast. At the same time, thanks to the stability and accuracy guarantee of the classic numerical integration scheme, this method can achieve stable and accurate evolution in a long time domain, effectively suppressing error accumulation.

[0111] S103: Calculate the physical residual of the prediction result according to the physical information constraint encoded in the mixed neural network model, and determine whether the physical residual exceeds a preset error threshold; if it does, perform optimization iteration of a preset number of steps with the prediction result as the initial value to minimize the physical residual, thereby quickly locally correcting the prediction result.

[0112] This step is the second part of the online application stage of the present invention, and is also a key link to ensure the physical fidelity of the final result. It constitutes an online, lightweight adaptive correction cycle.

[0113] S1031: Calculate the physical residual.

[0114] Substitute the initial prediction result generated in step S102 (for transient problems, it can be the prediction result at each time step) into the heat conduction partial differential equation, and calculate its physical residual using automatic differentiation . This process is equivalent to an online "check" to see if the prediction result satisfies the physical law.

[0115] S1032: Determine if correction is needed.

[0116] Compare the norm (e.g., maximum value or root mean square value) of the calculated physical residual with a pre-set error threshold . This threshold can be set according to the specific engineering accuracy requirements.

[0117]

[0118] where, is the pre-set upper limit of acceptable physical residual according to the specific engineering accuracy requirements.

[0119] If the residual is less than the threshold, it means that the physical consistency of the current prediction result is good enough to be accepted directly and output.

[0120] S1033: Perform a quick local correction.

[0121] If the physical residual exceeds the pre-set error threshold, it means that the initial prediction may deviate from the true physical behavior in some local regions. At this time, a quick local correction program is triggered: Take the prediction result as the initial value: take as the starting point of optimization iteration.

[0122] Perform a pre-set number of optimization iterations: minimize the physical residual as the goal, perform a very limited number of gradient descent optimization (e.g., 5-10 steps). This process is essentially a small, local PINN training, but since it starts from an initial value that is already very close to the solution and only a small number of iterations are performed, the computational cost is extremely low.

[0123] Output the corrected result: after a small number of iteration optimization, the corrected prediction result The result is that the local physical consistency is significantly improved while the overall shape of the initial prediction is maintained.

[0124] Through the online adaptive correction cycle, the method of the present application can provide a dynamic accuracy guarantee mechanism while ensuring near real-time simulation speed, ensuring that the final output simulation result is not only fast, but also reliable, accurate, and strictly in accordance with the physical law.

[0125] The embodiment of the present application also provides a fast heat transfer simulation device based on a neural network, referring to Figure 3 , a functional unit diagram of a fast heat transfer simulation device 300 based on a neural network is shown, which can include the following units: The model training unit 301 is configured to train a hybrid neural network model based on historical simulation data or physical equation constraints, and the hybrid neural network model is configured to learn the operator mapping from the input function to the output temperature field or heat flow field, and encode the heat conduction partial differential equation, initial condition, boundary condition and / or multi-layer material interface continuity condition into a loss function constraint. The online inference unit 302 is configured to receive new simulation task parameters and perform single forward inference using the learned operator mapping in the hybrid neural network model to generate an initial temperature field or heat flow field prediction result. The adaptive correction unit 303 is configured to calculate the physical residual of the prediction result according to the physical information constraint encoded in the hybrid neural network model, judge whether the physical residual exceeds the preset error threshold, and when the physical residual exceeds the error threshold, take the prediction result as the initial value, perform optimization iteration of a preset number of steps to minimize the physical residual, and thus quickly correct the prediction result locally.

[0126] Based on the same inventive concept, another embodiment of the present application provides an electronic device comprising a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory communicate with each other through the communication bus, The memory is used to store computer programs. The processor is configured to execute the programs stored on the memory to implement the fast heat transfer simulation method based on a neural network of the present application.

[0127] The communication bus mentioned above can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. The communication bus can be divided into an address bus, a data bus, a control bus, etc. For the convenience of representation, only one thick line is used in the figure, but it does not mean that there is only one bus or only one type of bus. The communication interface is used for communication between the terminal and other devices. The memory can include a Random Access Memory (RAM) and can also include a non-volatile memory, for example, at least one disk memory. Optionally, the memory can also be at least one storage device located away from the aforementioned processor.

[0128] The processor mentioned above can be a general-purpose processor, including a Central Processing Unit (CPU), a Network Processor (NP), etc.; can also be a Digital Signal Processing (DSP), an Application Specific Integrated Circuit (ASIC), a Field-Programmable Gate Array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0129] In addition, to achieve the above-mentioned purpose, the embodiment of the present application also provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to realize the neural network-based fast heat transfer simulation method of the embodiment of the present application.

[0130] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, an apparatus, or a computer program product. Therefore, the embodiments of the present application can adopt a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the embodiments of the present application can adopt the form of a computer program product implemented on one or more computer usable hardware (including but not limited to disk memory, CD-ROM, optical memory, etc.) containing computer usable program code.

[0131] The embodiments of the present application are described with reference to the flowchart illustrations and / or block diagrams of the methods, terminal devices (apparatus) and computer program products according to embodiments of the present application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing terminal devices to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal devices, create means for implementing the functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams.

[0132] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing terminal devices to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions means that implement the function specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams.

[0133] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal devices, such that a series of operational steps are performed on the computer or other programmable terminal devices to create a computer implemented process so that the instructions executed on the computer or other programmable terminal devices provide steps for implementing the functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams. Figure 1 one or more functions specified in the flowchart illustrations and / or block diagrams.

[0134] Finally, it should also be noted that, in the present text, the relational terms such as first and second, and the like, are used solely to distinguish one entity or action from another, without necessarily requiring or implying any actual such relationship or order between or among the entities or actions. The term "and / or" means that either one of the two, or both of the two, can be selected. Moreover, the terms "comprise", "comprises", or any other variant thereof are intended to cover non-exclusive inclusions, so that a process, method, article, or terminal device that comprises a list of elements does not only include those elements, but can also include other elements not expressly listed, or other elements inherent to such process, method, article, or terminal device. Without more limitations, the element defined by the phrase "comprises a" does not exclude the possibility that, in the process, method, article, or terminal device including the element, there can also be another identical element.

[0135] The above merely illustrates the specific embodiments of the present application, but the protection scope of the present application is not limited thereto, and any skilled person in the art can easily think of various equivalent modifications or replacements within the technical range disclosed by the present application, and these modifications or replacements should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A rapid heat transfer simulation method based on neural networks, characterized in that, The method includes: Based on historical simulation data or physical equation constraints, a hybrid neural network model is trained. The hybrid neural network model is configured to learn operator mappings from input functions to output temperature fields or heat flow fields, and encodes heat conduction partial differential equations, initial conditions, boundary conditions, and / or multilayer material interface continuity conditions as loss function constraints. Receive new simulation task parameters and perform a single forward inference using the operator mapping learned in the hybrid neural network model to generate initial temperature field or heat flow field prediction results. The physical residual of the prediction result is calculated based on the physical information constraints encoded in the hybrid neural network model, and it is determined whether the physical residual exceeds a preset error threshold. If it does, the prediction result is used as the initial value, and a preset number of optimization iterations are performed to minimize the physical residual, thereby quickly and locally correcting the prediction result.

2. The method according to claim 1, characterized in that, The steps for training a hybrid neural network model based on historical simulation data or physical equation constraints include: The norm error between the predicted output of the operator mapping and the true solution is used as the data-driven loss term, and the physical residual calculated according to the physical information constraints is used as the physical-driven loss term. A hybrid loss function is constructed by weighted summing of the data-driven loss term and the physics-driven loss term; and, An adaptive weight adjustment strategy is adopted to dynamically balance the contributions of the data-driven loss term and the physics-driven loss term during training.

3. The method according to claim 2, characterized in that, The step of training a hybrid neural network model adopts a multi-domain physical information neural network architecture, assigning an independent sub-neural network to each material domain, and additionally including an interface loss term in the hybrid loss function. The interface loss term is used to constrain the temperature values ​​predicted by each sub-neural network to satisfy continuity and heat flux density conservation at the interface of adjacent material domains.

4. The method according to claim 2, characterized in that, The step of training a hybrid neural network model further includes: using a multi-grid training strategy to accelerate the learning convergence of the operator mapping. The multi-grid training strategy includes first pre-training the hybrid neural network model on a low-resolution coarse grid, and then using the pre-trained model parameters as initial values ​​to transfer them to a high-resolution fine grid for further training.

5. The method according to claim 2, characterized in that, The step of training a hybrid neural network model further includes learning an operator mapping from the temperature field at the current time to the time derivative of the temperature field at the current time; the step of performing a single forward inference using the operator mapping learned in the hybrid neural network model includes: The temperature field at the current moment is input into the hybrid neural network model to obtain its time derivative; and... A numerical time-integration scheme is adopted, and the time derivative is used for iterative advancement to achieve stable evolution in the long time domain.

6. The method according to claim 5, characterized in that, When learning the operator mapping from the temperature field at the current moment to the time derivative of the temperature field at that moment, a dual-output structure is adopted, simultaneously outputting the reconstructed field of the temperature field at the current moment and the predicted time derivative; the hybrid loss function also includes a consistency loss term, which is used to minimize the difference between the predicted time derivative and the time derivative obtained by automatically differentiating the reconstructed field.

7. The method according to claim 5, characterized in that, The step of learning the operator mapping from the temperature field at the current moment to the time derivative of the temperature field at that moment adopts a pseudo-differential neural operator architecture. The pseudo-differential neural operator architecture parameterizes the symbol of the pseudo-differential operator through a time-varying symbol network. The symbol network takes frequency and time as input and outputs a symbol that depends on both space and frequency, thereby learning the evolution operator in continuous time.

8. The method according to claim 1, characterized in that, The method further includes: parameterizing the location and trajectory of the moving heat source to obtain a time or space function, and incorporating the time or space function into the source terms of the heat conduction partial differential equation to handle the time-varying source terms in the loss function constraint and physical residual calculation.

9. The method according to claim 1, characterized in that, The step of learning the operator mapping from the input function to the output temperature field or heat flux field employs a product-fourth-order neural operator architecture, the implementation of which includes: Two parallel low-dimensional Fourier neural operators are used to process the boundary function defined on the low-dimensional boundary to generate two independent low-dimensional feature representations. The two independent low-dimensional feature representations are combined into a feature field over a high-dimensional domain using a lift-off layer, wherein the lift-off layer performs an outer product operation on each feature channel; and Projecting the high-dimensional feature field onto the solution space yields the final global solution.

10. A rapid heat transfer simulation device based on neural networks, characterized in that, The device includes: The model training unit is used to train a hybrid neural network model based on historical simulation data or physical equation constraints. The hybrid neural network model is configured to learn operator mappings from input functions to output temperature fields or heat flow fields, and to encode heat conduction partial differential equations, initial conditions, boundary conditions and / or multilayer material interface continuity conditions as loss function constraints. An online inference unit is used to receive new simulation task parameters and perform a single forward inference using the operator mapping learned in the hybrid neural network model to generate an initial temperature field or heat flow field prediction result. An adaptive correction unit is used to calculate the physical residual of the prediction result based on the physical information constraints encoded in the hybrid neural network model, determine whether the physical residual exceeds a preset error threshold, and when the physical residual exceeds the error threshold, use the prediction result as the initial value to perform a preset number of optimization iterations to minimize the physical residual, thereby performing a fast local correction on the prediction result.

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