A forward-backward co-evolutionary method for constructing diffusion twin networks in beryllium-aluminum alloys

Abstract

This invention belongs to the field of material diffusion behavior modeling and microstructure evolution analysis. It proposes a method for constructing a forward-reverse co-evolution twin network for beryllium-aluminum alloy diffusion. A pair of coupled, co-evolving neural network models are constructed: a forward evolution model and a reverse correction model, forming a twin structure. It achieves bidirectional dynamic updates of diffusion behavior and microstructure state through iterative feedback loops. Based on data preparation, the characteristics of diffusion behavior and microstructure evolution are characterized separately. Two coupled neural network models are constructed: a forward evolution model and a reverse correction model. After constructing and training the forward evolution model and the reverse correction model, their co-evolution mechanism is established. The predicted results obtained through co-evolution simulation are output. The advantages of this invention are: it achieves multiple breakthroughs in principle, method, and engineering application effects in the field of intelligent modeling of material evolution processes.

Description

Technical Field

[0001] This invention belongs to the field of material diffusion behavior modeling and microstructure evolution analysis technology. Specifically, it relates to an intelligent modeling method for the complex bidirectional coupling relationship between element diffusion behavior and microstructure evolution in beryllium aluminum alloys. This method achieves a dynamic, bidirectional, and high-precision joint description of the diffusion process and microstructure evolution by constructing a twin network structure with forward mapping and backward correction functions and introducing a cooperative evolution iteration mechanism. Background Technology

[0002] Beryllium aluminum alloys, due to their low density, high specific stiffness, excellent thermal stability, and good dimensional retention, have found widespread application in engineering fields with extremely stringent requirements for material thermodynamic behavior, such as aerospace inertial navigation platforms, high-precision optical structural components, high-performance electronic packaging, and nuclear reactor components. During the preparation (e.g., casting, welding, heat treatment) and high-temperature service of these materials, the formation and evolution of the microstructure—including grain growth and recrystallization, second-phase precipitation and coarsening, and migration of grain boundaries and phase interfaces—are fundamentally controlled by the diffusion behavior of alloying elements. Atomic-scale migration, vacancy flow, and concentration gradient-driven diffusion flux jointly determine the evolution path and final morphology of the microstructure. Conversely, the real-time state of the microstructure (e.g., grain boundary density, phase distribution, dislocation configuration) significantly alters the effectiveness of diffusion channels, diffusion activation energy, and diffusion coefficient, thus exerting a feedback regulation effect on subsequent diffusion behavior. In other words, there is a strong, nonlinear, time-varying, two-way coupling relationship between diffusion behavior and microstructure evolution.

[0003] In existing technologies, modeling methods for material diffusion behavior or microstructure evolution can be broadly categorized into two types. The first type consists of classical physical models, such as diffusion equations based on Fick's law, phase-field models based on Ginzburg-Landau theory, and atomic simulations based on Monte Carlo or molecular dynamics. These models have a clear physical foundation and can describe some mechanisms of diffusion and microstructure evolution. However, they typically employ a one-way computational approach: given initial microstructure and boundary conditions, the diffusion field is solved, and then microstructure evolution is driven by the diffusion flux; or conversely, given microstructure characteristics, the equivalent diffusion coefficient is estimated. This one-way coupling makes it difficult to truly reflect the dynamic interaction and feedback between the two. Furthermore, physical models are computationally expensive, making them difficult to apply on an engineering scale. The second type consists of data-driven models developed in recent years, such as neural networks and support vector regression, which use experimental data to establish a statistical mapping between process parameters and the final microstructure. However, these models are essentially a "black box," lacking an internal description of the diffusion mechanism and the dynamics of microstructure evolution, and are unable to achieve continuous iterative updates and bidirectional corrections during the evolution process. They typically only allow input of initial conditions and output of final state results, but cannot simulate intermediate evolution paths. Furthermore, once the model is trained, its internal mapping relationships are fixed and cannot be dynamically adjusted based on intermediate states.

[0004] In summary, the fundamental deficiency of existing technologies in addressing the diffusion-microstructure coupling problem of beryllium aluminum alloys lies in the lack of a modeling framework capable of simultaneously, bidirectionally, and dynamically describing the coupling relationship between diffusion behavior and microstructure evolution. Specifically, this manifests as: the inability to dynamically adjust diffusion parameters based on real-time microstructure state during simulation, and the inability to adjust the microstructure evolution rate according to changes in the diffusion field; the lack of iterative update capabilities in the model, resulting in a significant decrease in prediction accuracy after long-term evolution; and the absence of an effective fusion path between the physical model and data-driven methods. Therefore, there is an urgent need to invent a novel modeling method that possesses bidirectional capabilities of forward prediction and backward correction, and can achieve consistent convergence of diffusion behavior and microstructure evolution through collaborative iteration. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for constructing a forward-reverse co-evolutionary diffusion twin network for beryllium-aluminum alloys. This method aims to solve the fundamental problem that traditional unidirectional models cannot describe the bidirectional coupling relationship between diffusion and microstructure, while overcoming the deficiencies of purely data-driven models that lack physical process support and cannot be dynamically iteratively updated. By constructing a twin network with dual functions of forward evolution and reverse correction, and introducing a co-iterative mechanism, dynamic, high-precision, and physically consistent joint modeling of diffusion behavior and microstructure evolution is achieved, significantly improving the predictive ability and engineering applicability of material evolution processes.

[0006] To achieve the aforementioned objectives and technical effects, this invention proposes a method for constructing a forward-backward co-evolutionary diffusion twin network for beryllium-aluminum alloys. The core idea of ​​this method is to construct a pair of coupled, co-evolving neural network models: a forward evolution model and a backward correction model. These two models form a "twin" structure, achieving bidirectional dynamic updates of diffusion behavior and tissue state through iterative feedback loops. Specifically, this method includes the following systematic and interrelated technical steps: First, a systematic acquisition and standardized preprocessing of multi-source data related to beryllium aluminum alloys were conducted. This invention extensively collected three types of key data: the first type is diffusion behavior data, specifically including elemental concentration distribution curves measured under different temperatures, times, and initial concentrations, diffusion path information (e.g., concentration penetration curves obtained through diffusion couple experiments), and the apparent diffusion coefficient and diffusion activation energy calculated from these; the second type is microstructure data, covering grain structure (average grain size, grain size distribution, grain boundary characteristic distribution), phase distribution (volume fraction of each phase, phase morphology and spatial arrangement), and interface characteristics (grain boundary curvature, interface roughness, etc.) at different evolution stages; the third type is process parameter data, including heat treatment temperature, holding time, cooling rate, and possible applied stress or strain states. The sources of the above data include: rigorously designed diffusion annealing and microstructure characterization experiments, high-resolution microscopic analysis (such as elemental surface distribution obtained by transmission electron microscopy combined with energy dispersive spectroscopy), and reliable data from published literature or historical databases. All data undergoes unified quality review and cleaning, continuous numerical variables are normalized or standardized, and image data (such as tissue images and concentration distribution maps) are feature extracted, ultimately constructing a structured and traceable multidimensional dataset.

[0007] Based on the prepared data, this invention characterizes diffusion behavior and microstructure evolution. The goal of diffusion behavior characterization is to extract physically meaningful key parameters from the raw diffusion data that can serve as model inputs and outputs. Specifically, the extracted diffusion behavior parameters include: diffusion coefficient (which can be the pre-exponential factor and activation energy in a temperature-dependent Arrhenius form, or a value at a specific temperature), concentration gradient (usually the spatial derivative along the diffusion direction), and diffusion flux (calculated according to Fick's first law, i.e., the product of the diffusion coefficient and the concentration gradient). Furthermore, for more complex systems, advanced features such as interdiffusion coefficient and diffusion path curvature can be extracted. These parameters collectively constitute the diffusion feature representation vector. Microstructure evolution characterization extracts feature parameters from the microstructure data that can quantitatively describe the microstructure state and its evolution trend. These specifically include: average grain size and its distribution width, volume fraction of each phase (e.g., beryllium and aluminum phases), and interface morphology parameters (e.g., average grain boundary curvature, grain boundary area density, and phase interface roughness index). These parameters constitute the microstructure feature representation vector. The dimensions of the two types of feature vectors can be adjusted according to the richness of the data, but physical interpretability must be guaranteed.

[0008] The core innovation of this invention lies in constructing two coupled neural network models: a forward evolution model and a backward correction model. The forward evolution model describes the driving effect of diffusion behavior on microstructure evolution, i.e., realizing a nonlinear mapping from diffusion characteristics to microstructure characteristics. This model takes the current diffusion behavior characteristics (such as diffusion coefficient and concentration gradient) and the current microstructure state (optionally, as contextual information) as input, and outputs the change in microstructure characteristics or the updated microstructure characteristic values ​​for the next time step or the next evolutionary stage. Mathematically, the forward evolution model can be viewed as a discretized approximation of a dynamic system, and its training objective is to minimize the error between the predicted microstructure characteristics and the experimentally observed microstructure characteristics. The network structure of this model can be a multilayer fully connected network, a long short-term memory network (if the data has time-series characteristics), or a physical information neural network. The backward correction model corrects the diffusion behavior parameters in reverse based on the current or observed microstructure characteristics. Specifically, this model takes the current microstructure characteristics (such as grain size and phase volume fraction) and possible process conditions (such as temperature) as input, and outputs the correction amount for the diffusion coefficient or directly outputs the updated diffusion characteristics. The theoretical basis of the inverse correction model is that microstructure (especially grain boundary density and phase interface area) significantly alters the effectiveness of diffusion channels, thus affecting the apparent diffusion coefficient. By training the inverse model, the diffusion characteristics of its output can be made consistent with diffusion data measured through independent experiments. The two models are trained using the same dataset but with different input-output pairs; they can be trained independently or alternately to enhance coupling.

[0009] After constructing and training the forward evolution model and the backward correction model respectively, the most crucial step in this invention is to construct a co-evolution mechanism between the two. This mechanism is an iterative update process designed to simulate the co-evolution of diffusion behavior and microstructure over time. The specific process is as follows: First, initial conditions are set, including the initial compositional distribution (corresponding to the initial diffusion characteristics) and the initial microstructure state (such as the grain size and phase distribution of the as-cast microstructure). Then, an iterative loop is entered: In the k-th iteration, based on the current diffusion characteristics, the forward evolution model predicts the changes in microstructure characteristics after a small time step Δt, obtaining the updated microstructure state; subsequently, based on the updated microstructure characteristics, the backward correction model calculates the correction amount of the diffusion characteristics, obtaining the updated diffusion characteristics; then, the updated diffusion characteristics and microstructure characteristics are used as inputs for the next iteration, and the above process is repeated. This iterative update process continues until a preset convergence condition is met (e.g., the change in microstructure characteristics is less than a threshold, or the preset total evolution time is reached). In this co-evolutionary mechanism, the forward and backward models form a closed-loop feedback system: diffusion drives tissue change, and tissue, in turn, modulates diffusion; the two gradually reach a self-consistent dynamic equilibrium through iteration. This bidirectional, dynamic coupling method is highly consistent with the physical processes of diffusion and tissue evolution in real materials, and is the core inventive aspect of this invention.

[0010] Finally, this invention outputs the prediction results obtained through co-evolutionary simulation. The output includes at least three parts: first, the prediction results of diffusion behavior, specifically the evolution trajectory of the diffusion coefficient (a curve showing its change over time or iteration steps) and the spatial profile of the concentration distribution (which can be output as a graph or pseudo-color image); second, the prediction results of microstructure evolution, including the curve showing the change of grain size over time, the evolution trend of the volume fraction of each phase, and the predicted microstructure image or characteristic parameters at the final moment; and third, a quantitative description of the diffusion-microstructure coupling relationship, for example, by calculating the correlation coefficient between the diffusion coefficient and grain size at different stages, or by outputting the convergence curves of the prediction errors of the forward and backward models during the iteration process, to prove the self-consistency of the model. All output results can be presented graphically for easy understanding and use by engineers.

[0011] Advantages of this invention: Compared with existing technologies, the forward-backward co-evolution method for constructing diffusion twin networks in beryllium-aluminum alloys proposed in this invention has the following significant and substantial beneficial effects: First, this invention is the first in the field to construct a bidirectional coupled twin network incorporating forward evolution and backward correction, fundamentally overcoming the limitation of traditional unidirectional models that cannot describe the bidirectional dynamic coupling relationship between diffusion and tissue. The forward model captures the physical process of diffusion-driven tissue evolution, while the backward model captures the feedback regulation effect of tissue on diffusion. Working together, they fully reproduce the closed-loop physical essence of material evolution. Second, by introducing a collaborative iterative update mechanism, this invention achieves dynamic and continuous evolution simulation of diffusion behavior and tissue state, rather than relying solely on traditional methods that predict initial and final states. This transparent modeling of the evolutionary process allows users to observe the trajectory of intermediate states, providing unprecedented detailed information for understanding the mechanism and optimizing processes. Third, due to the presence of the backward correction model, this invention can dynamically correct diffusion parameters based on the actual states that occur during tissue evolution, thereby significantly improving the accuracy of long-term evolution prediction. Experimental data verification shows that compared to traditional unidirectional models, the diffusion prediction error of this invention can be reduced by approximately 25%, and the tissue prediction error by approximately 20%. Fourth, the model architecture of this invention combines physical interpretability with data-driven flexibility. Although the mapping relationship between the forward and backward models is learned from data, the selection of its input and output variables strictly follows the physical laws of diffusion-organization coupling. Therefore, the model's prediction results do not violate fundamental physical principles and have high reliability. Fifth, this method can efficiently integrate multi-source heterogeneous data from diffusion experiments, organizational characterization, and process records. Through the bidirectional constraint effect of Siamese networks, stable prediction performance can be obtained even under relatively sparse data conditions, thereby effectively reducing dependence on expensive physical experiments, shortening the materials development cycle, and improving engineering application efficiency. In summary, this invention achieves multiple breakthroughs in principle, method, and engineering application effects in the field of intelligent modeling of materials evolution processes. Attached Figure Description

[0012] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments: Figure 1 This is a schematic diagram of the overall process of the forward-backward co-evolution method for constructing diffusion twin networks of beryllium aluminum alloys proposed in this invention; Figure 2 This is a schematic diagram of the forward evolution model in this invention; Figure 3 This is a schematic diagram of the reverse correction model in this invention; Figure 4 This is a schematic diagram of the cooperative evolution mechanism in this invention. Detailed Implementation

[0013] The present invention will be further explained below with reference to specific implementation schemes, but it is not limited to the present invention. The structures, proportions, sizes, etc. shown in the accompanying drawings are only used to complement the content disclosed in the specification, so as to enable those skilled in the art to understand and read, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modification of the structure, change of the proportion relationship or adjustment of the size, without affecting the effect and purpose that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0014] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings. The embodiments described herein are for illustrative purposes only and do not constitute any limitation on the scope of protection of this invention.

[0015] Figure 1 It fully demonstrates the logical chain from multi-source data acquisition, diffusion and organizational feature extraction, forward and backward model construction, collaborative iterative evolution to final result output.

[0016] Figure 2 A network architecture is described that takes diffusion characteristics (diffusion coefficient, concentration gradient, diffusion flux) as input and outputs changes in tissue characteristics or updated tissue characteristics.

[0017] Figure 3 A network architecture is shown that takes microstructure characteristics (grain size, phase volume fraction, interface morphology parameters) as input and outputs diffusion characteristic corrections.

[0018] Figure 4 The interaction between the forward and backward models in the iterative loop is shown in detail: the forward model predicts tissue updates, the backward model corrects diffusion parameters, and the two are executed alternately until convergence.

[0019] This embodiment focuses on the diffusion behavior of aluminum in beryllium-aluminum alloys during isothermal annealing and its coupled effect on grain growth. The alloy system is a typical beryllium-aluminum alloy with a beryllium content of 60% to 65% (mass percentage), and the balance being aluminum and trace impurities. The annealing temperature is set at 500℃. The implementation process and verification results of this method are described in detail below.

[0020] Step 1: Construction and preprocessing of multi-source data.

[0021] This study constructed a dataset containing 380 valid samples. The data sources consist of three parts: The first part (approximately 200 sets) comprises diffusion annealing experiments specifically designed for this study. Beryllium-aluminum diffusion couples (pure beryllium and pure aluminum bonded together by hot pressing) were prepared and subjected to isothermal annealing at 500℃ for different times (1 hour, 2 hours, 5 hours, 10 hours, 20 hours, 50 hours, and 100 hours). Subsequently, electron probe microanalysis was used to measure the concentration distribution curve of aluminum along the direction perpendicular to the interface, obtaining concentration-distance data. Simultaneously, electron backscattering diffraction analysis was performed on the samples at each annealing time point to obtain grain size and grain boundary distribution data. The second part (approximately 120 sets) comes from publicly available literature on diffusion coefficients and grain growth data of beryllium-aluminum alloys or similar two-phase alloys. The third part (approximately 60 sets) comes from the historical database of a collaborating institution. All data were standardized: concentration data were normalized to the range of 0-1, distance coordinates were normalized, and grain size was logarithmically transformed to improve linearity. The diffusion coefficient was derived from the concentration curve by fitting the analytical solution of Fick's second law.

[0022] Step 2: Extraction of diffusion behavior and organizational evolution characteristics.

[0023] For each sample, a diffusion feature vector is extracted, containing three parameters: the apparent diffusion coefficient D(m). 2 / s (logarithmic form), maximum concentration gradient at the interface (Calculated from the central difference of the concentration curve), and diffusion flux. The microstructure feature vector is extracted, containing three parameters: average grain size d (μm, logarithmic form), aluminum phase volume fraction fAl (this value fluctuates slightly between 0.35 and 0.40 due to the fixed composition), and grain boundary density ρGB (grain boundary length per unit area, μm / μm). 2 All features are numericalized, forming the input and output of the model.

[0024] Step 3: Construction of the forward evolution model and the backward correction model.

[0025] The task of the forward evolution model: given the diffusion characteristics at the current time step. The model uses the grain size *d* from the current tissue characteristics to predict the grain size increment *Δd* after a fixed time step *Δt* (in this example, a 1-hour evolution step). It employs a three-layer fully connected neural network with four nodes in the input layer, two hidden layers with 64 and 32 nodes respectively, and a single output node (*Δd*). The activation function is ReLU, and the output layer is linear. The training objective is to minimize the mean squared error between the predicted *Δd* and the experimentally measured *Δd*. In the training dataset, samples from adjacent time points are paired to form input-output pairs.

[0026] The task of the inverse correction model is: given the current tissue features (d, fAl, ρGB) and temperature (fixed at 500℃, which can be omitted as input or used as a constant bias), output a correction coefficient k for the diffusion coefficient (a scalar such that the corrected Dcorrected = k·Dinitial). This model also employs a three-layer fully connected network: an input layer with three nodes (d, fAl, ρGB), two hidden layers with 64 and 32 nodes respectively, and an output layer with one node (k). The training objective is to minimize the error between the corrected diffusion coefficient and the diffusion coefficient measured through independent diffusion experiments.

[0027] Both models used the Adam optimizer with a learning rate of 0.001, 2000 training epochs, and a batch size of 16. Early stopping was employed to prevent overfitting. After training, the forward model had a mean absolute percentage error (MASE) of 8.2% on the validation set, while the backward model had an MSE of 6.5%.

[0028] Step 4: Co-evolution and iteration.

[0029] Initial conditions are set as follows: the initial microstructure is as-cast, the average grain size d0 = 8.5 μm, and the grain boundary density ρGB = 0.25 μm / μm. 2 The volume fraction of the aluminum phase, fAl, is 0.38. Initial diffusion characteristics: Initial diffusion characteristics are calculated from the initial concentration distribution (a step exists at the diffusion couple interface). Approximately 1.2 μm -1 The initial apparent diffusion coefficient D0 is taken as 1.2 × 10⁻⁶ according to the literature. -13 m 2 / s (corresponding to 500℃). The total evolution time is set to 50 hours, with a time step Δt = 1 hour, for a total of 50 iterations. At the k-th step (corresponding to time t = k hours): First, the current diffusion characteristics are... Input the current grain size dk into the forward evolution model to predict Δdk, update the grain size d{k+1}=dk+Δdk, and update the grain boundary density ρGB{k+1} according to the empirical formula ρGB = α / d (α is a geometric factor, taken as 2.5). Then, input the updated microstructure features (d{k+1}, fAl, ρGB{k+1}) into the reverse correction model to obtain the correction coefficient k{k+1}, and update the diffusion coefficient D{k+1}=k{k+1}·Dk. Simultaneously, update the concentration distribution according to the numerical solution of Fick's second law of diffusion, thus obtaining the new ∇C{k+1} and J{k+1}. Repeat the above steps until 50 steps are completed. Record dk and Dk at each step.

[0030] Step 5: Output and Validation of Results.

[0031] After the co-evolution is complete, the following results are output: The evolution curve of the diffusion coefficient over time shows that D changes from an initial 1.2 × 10⁻⁶. -13 m 2 The value gradually decreased and stabilized at approximately 8.5 × 10⁻⁶ after about 10 hours. -14 m 2 / s, a decrease of approximately 29%. The grain size evolution curve shows that d grows from 8.5 μm to approximately 21.3 μm, conforming to a parabolic growth law (d 2 ∝ t). At the same time, the predicted concentration distribution curve at the final moment is output, showing that the concentration gradient at the interface has become significantly flat.

[0032] To verify the effectiveness of this method, independent verification experiments were conducted under the same initial conditions and annealing regime (500℃, 50 hours) in this embodiment. The experiments yielded the following results: the final grain size was 22.1 μm, with a relative error of 3.6% compared to the predicted value of 21.3 μm; the experimentally measured apparent diffusion coefficient (derived from the concentration curve) was 8.2 × 10⁻⁶. -14 m 2 / s, compared to the predicted 8.5×10 -14 m 2 The relative error is 3.7%. In contrast, if only the forward model (without backward correction, i.e., D is fixed as the initial value) is used for evolution prediction, the predicted grain size after 50 hours is 25.8 μm, with an error of 16.7% compared to the experimental value; if only the backward model is used for correction but without forward evolution iteration, no time series prediction can be obtained. Furthermore, compared to traditional phase-field simulation (which requires significant computational resources and takes approximately 40 hours), the co-evolutionary model of this invention completes 50 iterations on a single GPU in only about 2 minutes, with comparable or even higher prediction accuracy (the grain size error in phase-field simulation is approximately 5%). These results demonstrate that the forward-backward co-evolutionary twin network constructed in this invention can describe the bidirectional coupled dynamic process of diffusion behavior and microstructure evolution in beryllium aluminum alloys with extremely high accuracy and extremely low computational cost. The diffusion prediction error is reduced by approximately 25% compared to the traditional unidirectional model, and the microstructure prediction error is reduced by approximately 20%, indicating good stability and engineering applicability of the model.

[0033] In summary, this invention provides a method for constructing a forward-reverse co-evolutionary diffusion twin network for beryllium-aluminum alloys. By constructing a bidirectionally coupled twin network and introducing a cooperative iteration mechanism, dynamic joint evolution simulation of diffusion and organization is achieved, significantly improving prediction accuracy and physical consistency. The described embodiments are merely one specific application form. Any modifications, equivalent substitutions, or improvements made to the above technical solutions within the spirit and principles of this invention should be included within the scope of protection of the claims of this invention.

[0034] Matters not covered in this invention are common knowledge.

[0035] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for constructing a forward-reverse co-evolutionary diffusion twin network for beryllium-aluminum alloys, characterized in that, The method includes the following steps: First, diffusion behavior data, microstructure data, and process parameter data of beryllium aluminum alloy are acquired, and the data are standardized and preprocessed to construct a multi-source dataset. The diffusion behavior data includes at least elemental concentration distribution or diffusion path information, and the microstructure data includes at least grain structure, phase distribution, or interface features. Second, diffusion behavior feature parameters are extracted based on the diffusion behavior data. These feature parameters include at least diffusion coefficient, concentration gradient, and diffusion flux, and a diffusion feature representation is constructed. Simultaneously, microstructure evolution feature parameters are extracted based on the microstructure data. These feature parameters include at least grain size, phase volume fraction, and interface morphology parameters, and a microstructure feature representation is constructed. Finally, a forward evolution model is constructed to describe the influence of diffusion behavior on microstructure evolution. This model realizes the evolution from... The model establishes a mapping relationship from diffusion features to organizational features, with diffusion behavior features as input and corresponding microstructural parameters as output. A reverse correction model is constructed to correct diffusion behavior based on organizational features. This model implements a corrected mapping from organizational features to diffusion features, with organizational feature parameters as input and diffusion behavior correction parameters as output. Then, the forward evolution model and the reverse correction model are coupled to construct a co-evolution mechanism. This mechanism achieves dynamic convergence of diffusion behavior and microstructural structure through iterative updates, specifically including predicting organizational structure updates based on the forward model, correcting diffusion parameters based on the reverse model, and iterating repeatedly until convergence conditions are met. Finally, the model outputs the diffusion behavior prediction results and organizational evolution results, which include at least the diffusion coefficient distribution, organizational structure features, and the diffusion-organization coupling relationship.

2. The method for constructing a beryllium-aluminum alloy diffusion twin network based on forward-reverse co-evolution according to claim 1, characterized in that, The diffusion behavior data specifically comes from diffusion couple experiments, elemental surface distribution analysis, or isotope tracing experiments. The microstructure data comes from scanning electron microscopy, electron backscatter diffraction, or transmission electron microscopy image analysis. The process parameters include at least temperature, time, and cooling rate.

3. The method for constructing a beryllium-aluminum alloy diffusion twin network based on forward-reverse co-evolution according to claim 1, characterized in that, The diffusion coefficient in the diffusion characteristic representation is the pre-exponential factor and activation energy in the Arrhenius form, or the apparent diffusion coefficient value at a specific temperature; the concentration gradient is the spatial derivative along the diffusion direction; the diffusion flux is calculated according to Fick's first law as the product of the diffusion coefficient and the concentration gradient.

4. The method for constructing a forward-reverse co-evolutionary diffusion twin network of beryllium-aluminum alloy according to claim 1, characterized in that, The grain size in the organizational feature representation includes the average grain size and its distribution width, the phase volume fraction is calculated by image segmentation, and the interface morphology parameters include the average grain boundary curvature, grain boundary area density, or phase interface roughness index.

5. The method for constructing a forward-reverse co-evolutionary beryllium-aluminum alloy diffusion twin network according to claim 1, characterized in that, Both the forward evolution model and the backward correction model are neural network models. Their network structures are selected from multilayer fully connected networks, long short-term memory networks, or physical information neural networks. The two models use the same dataset but different input-output pairs for independent or alternating training.

6. The method for constructing a beryllium-aluminum alloy diffusion twin network based on forward-reverse co-evolution according to claim 1, characterized in that, The iterative update process in the co-evolution mechanism is as follows: In the kth iteration, based on the current diffusion characteristics, the changes in organizational characteristics after a small time step are predicted by the forward evolution model to obtain the updated organizational state; based on the updated organizational characteristics, the correction amount of the diffusion characteristics is calculated by the back correction model to obtain the updated diffusion characteristics. The updated diffusion and organization features are used as inputs for the next iteration. The above process is repeated until the change in organization features is less than a preset threshold or the preset total evolution time is reached.

7. The method for constructing a beryllium-aluminum alloy diffusion twin network based on forward-reverse co-evolution according to claim 1, characterized in that, The output diffusion behavior prediction results include the evolution trajectory curve of the diffusion coefficient or the spatial profile of the concentration distribution, and the microstructure evolution results include the grain size change curve over time, the phase volume fraction evolution trend, or the predicted microstructure image at the final moment.

8. The method for constructing a beryllium-aluminum alloy diffusion twin network based on forward-reverse co-evolution according to claim 1, characterized in that, The output diffusion-organization coupling relationship includes the correlation coefficient between the diffusion coefficient and grain size at different evolution stages, or the convergence curve of the prediction error of the forward and backward models during the iteration process, which is used to verify the self-consistency of the model.

9. The method for constructing a beryllium-aluminum alloy diffusion twin network based on forward-reverse co-evolution according to claim 1, characterized in that, The method is used to describe the bidirectional coupling relationship between the diffusion behavior of aluminum or beryllium elements and grain growth and phase precipitation in beryllium aluminum alloys during isothermal annealing or hot working.

10. The method for constructing a forward-reverse co-evolutionary beryllium-aluminum alloy diffusion twin network according to claim 1, characterized in that, The method reduces diffusion prediction error by at least 20% and tissue prediction error by at least 15% compared to the traditional unidirectional model through the coordinated iteration of forward and backward models, while realizing the simulation of the entire evolution process from the initial state to the final state.

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