A method for generating microstructure of beryllium aluminum alloy embedded with multi-physical constraints

Abstract

The present application belongs to the technical field of the intersection of material science and computational materials science, and proposes a beryllium aluminum alloy microstructure generation method embedded with multiple physical constraints, which comprises the following links: systematic acquisition and standardized construction of beryllium aluminum alloy microstructure data; deep extraction and quantitative characterization of organizational characteristics; construction of an intelligent generation model capable of generating microstructure structure based on composition parameters and process parameters; introduction of a post-processing link of organizational optimization and screening; and output of microstructure generation results meeting multiple physical constraint conditions in an intuitive and convenient engineering application form. The present application has the following advantages: it breaks through the limitation of traditional methods that can only make statistical parameter prediction, so that the generated microstructure is significantly better than existing methods in terms of phase stability, evolution law rationality and interface morphology authenticity. Breakthrough progress has been made in the aspects of microstructure intelligent generation theory and engineering application.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of materials science and computational materials science. Specifically, it relates to an innovative method for intelligent generation and precise control of the microstructure of beryllium aluminum alloys by deeply integrating multi-physics field constraint mechanisms such as thermodynamics, kinetics and interface energy, thereby achieving physical rational constraints. Background Technology

[0002] Beryllium aluminum alloys, as lightweight structural materials possessing low density, high specific stiffness, excellent dimensional stability, and good machinability, play an indispensable role in cutting-edge engineering fields such as aerospace inertial navigation systems, high-precision optical platforms, and high-performance electronic packaging. The macroscopic service performance of these alloys, particularly their corrosion resistance, mechanical strength, and fatigue life, is inherently highly dependent on the specific characteristics of their microstructure, including but not limited to the statistical distribution of grain size, the volume fraction and spatial arrangement of the second phase, and the geometry and connectivity of grain boundary networks. Therefore, achieving precise control and reasonable prediction of the microstructure is one of the core scientific issues for overcoming the performance bottlenecks of beryllium aluminum alloys and expanding their high-end applications.

[0003] For a long time, the microstructure control of beryllium aluminum alloys has mainly relied on the traditional "preparation-characterization-trial and error" experimental paradigm. Researchers typically prepare a large number of samples by adjusting alloy composition, melting temperature, cooling rate, and subsequent heat treatment process parameters, and then use tools such as optical microscopes and scanning electron microscopes to observe and statistically analyze the microstructure in order to obtain the target microstructure. However, this experience-driven method has significant drawbacks: First, due to the high dimensionality of the parameter space (involving multiple continuous variables such as composition, temperature, time, and rate), relying entirely on experimental exploration is extremely inefficient, resulting in long research and development cycles and high costs; Second, the formation of microstructure is a highly nonlinear and complex evolutionary process governed by both thermodynamics and kinetics, and empirical methods are unable to systematically reveal the interaction and synergistic mechanisms between different parameters, often getting stuck in local optima and failing to obtain the globally ideal microstructure; Third, for certain extreme or non-equilibrium conditions, such as fine grains, ultrafine grains, and metastable phase distributions, experimental trial and error methods are even difficult to apply.

[0004] In recent years, with the rise of data-driven methods in materials science, some studies have attempted to use machine learning models to establish statistical mapping relationships between process parameters and microstructure characteristics in order to predict microstructure parameters. However, existing methods generally suffer from two fundamental limitations: First, most models only focus on numerical prediction of statistical microstructure characteristics (such as average grain size), lacking the ability to directly generate complete microstructure topology (i.e., image-level microstructure morphology), while the details of microstructure morphology (such as grain shape, grain boundary curvature, and phase distribution inhomogeneity) often have a critical impact on service performance. Second, and more importantly, existing methods almost entirely fail to incorporate constraints from the fundamental physical properties of materials, such as the phase stability conditions determined by phase transition thermodynamics, the diffusion and curvature-driven laws followed by grain growth kinetics, and the grain boundary morphology evolution law dominated by interface energy minimization. Due to the lack of these physical constraints, the microstructures generated by purely data-driven models are prone to deviating from basic physical laws in terms of phase composition, grain size distribution, and interface morphology, thus losing engineering credibility and practical application value. Therefore, there is an urgent need to develop a new method that can deeply integrate the laws of materials physics and has end-to-end microstructure generation capability, so as to achieve the efficient generation of physically rational, controllable and adjustable microstructures of beryllium aluminum alloys. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for generating the microstructure of beryllium aluminum alloys with embedded multi-physical constraints. This method aims to solve the problems of low efficiency and insufficient parameter space exploration in traditional experimental trial-and-error methods, while overcoming the defects of existing data-driven methods that lack physically reasonable constraints, struggle to generate image-level microstructures, and whose generated results easily deviate from the actual evolution of materials. Ultimately, it achieves physically reasonable generation and high-precision control of the microstructure of beryllium aluminum alloys.

[0006] To achieve the aforementioned objectives and technical effects, this invention proposes an innovative method for generating the microstructure of beryllium-aluminum alloys, embedding multiple physical constraints. This method is not a simple statistical learning or image synthesis approach, but rather a systematic intelligent framework that deeply integrates prior knowledge of materials physics with advanced generative models. Specifically, this method includes the following interrelated and progressively layered technical steps: First, a systematic acquisition and standardized construction of microstructure data for beryllium-aluminum alloys was conducted. This invention extensively collected microstructure data from various sources, specifically including: high-resolution microstructure images directly acquired through scanning electron microscopy or metallographic microscopy; statistical distribution data of grain size obtained based on image analysis or the truncation method; phase composition and volume fraction data of each phase obtained through energy dispersive spectroscopy or electron backscatter diffraction; and relevant indicators characterizing phase distribution uniformity and grain boundary connectivity. The data sources cover three aspects: first, experimental test data specifically designed for this invention, i.e., samples prepared and characterized under set composition and process conditions; second, high-quality microstructure data systematically extracted from publicly available academic literature and peer-reviewed; and third, historical microstructure data accumulated within existing material databases or within the company. All the above data underwent unified format conversion and standardized preprocessing, including image size normalization, grayscale range adjustment, noise filtering, and numerical normalization of microstructure characteristic parameters, ultimately constructing a structured and traceable microstructure dataset.

[0007] Based on this, in-depth extraction and quantitative characterization of tissue features are performed. This invention does not simply use the original image pixels as model input and output, but first extracts tissue feature parameters with clear physical meaning from the microscopic tissue image to reduce redundant degrees of freedom in the model and enhance interpretability. Specifically extracted feature parameters include: average grain size and its distribution width (e.g., calculated using the equivalent circle diameter method), grain boundary density (i.e., grain boundary length per unit area), volume fraction of each phase (e.g., beryllium phase, aluminum phase, and possible intermetallic compound phases), and phase distribution uniformity indices (e.g., calculated using nearest neighbor distance analysis or spatial variance). These feature parameters are uniformly constructed into a multidimensional tissue feature vector, which can serve as both the output target of the subsequent generative model and an important basis for evaluating the quality of the generated tissue. Simultaneously, the original tissue image itself is also preserved for training the end-to-end generative model, enabling this invention to simultaneously support statistical feature-level and image-level tissue generation.

[0008] Furthermore, an intelligent generative model capable of generating microstructures based on compositional and process parameters is constructed. The core architecture of this model is a deep generative network comprising three sequentially connected modules: an input module, responsible for receiving beryllium-aluminum alloy compositional parameters (such as beryllium mass percentage, aluminum content, and trace element content) and key process parameters (such as melting temperature, cooling rate, and holding time) represented as vectors; a feature mapping module, consisting of a multi-layer fully connected network or attention mechanism network, which learns and establishes a highly nonlinear mapping relationship between the input composition, process parameters, and intermediate microstructure feature representations; and a microstructure generation module, which, conditioned by the output of the feature mapping module, introduces controllable random perturbations into its latent feature space and performs iterative updates (e.g., using a generative adversarial network or the decoder part of a diffusion probability model), ultimately generating the corresponding microstructure information. The output of this generative model can be one of two forms or a combination of both: either directly outputting a synthesized high-resolution microstructure image (with texture and morphology similar to actual electron micrographs), or outputting the aforementioned microstructure feature vectors. Through this design, the model possesses the ability to directly generate microstructure space from the design parameter space.

[0009] To ensure that the microstructures output by the generative model not only resemble the training data in statistical distribution but, more importantly, conform to the fundamental laws of material evolution in physics, this invention creatively embeds a multiphysics constraint mechanism into the model's training and generation process. These constraints, in the form of soft constraints—that is, as additional regularization terms or discriminator conditions—are integrated into the overall optimization objective of the model. Specifically, they include three levels of physical constraints: First, thermodynamic constraints. These constraints, constructed based on calculated phase diagrams or phase stability functions, limit the types and relative amounts of each phase in the generated microstructure to meet thermodynamic equilibrium requirements under given composition and temperature conditions. For example, for a given beryllium-aluminum composition, the model is required to have a volume fraction ratio of beryllium to aluminum that is close to the equilibrium phase fraction calculated by the CALPHAD method; any significant deviation will be penalized. This constraint ensures the thermodynamic feasibility of the generated microstructure in terms of phase composition, avoiding non-equilibrium spurious phase combinations that violate the phase rule.

[0010] Second, kinetic constraints. These constraints are built upon classical diffusion-controlled phase transition theory and grain growth kinetics models to regulate the causal relationship between grain size and morphology in the generated microstructure and the input process parameters (especially cooling rate and holding time). For example, according to the grain growth exponential law, at a given cooling rate, the generated grain size should fall within a reasonable physical tolerance range—excessively high cooling rates should not generate coarse grains, while excessively low cooling rates should not generate nanoscale grains. Kinetic constraints guide the model to learn physically consistent process-microstructure mapping relationships by penalizing generation results that violate these fundamental kinetic laws.

[0011] Third, interface energy constraints. These constraints are based on the principle of minimizing grain boundary energy and interface structure, and are used to regulate the grain boundary structure, grain shape, and interface morphology in the generated microstructure. In real materials, grain boundaries tend to form straight or equiaxed morphologies driven by curvature to reduce the total interface energy. This invention constructs an interface energy constraint term by calculating the average curvature of grain boundaries, the angular distribution of grain boundaries, and the grain shape factor in the generated image, and comparing them with physically reasonable ranges. This constraint prompts the model to generate microstructures with physically reasonable grain boundary networks, avoiding the generation of artificially created grain boundary structures that are overly tortuous, excessively bifurcated, or topologically impossible.

[0012] The three physical constraints mentioned above are used to construct a differentiable constraint loss function, which, through a weighted summation, together with the original loss of the generative model (such as image reconstruction loss or adversarial loss) to form the total loss function. During model training, this total loss function drives the model parameters to be updated in a direction that simultaneously satisfies data fitting and physical reasonableness.

[0013] After model training, this invention introduces a post-processing step for tissue optimization and screening. For any given input components and process parameters, the generation model may output multiple candidate tissue samples (through sampling with different random perturbations in the potential space). This invention quantifies and evaluates each candidate tissue based on the aforementioned multi-physics constraints, calculating the overall degree of violation of its thermodynamic, kinetic, and interfacial energy constraints. Only tissue samples with all constraint violations below a preset threshold are retained. For the retained tissues, morphological optimization algorithms (such as grain boundary smoothing filtering or interface evolution based on curvature flow) are further used for fine-tuning to make them closer to the physical ideal state. Through this screening and optimization step, the final tissue results have higher physical reliability.

[0014] Finally, this invention outputs microstructure generation results that satisfy multiple physical constraints in an intuitive and engineering-friendly manner. The output specifically includes: a synthesized microstructure image (which can be saved in a standard image format and includes a scale); a histogram or statistical parameters of grain size distribution (such as mean, standard deviation, maximum and minimum values); characteristic descriptions of each phase distribution (including phase volume fraction and spatial distribution uniformity index); and quantitative indicators for comprehensively evaluating microstructure uniformity (such as grain size variation coefficient, phase segregation degree, etc.). These output results can be directly used to guide subsequent process verification or performance prediction.

[0015] Advantages of this invention: Compared with existing technologies, the beryllium aluminum alloy microstructure generation method with embedded multi-physical constraints proposed in this invention has the following significant and substantial beneficial effects: First, this invention is the first in the field to construct an end-to-end intelligent generation model for the microstructure of beryllium-aluminum alloys, realizing the direct generation from composition and process parameters to complete microstructure images or microstructure feature vectors. This completely breaks through the limitations of traditional methods that can only predict statistical parameters, providing richer structural information for material design. Second, by innovatively embedding the three major physical constraints of thermodynamics, kinetics, and interface energy, this invention effectively overcomes the inherent defect of purely data-driven generation models that easily produce physically infeasible microstructures. This method, which deeply integrates physical prior knowledge as hard or soft constraints into the generation model, makes the generated microstructure significantly superior to existing methods in terms of phase stability, rationality of evolution laws, and authenticity of interface morphology. Third, the microstructure screening and optimization post-processing mechanism introduced in this invention further improves the reliability and engineering practicality of the final generation results, ensuring that the output microstructure meets all physical constraints. Fourth, this method can efficiently utilize multi-source, small-sample microstructure data, reducing dependence on large-scale training data through the guidance of physical constraints, thus achieving high-quality generation even in beryllium-aluminum alloy systems with limited data. Fifth, by significantly reducing the number of iterations in physical preparation and microscopic characterization, this invention can significantly shorten the R&D cycle for beryllium-aluminum alloy microstructure control, reduce experimental costs, and provide a powerful virtual experimental platform for exploring innovative microstructures beyond the scope of traditional experience (such as gradient grain structures, dual-mode distributions, etc.). In summary, this invention has achieved groundbreaking progress in both the theory and engineering application of intelligent microstructure generation. Attached Figure Description

[0016] 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 method for generating microstructure of beryllium aluminum alloy with embedded multi-physical constraints proposed in this invention. Figure 2This is a schematic diagram of the structure of the microstructure generation model in this invention; Figure 3 This is a schematic diagram of a multi-physics constraint embedding mechanism. Detailed Implementation

[0017] The present invention will be further explained below with reference to specific implementation schemes, but this explanation does not limit the invention. The structures, proportions, sizes, etc., shown in the accompanying drawings are only for the purpose of assisting those skilled in the art in understanding and reading the content disclosed in the specification, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportional relationships, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention. At the same time, terms such as "upper," "lower," "front," "rear," and "middle" used in this specification are only for clarity of description and are not intended to limit the scope of the present invention. Changes or adjustments to their relative relationships, without substantially altering the technical content, should also be considered within the scope of the present invention.

[0018] 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. It should be noted that the embodiments described herein are merely illustrative of the invention and do not constitute any limitation on the scope of protection of the invention.

[0019] Figure 1 It clearly demonstrates the complete logical chain from data acquisition, feature extraction, model building, physical constraint embedding, organizational optimization and screening to the final result output; Figure 2 The hierarchical connection relationship between the input module, feature mapping module and organization generation module is described in detail, as well as the working mechanism of random perturbation and iterative update in the latent space; Figure 3 The paper demonstrates how thermodynamic constraints (based on phase stable regions), kinetic constraints (based on grain growth kinetic curves), and interfacial energy constraints (based on grain boundary curvature distribution) can be integrated into the model training and generation process as additional loss terms or discrimination conditions.

[0020] Example 1 This embodiment takes a typical beryllium-aluminum alloy system (beryllium content of 60% to 65% by mass, with the balance being aluminum and trace impurities) as the research object, and elaborates in detail the specific implementation process and verification results of the method of the present invention.

[0021] Step 1: Acquisition and construction of micro-organism data.

[0022] This study constructed a dataset containing 320 high-quality microstructure samples. The data sources are divided into three parts: The first part (approximately 150 samples) was obtained through systematic experiments in this study. Different combinations of beryllium contents (61%, 63%, 65%) and different cooling rates (5℃ / s, 10℃ / s, 15℃ / s, 20℃ / s) were selected to prepare corresponding beryllium-aluminum alloy samples. After mounting, grinding, polishing, and chemical etching, microstructure images were acquired using a field emission scanning electron microscope in backscattered electron mode. Each image had a resolution of 1024×1024 pixels, and image analysis software was used to statistically analyze the average grain size, grain boundary density, and volume fraction of the second phase (mainly aluminum-rich phase). The second part (approximately 120 samples) came from papers on the microstructure evolution of beryllium-aluminum alloys published in authoritative domestic and international journals in the past decade. Microstructure images and characteristic parameters that conform to the composition range of this embodiment were extracted from these papers. The third part (approximately 50 samples) came from the historical database of a collaborating institution. All images were uniformly scaled to 512×512 pixels, and adaptive histogram equalization was used to enhance contrast. Organizational feature parameters were standardized to form a unified dataset.

[0023] Step 2: Organizational feature extraction and characterization.

[0024] For each tissue image in the dataset, the following steps were used to extract features: First, a grain segmentation method based on the watershed algorithm was used to identify the boundaries of each grain, and the equivalent circle diameter of each grain was calculated to obtain the average grain size and the standard deviation of the grain size distribution. Second, a grain boundary network was extracted using a skeletonization algorithm, and the total length of grain boundaries per unit area was calculated as the grain boundary density. Third, a gray-scale thresholding method was used to distinguish between the beryllium phase (brighter) and the aluminum phase (darker), and the area fraction of the aluminum phase was calculated as the volume fraction of the second phase. Finally, the spatial nearest neighbor distance analysis method was used to calculate the spatial variance of the aluminum phase particle distribution as a homogeneity index. The above feature parameters constitute a five-dimensional tissue feature vector, which is used as a supervision signal in subsequent model training.

[0025] Step 3: Construction of microstructure generation model and embedding of multiple physical constraints.

[0026] This embodiment employs a conditional generative adversarial network (GAN) architecture as the microstructure generation model. The generator takes a concatenated vector of component parameters (beryllium content, continuous values) and process parameters (cooling rate, continuous values) as input, and progressively upsamples through six convolutional layers to generate a 512×512×1 grayscale tissue image. The discriminator uses a PatchGAN structure to adversarially distinguish between the generated and real images. The original loss function for model training includes adversarial loss and L1 reconstruction loss. Based on this, a triple physical constraint loss is embedded according to the design of this invention: Thermodynamic constraint loss: Based on the beryllium-aluminum binary phase diagram, the equilibrium microstructure at room temperature is a two-phase mixture of beryllium and aluminum phases, and the volume fraction of the aluminum phase is monotonically related to the beryllium content. The theoretical volume fraction of the aluminum phase is calculated based on the input composition, and the absolute deviation between the aluminum phase fraction segmented in the generated image and the theoretical value is penalized. This penalty is set to a weight of 0.1.

[0027] Kinetic constraint loss: According to classical grain growth kinetics, during solidification and cooling, the grain size is approximately linearly inversely proportional to the logarithm of the cooling rate. The average grain size extracted from the generated image and the input cooling rate are compared, and the deviation from this empirical linear relationship is calculated. The squared value is then used as a penalty term with a weight of 0.05.

[0028] Interface energy constraint loss: Calculate the average curvature of the grain boundary network in the generated image. In real-world structures, grain boundaries tend to be straight due to minimized interface energy, resulting in a low average curvature. For average curvature exceeding a preset threshold (0.15 μm in this example), the loss is considered. -1 The generated image is subject to a secondary penalty with a weight of 0.08.

[0029] The total loss function is the sum of the four parts mentioned above. The model was trained for 2500 epochs using the Adam optimizer, with an initial learning rate of 0.001 and a batch size of 8. Training was performed on a single NVIDIA Tesla V100 GPU and took approximately 18 hours.

[0030] Step 4: Organization generation, screening, and optimization.

[0031] After training, for a given input parameter (e.g., beryllium content 62.5%, cooling rate 15℃ / s), 20 candidate tissue images are generated by introducing different random seeds into the generator's latent noise vector. For each candidate image, the violation values ​​of thermodynamic, kinetic, and interfacial energy constraints are calculated. A screening condition is set: the violation values ​​of all three constraints must be less than 1.2 times their respective thresholds. After screening, 15 out of the 20 samples pass. Subsequently, the selected tissue images are post-processed and optimized using a curvature-driven grain boundary smoothing filter algorithm, iterated 10 times, to further reduce the interfacial energy. Finally, the tissue with the smallest total constraint violation is selected as the output.

[0032] Step 5: Output Results and Experimental Verification.

[0033] The final microstructure results output by the model are as follows: The synthesized microstructure image shows that the grains are equiaxed, with uniform distribution of beryllium phase (light color) and aluminum phase (dark color), an average grain size of 12.8 μm, a standard deviation of grain size distribution of 2.1 μm, an aluminum phase volume fraction of 36.5%, and a grain boundary density of 0.42 μm / μm. 2The uniformity index of the generated microstructure was 0.08. To verify the reliability of the generated microstructure, beryllium aluminum alloy samples were actually prepared under the same input parameters (Be 62.5%, cooling rate 15℃ / s), and real scanning electron microscope images were acquired under the same conditions. Comparative analysis showed that the generated microstructure images and the real microstructure images had high consistency in grain morphology, phase distribution, and grain boundary network characteristics, with a structural similarity index of 0.89; the error between the generated average grain size and the actual measured value (12.2 μm) was less than 5%; the error in aluminum phase volume fraction was less than 3%; and the error in grain boundary density was approximately 7%. Furthermore, compared with the baseline generation model without embedded multi-physics constraints, the generation results of this invention showed significant improvements in grain boundary curvature rationality (reducing the number of false high curvature points by approximately 65%) and phase composition thermodynamic consistency (reducing the probability of violating phase fraction constraints from 42% to 6%). The above experimental verification results fully demonstrate the physical rationality, high fidelity, and engineering reliability of the method of this invention in generating beryllium aluminum alloy microstructures.

[0034] In summary, this invention provides a method for generating the microstructure of beryllium-aluminum alloys by embedding multiple physical constraints. By deeply integrating thermodynamic, kinetic, and interfacial energy constraints into the generative model, and combining this with post-processing screening and optimization, a physically reasonable, high-precision, and controllable intelligent generation of microstructures is achieved. 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.

[0035] Matters not covered in this invention are common knowledge.

[0036] 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 generating microstructures of beryllium aluminum alloys with embedded multi-physical constraints, characterized in that, The method includes the following steps: First, acquiring microstructure data of beryllium aluminum alloy, including scanning electron microscope or metallographic microscope images, grain size statistics, phase composition and phase distribution data, and performing standardized preprocessing on the data to construct a microstructure dataset; Second, extracting features from the microstructure images to obtain microstructure feature parameters including average grain size, grain boundary density, volume fraction of each phase, and phase distribution uniformity index, and constructing these parameters as microstructure feature vectors; Third, constructing a microstructure generation model, which includes an input module, a feature mapping module, and a microstructure generation module, capable of generating corresponding microstructures based on input composition parameters and process parameters by introducing random perturbations into the latent feature space and iteratively updating. The model generates microstructure information; simultaneously, a multi-physics constraint mechanism is embedded during the training and generation process of the model. This multi-physics constraint includes at least thermodynamic constraints to ensure the phase composition of each phase in the generated microstructure meets phase stability conditions, kinetic constraints to ensure grain growth behavior conforms to diffusion and precipitation laws, and interfacial energy constraints to regulate grain boundary structure and interface morphology to achieve a reasonable interface distribution. Then, the generated microstructure is screened and optimized based on these multi-physics constraints, eliminating structures that do not meet the constraints and performing morphological optimization on the retained structures to obtain a stable microstructure distribution. Finally, the generated microstructure that meets the constraints is output, including microstructure images, grain size distribution range, phase distribution characteristics, and microstructure uniformity indices.

2. The method according to claim 1, characterized in that, The tissue images in the microstructure data are derived from scanning electron microscopy or metallurgical microscopy, and the dataset simultaneously includes experimental measurement data and historical data from literature or databases.

3. The method according to claim 1, characterized in that, The grain size in the structure feature vector is represented by the equivalent circle diameter or the squaring method, the grain boundary density is represented by the total grain boundary length per unit area, the volume fraction of each phase is determined by the image segmentation threshold method or energy spectrum analysis, and the phase distribution uniformity is characterized by the spatial nearest neighbor distance variance or segregation index.

4. The method according to claim 1, characterized in that, The microstructure generation model adopts a generative adversarial network, variational autoencoder, or diffusion probability model architecture. Its tissue generation module can directly output a synthesized high-resolution tissue image or output tissue feature vectors and then reconstruct them into an image.

5. The method according to claim 1, characterized in that, The thermodynamic constraints are constructed based on calculated phase diagrams or phase stability functions, and are achieved by penalizing the deviation between the volume fraction of each phase in the generated structure and the theoretical value obtained from the input components through thermodynamic equilibrium calculation.

6. The method according to claim 1, characterized in that, The kinetic constraints are constructed based on a grain growth kinetic model and are achieved by penalizing unreasonable deviations between the grain size in the generated microstructure and the theoretical values ​​predicted by the input process parameters (including cooling rate and holding time) according to the classical kinetic equations.

7. The method according to claim 1, characterized in that, The interface energy constraint is constructed based on the principle of grain boundary curvature distribution and interface minimization, and is achieved by penalizing the average curvature of the grain boundary network or the grain shape factor in the generated image from exceeding the physically reasonable range.

8. The method according to claim 1, 5, 6, or 7, characterized in that, The multi-physics constraint mechanism is implemented in the form of soft constraints, that is, the degree of violation of each constraint is quantified into a differentiable regularization loss term, and weighted and superimposed into the overall training loss function of the generative model, thereby guiding the model to generate a physically reasonable organizational structure during the model training stage.

9. The method according to claim 1, characterized in that, The steps for screening and optimizing the generated microstructures include: generating multiple candidate tissue samples for the same set of input parameters, calculating the comprehensive degree of violation of thermodynamic, kinetic and interfacial energy constraints for each candidate sample, retaining only samples with a violation degree below a preset threshold, and performing interface smoothing optimization based on curvature flow or morphological filtering on the retained samples.

10. The method according to claim 1, characterized in that, The method is used to optimize the microstructure uniformity of beryllium aluminum alloys. The output microstructure uniformity indicators include the grain size variation coefficient and the phase distribution segregation index, which are used to quantitatively evaluate the quality of the generated microstructure.

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