Prediction method, training method and system

Abstract

Embodiments of the present specification provide a prediction method, a training method and a system. In the prediction method, a prediction system generates a plurality of core descriptors and a plurality of non-core descriptors describing a target material based on proportion information corresponding to each element in the target material and attribute values of a plurality of attributes, and inputs at least part of the descriptors into a target network to obtain a predicted value of a critical cooling rate of amorphization of the target material. The target network is a network trained by a training system using a plurality of sample materials, and includes a plurality of sub-networks with the same structure and arranged in a hierarchical manner. Each sub-network includes N input nodes and one output node. The output node of a sub-network in an i-th level is used as the input node of a sub-network in an (i+1)-th level. The N core descriptors input into each sub-network in the first level are the same, and the N-N1 non-core descriptors are not completely the same. N and N1 are both greater than 1, and i is greater than or equal to 1.

Description

TECHNICAL FIELD

[0001] The present specification relates to the field of chemical materials, and in particular, to a prediction method, a training method and a system. BACKGROUND

[0002] Materials usually have two states, crystalline state and amorphous state. Crystalline materials have regular atomic arrangement structure, and the research on the equilibrium state of crystalline materials has formed a relatively complete theoretical system. However, for amorphous materials, although they show great potential in scientific research and industrial applications, the related research on them is insufficient due to the complexity of the preparation process of amorphous materials.

[0003] Metallic glass, as a kind of amorphous material, has attracted widespread attention from researchers in recent years due to its unique mechanical and physical properties. In 1960, Duwez introduced a rapid cooling technology, which realized the cooling of liquid metal above the critical cooling rate (hereinafter referred to as the critical cooling rate, R c ) of amorphization, i.e. R c >10 7 K / s, which opened a new era of research on metallic glass. In the preparation process of metallic glass, the critical cooling rate of amorphization is a crucial parameter, which determines whether the liquid metal can be successfully converted into an amorphous structure.

[0004] At present, the research on the critical cooling rate of amorphization of materials mainly depends on experimental methods, and due to the complexity of experimental conditions, it takes a lot of time and cost to measure the critical cooling rate of amorphization of materials by experiments.

[0005] The content of the background section is only the information known to the inventor, and does not mean that the above information has entered the public domain before the filing date of the present disclosure, nor does it mean that it can be prior art of the present disclosure. SUMMARY

[0006] The present specification provides a prediction method, a training method and a system, which can accurately predict the critical cooling rate of amorphization of materials through a pre-trained target network, and reduce the time and cost of research on amorphous materials.

[0007] In a first aspect, the present specification provides a method for predicting a critical cooling rate of amorphization, comprising: generating K descriptors for describing a target material based on information about a proportion of at least one element included in the target material in the target material and attribute values of X attributes corresponding to the at least one element respectively; determining N1 core descriptors and K-N1 non-core descriptors from the K descriptors, wherein an influence degree of the core descriptors on the critical cooling rate of amorphization is higher than an influence degree of the non-core descriptors on the critical cooling rate of amorphization; and inputting at least part of the K descriptors into a target network for prediction to obtain a predicted value corresponding to the critical cooling rate of amorphization of the target material, wherein the target network is a network trained by Y sample materials, the target network comprises a plurality of sub-networks with the same structure and arranged in a hierarchical manner, each sub-network comprises N input nodes and 1 output node, the output node of a sub-network in an i-th level is used as the input node of a sub-network in an (i+1)-th level, each sub-network in a first level is inputted with the N1 core descriptors and N-N1 non-core descriptors, the N-N1 non-core descriptors are part of the K-N1 non-core descriptors, and the non-core descriptors inputted into different sub-networks are not completely the same; wherein the X, the K, the N1, the Y, and the N are integers greater than 1, and the i is an integer greater than or equal to 1.

[0008] In a second aspect, the specification provides a training method of a target network, the target network being configured to predict a critical cooling rate of amorphization of a material, the method comprising: obtaining an experimental value of each of Y sample materials on the critical cooling rate of amorphization, each sample material comprising at least one element; for each sample material, generating K descriptors for describing the sample material based on proportion information of the at least one element in the sample material and attribute values of X attributes corresponding to the at least one element respectively, and determining N1 core descriptors and K-N1 non-core descriptors from the K descriptors, the core descriptors having a higher influence on the critical cooling rate of amorphization than the non-core descriptors; inputting part of the K descriptors corresponding to each sample material into the target network to obtain a predicted value corresponding to the critical cooling rate of amorphization of the sample material, wherein: the target network comprises a plurality of sub-networks having the same structure and arranged in a hierarchical manner, each sub-network comprising N input nodes and 1 output node, the output node of a sub-network in an i-th level being used as the input node of a sub-network in an (i+1)-th level, each sub-network in the first level being inputted with the N1 core descriptors and N-N1 non-core descriptors, the N-N1 non-core descriptors being part of the K-N1 non-core descriptors, and the non-core descriptors inputted into different sub-networks being not completely the same; and updating parameters of the target network with a training target of minimizing a difference between the predicted value and the experimental value; wherein the X, the K, the N1, the Y, and the N are integers greater than 1, and the i is an integer greater than or equal to 1.

[0009] In a third aspect, the specification provides a prediction method of a eutectic point, comprising: predicting critical cooling rates of amorphization of a plurality of materials formed by a plurality of elements in a target multi-element system based on the method of the first aspect, each material in the plurality of materials comprising the plurality of elements and having different proportion information of the plurality of elements; and determining a target material with a minimum critical cooling rate of amorphization from the plurality of materials, and determining the eutectic point of the target multi-element system based on the target material.

[0010] In a fourth aspect, the specification further provides a prediction system configured to predict a critical cooling rate of amorphization of a target material, comprising: at least one storage medium storing at least one instruction set; and at least one processor in communication connection with the at least one storage medium, wherein when the prediction system is running, the at least one processor reads the at least one instruction set, and executes the prediction method of the first aspect according to an indication of the at least one instruction set.

[0011] In a fifth aspect, the present specification also provides a training system configured to train a target network for predicting a critical cooling rate of amorphization of a material, comprising: at least one storage medium storing at least one instruction set; and at least one processor in communication with the at least one storage medium, wherein, when the training system is running, the at least one processor reads the at least one instruction set and executes the training method of the second aspect according to the indication of the at least one instruction set.

[0012] In a sixth aspect, the present specification also provides a prediction system configured to predict a eutectic point of a multi-element system, comprising: at least one storage medium storing at least one instruction set; and at least one processor in communication with the at least one storage medium, wherein, when the prediction system is running, the at least one processor reads the at least one instruction set and executes the prediction method of the third aspect according to the indication of the at least one instruction set.

[0013] Other functions of the prediction method, the training method and the system provided by the present specification will be partially listed in the following description. The creative aspects of the prediction method, the training method and the system provided by the present specification can be fully explained by practicing or using the methods, systems and combinations described in the following detailed examples. BRIEF DESCRIPTION OF DRAWINGS

[0014] In order to more clearly illustrate the technical solutions in the embodiments of the present specification, the following will briefly introduce the drawings needed to be used in the embodiment description. Obviously, the drawings in the following description are only some embodiments of the present specification, and other drawings can also be obtained by those skilled in the art without creative labor on the basis of these drawings.

[0015] Figure 1 A schematic diagram of a TTT curve provided by an embodiment of the present specification is shown;

[0016] Figure 2 A schematic diagram of a hierarchical structure of a target network provided by an embodiment of the present specification is shown;

[0017] Figure 3 A schematic diagram of a structure of a sub-network provided by an embodiment of the present specification is shown;

[0018] Figure 4 A hardware structure diagram of a system provided by an embodiment of the present specification is shown;

[0019] Figure 5 A flowchart of a training method of a target network provided by an embodiment of the present specification is shown;

[0020] Figure 6An iterative schematic diagram of a genetic algorithm provided according to an embodiment of the present specification is shown;

[0021] Figure 7 A schematic diagram of an inference process of a target network provided according to an embodiment of the present specification is shown;

[0022] Figure 8 A prediction result schematic diagram of different network models provided according to an embodiment of the present specification is shown;

[0023] Figure 9 A prediction result schematic diagram of different element systems using a target network provided according to an embodiment of the present specification is shown;

[0024] Figure 10 A flowchart of a prediction method of an amorphization critical cooling rate provided according to an embodiment of the present specification is shown; and

[0025] Figure 11 A flowchart of a prediction method of a eutectic point provided according to an embodiment of the present specification is shown. DETAILED DESCRIPTION

[0026] The following description provides specific applications and requirements of the present specification, which is intended to enable a person skilled in the art to manufacture and use the contents of the present specification. Various modifications to the disclosed embodiments are apparent to those skilled in the art, and the general principles defined herein can be applied to other embodiments and applications without departing from the spirit and scope of the present specification. Therefore, the present specification is not limited to the embodiments shown, but is consistent with the widest scope of the claims.

[0027] The terms used herein are used only for the purpose of describing specific example embodiments, and are not limiting. For example, unless the context clearly indicates otherwise, as used herein, the singular forms "a", "an", and "the" can also include the plural forms. When used in the present specification, the terms "comprise", "include" and / or "contain" mean that the associated integer, step, operation, element and / or component exists, but do not exclude the presence of one or more other features, integers, steps, operations, elements, components and / or groups.

[0028] In view of the following description, these features of the present specification and other features, as well as the operation and function of related elements of the structure, and the economy of combination and manufacture of components can be significantly improved. Referring to the drawings, all of which form part of the present specification. However, it should be clearly understood that the drawings are for illustrative and descriptive purposes only and are not intended to limit the scope of the present specification. It should also be understood that the drawings are not drawn to scale.

[0029] The flowcharts used in this specification illustrate operations implemented according to some embodiments of this specification. It should be clearly understood that the operations in the flowcharts may not be implemented in a sequential order. Instead, the operations may be implemented in reverse order or simultaneously. Furthermore, one or more additional operations may be added to the flowcharts. One or more operations may be removed from the flowcharts.

[0030] Previously, researchers proposed various critical cooling rates (Rc) for the amorphization of materials. c Theories such as Johnson's theory, which states that the critical cooling rate for amorphization is related to the critical size of a material, are relevant.

[0031] Figure 1 In Figure a), the relationship between the theoretical and experimental values ​​of the critical cooling rate for amorphization, derived from Johnson's theory, is shown. Blue dots represent the theoretical value of the critical cooling rate for amorphization before correction, while red dots represent the theoretical value after correction using a coefficient. Overall, there is still a certain discrepancy between the theoretical and experimental values ​​of the critical cooling rate for amorphization before and after correction; therefore, this theory cannot accurately determine the critical cooling rate for amorphization of materials.

[0032] In addition, researchers can also plot the time-temperature-transformation (TTT) curve of materials, for example... Figure 1 (b), (c), and (d) are used to determine the critical cooling rate for amorphization of the material. For example, the critical cooling rate for amorphization can be calculated using the following formula:

[0033] R c =(T m -T n ) / t n

[0034] Wherein: T m T is the melting point temperature. n The temperature at the tip of the nose, t n The nucleation time is the time on the TTT curve, and the parameters in the formula can be obtained based on the TTT curve.

[0035] Although TTT curves are crucial for understanding the formation process of amorphous materials, constructing them requires precise isothermal crystallization behavior measurements over a wide temperature range. This necessitates accurate control of experimental conditions such as temperature and time, and the measurements must be performed over a broad temperature range. In other words, numerous experiments are required, with independent isothermal crystallization measurements at each temperature point. This high level of experimental complexity and difficulty hinders the rapid study of amorphous materials.

[0036] In recent years, machine learning (ML) techniques have been rapidly developed in the field of material science. Related models can learn the rules from a large amount of experimental data, and construct the mapping relationship between the performance to be studied of the material and the material attributes (for example, descriptors), so as to predict the related performance of the material. Descriptors refer to information describing various attributes or characteristics of the material.

[0037] Generally, the prediction performance of the machine learning model is highly dependent on the number and quality of the training samples. For sample materials, the more the number of descriptors describing the sample materials, the more likely it is to train a good prediction network. However, the more the number of descriptors, the more the number of experimental data of the critical cooling rate of amorphization of the sample materials is needed. Since the experimental data of the critical cooling rate of amorphization is difficult to obtain and requires a large amount of time cost. Therefore, how to ensure the accuracy of the prediction results under the premise of overcoming the difficulty of training the prediction network due to the lack of samples and the large number of descriptors of the material is a difficult problem in the current research process.

[0038] The following will be combined Figure 2 The application scenarios of predicting the critical cooling rate of amorphization provided by the present specification are introduced.

[0039] Figure 2 The application scenarios of predicting the critical cooling rate of amorphization provided by the present specification are introduced. Figure 2 As shown in the figure, scenario 001 can include a training system 100 and a prediction system 200.

[0040] Scenario 001 can be divided into two stages, a training stage and a prediction stage.

[0041] Training stage

[0042] The training system 100 can train a target network capable of predicting the critical cooling rate of amorphization of the material based on a plurality of sample materials. After the training system 100 is trained, the target network can be deployed in the prediction system 200.

[0043] Prediction stage

[0044] The prediction system 200 can call the target network to predict the critical cooling rate of amorphization of the target material. In addition, the prediction system 200 can also be used to predict the eutectic point of a multi-element system.

[0045] Eutectic Point: the material with a certain element ratio in a multi-element system can have a eutectic reaction (the material simultaneously changes from a liquid state to a solid state of each element) at a constant temperature, and the certain element ratio is the eutectic point in the multi-element system. For example, the multi-element system is Zr-Cu-Al, and the element ratio information of elements Zr, Cu and Al in the material is 50:40:10. Then, the eutectic reaction can occur at a constant temperature, and Zr 50 Cu 40 Al 10 is the eutectic point in the Zr-Cu-Al system.

[0046] In some embodiments, the training system 100 can store data and instructions for implementing the training method of the target network, and can execute or be used to execute the data and instructions. In some embodiments, the training system 100 can include a hardware device with data information processing function and necessary programs required to drive the hardware device to work.

[0047] In some embodiments, the prediction system 200 can store data and instructions for implementing the prediction method of the amorphization critical cooling rate or eutectic point, and can execute or be used to execute the data and instructions. In some embodiments, the prediction system 200 can include a hardware device with data information processing function and necessary programs required to drive the hardware device to work.

[0048] It can be understood that the training system 100 and the prediction system 200 can correspond to the same system or different systems, and the present specification does not limit this.

[0049] It should be noted that the training system 100 can correspond to one device or a device cluster, and the present specification does not limit this. When the training system 100 corresponds to one device, the training method of the target network can be completely executed on the device. When the training system 100 corresponds to a device cluster, the training method of the target network can be cooperatively executed on multiple devices corresponding to the device cluster, or the training method of the target network can have other execution manners, and the present specification does not limit this.

[0050] The prediction system 200 can correspond to one device or a device cluster, and the present specification does not limit this. When the prediction system 200 corresponds to one device, the prediction method of the amorphization critical cooling rate or eutectic point can be completely executed on the device. When the prediction system 200 corresponds to a device cluster, the prediction method of the amorphization critical cooling rate or eutectic point can be cooperatively executed on multiple devices corresponding to the device cluster, or the prediction method of the amorphization critical cooling rate or eutectic point can have other execution manners, and the present specification does not limit this.

[0051] The target network is a hierarchical neural network, which has a network structure as shown in FIG. 1, including F levels, i.e., a first level network to an Fth level network. Each level network can include one or more sub-networks, and the number of sub-networks included in each level network gradually decreases from the first level to the Fth level. For example, the first level network includes m1 sub-networks, the second level network includes m2 sub-networks, m2 < m1, and so on. Figure 3 represents a first sub-network in the first level, represents a first sub-network in the second level, and so on. The Fth level network includes one sub-network. The output of each sub-network in the first level is taken as the input of each sub-network in the second level, and so on. The network structure of each sub-network can be the same, which is not limited in the present specification.

[0052] The present specification does not limit the decreasing manner of the number of sub-networks in each level. For example, the number of sub-networks in each level decreases regularly, such as decreasing by a fixed number, i.e., the difference between the number of sub-networks in the first level and the number of sub-networks in the second level is the same as the difference between the number of sub-networks in the second level and the number of sub-networks in the third level. For another example, the number of sub-networks in each level decreases irregularly, such as decreasing by a non-fixed number.

[0053] It should be noted that the present specification does not limit the number of network levels of the target network, and the number of sub-networks included in each level.

[0054] For example, the sub-network is an artificial neural network (ANN) or a convolutional neural network (CNN), and the present specification does not limit the network type of the sub-network.

[0055] Figure 4 A hardware structure diagram of a system 400 provided according to an embodiment of the present specification is shown.

[0056] As shown in FIG. 4, the system 400 can be the training system 100 or the prediction system 200 in FIG. 1. Figure 4 Figure 1 The system 400 includes at least one storage medium 430 and at least one processor 420. In some embodiments, the system 400 can further include a communication port 450 and an internal communication bus 410. In addition, the system 400 can further include an I / O component 460.

[0057] The system 400 includes at least one storage medium 430 and at least one processor 420. In some embodiments, the system 400 can further include a communication port 450 and an internal communication bus 410. In addition, the system 400 can further include an I / O component 460.

[0058] ​​The internal communication bus 410 can connect different system components. For example, the internal communication bus 410 can connect the storage medium 430, the processor 420, the communication port 450, and the I / O component 460.

[0059] The I / O component 460 supports input / output between the system 400 and other components.

[0060] The communication port 450 is used for data communication between the system 400 and the outside world. For example, the communication port 450 can be used for data communication between the system 400 and a network. The communication port 450 can be a wired communication port or a wireless communication port.

[0061] In some embodiments, the network can be any type of wired or wireless network, or a combination thereof. For example, the network can include a cable network, a wired network, a fiber optic network, a telecommunications network, an intranet, the Internet, a Local Area Network (LAN), a Wide Area Network (WAN), a Wireless Local Area Network (WLAN), a Metropolitan Area Network (MAN), a Public Switched Telephone Network (PSTN), a Bluetooth network™, a short-range wireless network (ZigBee™), a Near Field Communication (NFC) network, or the like.

[0062] In some embodiments, the network can include one or more network access points. For example, the network can include wired or wireless network access points, such as a base station or an Internet exchange point. Through the access point, one or more components of each device corresponding to the system 400 can be connected to the network to exchange data or information.

[0063] The storage medium 430 can include a data storage device. The data storage device can be a non-transitory storage medium or a transitory storage medium. For example, the data storage device can include one or more of a disk 432, a read-only memory (ROM) 434, or a random access memory (RAM) 436. The storage medium 430 also includes at least one instruction set stored in the data storage device. The instruction set can include computer program code, which can include programs, routines, objects, components, data structures, processes, modules, and the like, that perform the method of predicting the amorphous critical cooling rate or eutectic point or the method of training the target network provided in the present specification.

[0064] The processor 420 can be communicatively connected with the storage medium 430. The processor 420 is configured to execute the at least one instruction set. When the system 400 is running, the processor 420 reads the at least one instruction set and executes the prediction method of the amorphization critical cooling rate or eutectic point or the training method of the target network according to the indication of the at least one instruction set.

[0065] The processor 420 can be in the form of one or more processors. In some embodiments, the processor 420 can include one or more hardware processors, such as a microcontroller, a microprocessor, a reduced instruction set computer (RISC), an application-specific integrated circuit (ASIC), an application-specific instruction set processor (ASIP), a central processing unit (CPU), a graphics processing unit (GPU), a physics processing unit (PPU), a microcontroller unit, a digital signal processor (DSP), a field programmable gate array (FPGA), an advanced RISC machine (ARM), a programmable logic device (PLD), any circuit or processor capable of executing one or more functions, or the like, or any combination thereof.

[0066] For the sake of illustration only, only one processor 420 is shown in the system 400 in the accompanying drawings. However, it should be noted that the system 400 in the present specification can also include multiple processors. Therefore, the operations and / or method steps disclosed in the present specification can be executed by one processor as described in the present specification, or jointly executed by multiple processors. For example, if the processor 420 of the system 400 in the present specification executes step A and step B, it should be understood that step A and step B can also be executed jointly or separately by two different processors 420 (for example, a first processor executes step A, a second processor executes step B, or the first and second processors jointly execute steps A and B).

[0067] Figure 5 A flowchart of a training method P500 of a target network is shown, which is provided according to an embodiment of the present specification. The training system 100 can execute the training method P500 of the target network, which is used to predict the amorphization critical cooling rate of a material. As shown in the flowchart, the training method P500 of the target network includes the following steps. Figure 5

[0068] S510: Obtain Y experimental values of each sample material on the amorphization critical cooling rate, each sample material including at least one element.

[0069] Wherein Y is an integer greater than 1. The number of elements included in different sample materials can be different, and the proportion information corresponding to the elements can also be different. The sample material is, for example, an alloy material. For example, the sample material Ti 63 Be 37 ​For example, 63 is the proportion information corresponding to the element Ti, and 37 is the proportion information corresponding to the element Be.

[0070] The present specification collects experimental data of 119 metallic glasses, and cleanses the data to obtain Y sample materials each having an experimental value of a critical cooling rate for amorphization.

[0071] S520: For each sample material, based on the proportion information of at least one element in the sample material and the attribute values of X attributes corresponding to the at least one element respectively, K descriptors for describing the sample material are generated, and N1 core descriptors and K1 non-core descriptors are determined in the K descriptors, the influence degree of the core descriptors on the critical cooling rate for amorphization is higher than that of the non-core descriptors, K1 = K-N1.

[0072] In some embodiments, the X attributes include at least two dimensions of the following: periodic table dimension; thermodynamic dimension; physical dimension; and crystallographic dimension. In this embodiment, the element attributes of multiple dimensions are considered, so that the K descriptors obtained can more comprehensively describe the sample materials, widely cover the material properties, avoid missing important descriptors, and provide a good foundation for improving the prediction accuracy and generalization ability of the target network.

[0073] For example, the X attributes refer to at least part of Table 1.

[0074] Table 1

[0075]

[0076]

[0077] In Table 1, BCC refers to body-centered cubic (Body Center Cubic), FCC refers to face-centered cubic (Face Center Cubic), ICSD refers to inorganic crystal structure database (Inorganic Crystal Structure Database), and GS refers to ground state (Ground State).

[0078] For example, the sample material is Zr 55 Al 19 Co 19 Cu7, the K descriptors of Zr 55 Al 19 Co 19 Cu7 can be generated based on the following: the proportion of the element Zr the proportion of the element Al the proportion of the element Co The proportion of the Cu element and the attribute values of at least part of the attributes listed in Table 1 corresponding to the Zr element, the attribute values of the at least part of the attributes corresponding to the Al element, the attribute values of the at least part of the attributes corresponding to the Co element, and the attribute values of the at least part of the attributes corresponding to the Cu element.

[0079] The following describes the generation of the K descriptors of the sample material #1, and the K descriptors of other sample materials can be similarly generated.

[0080] In some embodiments, the K descriptors of the sample material #1 include at least one of the following groups:

[0081] The first group of descriptors is used to describe the statistical characteristics of the sample material #1 on the X attributes.

[0082] The second group of descriptors is used to describe the valence electron occupation state of the sample material #1.

[0083] The third group of descriptors is used to describe the ionicity of the sample material #1.

[0084] The fourth group of descriptors is used to describe the conformational entropy (CE) of the sample material #1.

[0085] In this embodiment, the K descriptors can describe different aspects of the characteristics of the sample material, and the description of the sample material is more comprehensive, which can support the prediction of complex multi-element materials, improve the prediction accuracy of the target network, and enhance the generalization ability of the target network.

[0086] For example, the first group of descriptors is generated by training the system 100 to obtain P statistical values of the characteristics of the sample material #1 on each of the X attributes from multiple statistical dimensions based on the proportion information of each element included in the sample material #1 in the sample material #1 and the attribute values of each element on the attribute, and then generating the first group of descriptors based on the P statistical values of the sample material #1 on each of the X attributes. The number of the first group of descriptors is equal to X*P. In this example, the first group of descriptors involves multiple statistical dimensions, the number of descriptors and the statistical dimensions involved in the descriptors are more, the basic statistical characteristics of the sample material are mined, the sample material can be accurately and comprehensively described, and the training of the target network is facilitated.

[0087] Taking attribute #1 as an example, the training system 100 can obtain P statistical values of the characteristics of the sample material #1 in attribute #1 from multiple statistical dimensions, and the P statistical values are all the descriptors corresponding to attribute #1 in the first group of descriptors. The generation process of all the descriptors corresponding to attribute #1 in the first group of descriptors is mainly introduced below, and the descriptors corresponding to other attributes in the first group of descriptors are similar and will not be repeated.

[0088] For example, the multiple statistical dimensions include statistical dimension #1, statistical dimension #2, statistical dimension #3, statistical dimension #4 and statistical dimension #5. The statistical dimension #1 is used to statistically obtain the weighted average value of the attribute values of each element included in the sample material #1 in attribute #1. The formula corresponding to the statistical dimension #1 is as follows:

[0089]

[0090] Wherein, x i represents the proportion of the i-th element in the chemical formula of the sample material #1, f i represents the attribute value of the i-th element in attribute #1, represents the descriptor corresponding to attribute #1 obtained from the statistical dimension #1. Assuming that the sample material #1 is Zr 55 Al 19 Co 19 Cu7, the training system 100 can determine

[0091] The statistical dimension #2 is used to statistically obtain the weighted deviation of the attribute values of each element included in the sample material #1 in attribute #1. The formula corresponding to the statistical dimension #2 is as follows:

[0092]

[0093] Wherein, represents the descriptor corresponding to attribute #1 obtained from the statistical dimension #2.

[0094] The statistical dimension #3 is used to statistically obtain the standard deviation of the attribute values of each element included in the sample material #1 in attribute #1. The formula corresponding to the statistical dimension #3 is as follows:

[0095]

[0096] Wherein, f represents the descriptor corresponding to attribute #1 obtained from the statistical dimension #3.

[0097] The statistical dimension #4 is used to statistically obtain the maximum value, the minimum value, the value range in the attribute values or the weighted attribute values of each element included in the sample material #1 in attribute #1. The formula corresponding to the statistical dimension #4 is as follows:

[0098] (f i )_min,max,range (4)

[0099] (x i *f i )_min,max,range (5)

[0100] The training system 100 can obtain 6 descriptors corresponding to attribute #1 from the statistical dimension #4 statistics as follows:

[0101] (f i )_min represents the minimum value of the attribute value of each element included in the sample material #1 on attribute #1;(f i )_max represents the maximum value of the attribute value of each element included in the sample material #1 on attribute #1;(f i )_range represents the value range of the attribute value of each element included in the sample material #1 on attribute #1, which can be the difference between (f i )_max and (f i )_min.(x i *f i )_min represents the minimum value of the weighted attribute value of each element included in the sample material #1 on attribute #1;(x i *f i )_max represents the maximum value of the weighted attribute value of each element included in the sample material #1 on attribute #1;(x i *f i )_range represents the value range of the weighted attribute value of each element included in the sample material #1 on attribute #1, which can be the difference between (x i *f i )_max and (x i *f i )_min.

[0102] The statistical dimension #5 is used to statistically the deviation degree of different elements in the sample material #1 on attribute #1. The formula corresponding to the statistical dimension #5 is as follows:

[0103]

[0104] Wherein, x i1 represents the proportion of the i1th element in the chemical formula of the sample material #1, x i2 represents the proportion of the i2th element in the chemical formula of the sample material #1, f i1 represents the attribute value of the i1th element on attribute #1, f i2represents the property value of the ith2 element on property #1, AP represents the degree of deviation of the weighted property value of different elements on property #1, AP 加权 represents the degree of deviation of the weighted property value of different elements on property #1.

[0105] The training system 100 can obtain 8 descriptors corresponding to property #1 from the statistical dimension #5 statistics as follows:

[0106] AP_ave represents the average value of the deviation of different elements on property #1 in all elements included in the sample material #1; AP_min represents the minimum value of the deviation of different elements on property #1 in all elements included in the sample material #1; AP_max represents the maximum value of the deviation of different elements on property #1 in all elements included in the sample material #1; AP_range represents the value range of the deviation of different elements on property #1 in all elements included in the sample material #1, which can be the difference between AP_max and AP_min; AP 加权 _ave represents the average value of the weighted property value deviation of different elements on property #1 in all elements included in the sample material #1; AP 加权 _min represents the minimum value of the weighted property value deviation of different elements on property #1 in all elements included in the sample material #1; AP 加权 _max represents the maximum value of the weighted property value deviation of different elements on property #1 in all elements included in the sample material #1; AP 加权 _range represents the value range of the weighted property value deviation of different elements on property #1 in all elements included in the sample material #1, which can be the difference between AP 加权 _max and AP 加权 _min. AP, AP 加权 and the atomic size and electronegativity change between different elements, which will have an important influence on the structure and performance of the material, and the training system 100 considers AP, AP 加权 is very important to describe the comprehensiveness of the material. In addition, if the sample material #1 is composed of a single element, the above 8 descriptors are all zero.

[0107] As can be seen, the training system 100 can obtain 17 descriptors corresponding to property #1 through the above multiple statistical dimensions. If the X attributes are the 53 kinds shown in Table 1, the first group of descriptors obtained by the training system 100 for the sample material #1 can include 17*53=901 descriptors, which comprehensively cover the basic statistical properties of the sample material #1.

[0108] In some embodiments, the second group of descriptors comprises: occupation information of Q valence electrons in the sample material #1, wherein the occupation information of the z-th valence electron is obtained by:

[0109] For each element in the sample material #1, the training system 100 determines the number of each valence electron and the total number of valence electrons in the element based on the attribute values of at least part of the X attributes corresponding to the element; and for the z-th valence electron, the training system 100 determines the occupation information of the z-th valence electron based on the proportion information corresponding to each element in the sample material #1, the number of the z-th valence electron, and the total number of valence electrons corresponding to each element.

[0110] That is, each descriptor in the second group of descriptors is used to describe the valence electron occupation state, and the second group of descriptors obtained by the training system 100 comprises Q descriptors, and each valence electron can correspond to a descriptor. The valence electron has an important influence in the preparation process of the amorphous material, and therefore, considering the occupation states of multiple valence electrons in the descriptors can characterize the key attributes of the sample material, and can improve the prediction accuracy of the target network on the amorphization critical cooling rate.

[0111] For example, the training system 100 obtains the descriptor corresponding to the z-th valence electron based on the following formula:

[0112]

[0113] wherein F z represents the descriptor corresponding to the z-th valence electron, E z represents the number of the z-th valence electron in the i-th element in the chemical formula of the sample material #1, E n represents the total number of Q valence electrons in the i-th element, such as valence electrons p, s, d, and f. Specifically, the descriptor corresponding to the valence electron p is The descriptors corresponding to other valence electrons are similar, and thus the training system 100 can obtain four descriptors.

[0114] In some embodiments, the third group of descriptors is obtained based on the proportion information corresponding to each element in the sample material #1, and the electronegativity corresponding to each element and any one of the following: the maximum value of the electronegativity corresponding to each element included in the sample material #1; and the average value of the electronegativity corresponding to each element included in the sample material #1. The electronegativity is a measure of the ability of an atom of an element to attract electrons in a compound, and therefore, considering the electronegativity in the descriptors can characterize the key attributes of the sample material, and can improve the prediction accuracy of the target network on the amorphization critical cooling rate.

[0115] Exemplarily, the training system 100 obtains the third group of descriptors based on the following formula:

[0116]

[0117] wherein I represents the third group of descriptors, represents the maximum value of the electronegativity corresponding to each element included in the sample material #1, or the average value of the electronegativity corresponding to each element included in the sample material #1; when represents the maximum value of the electronegativity, the training system 100 can obtain the first descriptor in the third group of descriptors based on formula (9); when represents the average value of the electronegativity, the training system 100 can obtain the second descriptor in the third group of descriptors based on formula (9); when represents the average value of the electronegativity, the training system 100 can further obtain the third descriptor in the third group of descriptors, specifically, when the I calculated by the training system 100 based on formula (9) is greater than 1.7, the third descriptor is 1, and if the I calculated by the training system 100 based on formula (9) is not greater than 1.7, the third descriptor is 0 (which is also the standard for determining the formation of ionic bonds).

[0118] In some embodiments, the fourth group of descriptors is obtained based on the proportion information corresponding to each element in the sample material #1, the Boltzmann constant and the room temperature. The configurational entropy is an important parameter for measuring the degree of disorder of atomic distribution, and is closely related to the critical cooling rate of amorphization of amorphous materials. Considering the configurational entropy when generating the descriptors can describe the key attributes of the sample material, and can improve the prediction accuracy of the target network for the critical cooling rate of amorphization.

[0119] Exemplarily, the training system 100 obtains the fourth group of descriptors based on the following formula:

[0120] ΔS con =-k B T∑x i *lnx i (10)

[0121] wherein ΔS con represents the configurational entropy; k B represents the Boltzmann constant; and T represents the room temperature, such as 298K. The training system 100 can obtain one descriptor based on formula (10).

[0122] In summary, in the case of 53 element attributes, for each sample material, the training system 100 generates 901 first group of descriptors, 4 second group of descriptors, 3 third group of descriptors and 1 fourth group of descriptors based on formulas (1) to (10), i.e., the total number of K descriptors is 909.

[0123] In the field of materials science, obtaining the critical cooling rate for amorphization of materials experimentally is extremely time-consuming. Therefore, when the number of available sample materials is limited, training a neural network using only 909 descriptors as features of a single sample material is prone to overfitting, especially when the sample material contains a large number of elements, making it even more difficult to train a network with accurate predictions. For example, in an ANN with two hidden layers, inputting 909 descriptors would require training to determine over a billion hyperparameters, which is difficult to achieve the desired results with a limited number of sample materials. Therefore, this specification employs a Genetic Algorithm (GA) to reduce the number of input descriptors in individual subnetworks of the target network.

[0124] For example, the training system 100 groups the K descriptors based on the competitive swarm optimizer (CSO) algorithm, with descriptors within each group competing in pairs. After each competition, the winning descriptor proceeds to the next iteration, while the losing descriptors can learn from the winning descriptor to update their position and velocity. The basic principle of the CSO algorithm can be seen in the following formula:

[0125]

[0126]

[0127] Where t represents the number of iterations; and It is in [0,1] n Three vectors randomly generated within the range; for each descriptor, '1' indicates that the descriptor was selected after the competition, and '0' indicates that the descriptor was not selected after the competition; 'n' represents the number of descriptors, for example, 'n' is 909; variables and These represent the winning and losing descriptors, respectively. φ represents the average position of the descriptor population in the t-th iteration, and φ determines the position of the population. The influence This represents the velocity of the i-th descriptor in the t-th iteration.

[0128] In this example, the training system 100 uses 1-R from the test set (at least a portion of the materials in the Y sample materials). 2As the fitness function, the fitness function is minimized through strategic selection of descriptors. Specifically, in the early stage of iteration, the training system 100 randomly selects multiple combinations of descriptors and their speeds, and then randomly selects two combinations of descriptors to evaluate the fitness function. The descriptor combination with the lower fitness function value is the winner, and the descriptor combination with the higher fitness function value is the loser. During the iteration process, updates and iterations are performed according to formulas (11) and (12). The iteration process terminates when the fitness function value no longer decreases.

[0129] Figure 6 The GA iteration process is illustrated, with the x-axis representing the number of GA iterations, the left y-axis representing the number of descriptors (d), and the right y-axis representing the test R. 2 During the GA iteration process, multiple preferred descriptor combinations will emerge. The difference between the predicted value and the experimental value of the amorphization critical cooling rate of the sample material obtained by the preferred descriptor combination is less than or equal to a first preset threshold.

[0130] For example, see [link to previous article] Figure 6 After iterative selection, the training system determined that when N = 25, the prediction accuracy reached an inflection point, and the test R... 2 It tends to stabilize. In other words, when the number of descriptors for each subnetwork input is 25, the critical cooling rate for amorphization of the material can be predicted relatively accurately.

[0131] It should be noted that the determination of N may be related to the number of sample materials participating in GA, therefore this specification does not limit the specific value of N.

[0132] In addition, during the iteration process, descriptors that appear more frequently than or equal to a second preset threshold among multiple preferred descriptor combinations are used as core descriptors required to predict the critical cooling rate of amorphization, while descriptors that appear less frequently than the second preset threshold are used as non-core descriptors required to predict the critical cooling rate of amorphization.

[0133] Table 2 shows the six core descriptors required to predict the critical cooling rate of amorphization.

[0134] Table 2

[0135]

[0136]

[0137] For example, AP_ave_GSvolume_pa represents the average deviation of different elements in the ground-state atomic volume of the sample material, which can be obtained based on formula (6). AP_max_weighted_Atomic_Number represents the maximum weighted deviation of different elements in the atomic number of the sample material, which can be obtained based on formula (7). std_phi represents the standard deviation of the attribute value of each element in the work function of the sample material, which can be obtained based on formula (3). std_Melting T represents the standard deviation of the attribute value of each element in the melting point of the sample material, which can be obtained based on formula (3). range_weight_HeatCapacityMolar represents the range of the weighted attribute value of different elements in the molar heat capacity of the sample material, which can be obtained based on formula (5). AP_ave_phi represents the average deviation of different elements in the work function of the sample material, which can be obtained based on formula (6).

[0138] This specification employs a genetic algorithm to select 25 key descriptors from 909 descriptors, and further refines them into 6 core descriptors. This significantly reduces the training complexity of the target network while retaining descriptors crucial for predicting the critical cooling rate of amorphization. Furthermore, existing research indicates that the formation process of amorphous materials is closely related to properties such as atomic volume. The nonlinear relationship between the aforementioned 6 core descriptors and the critical cooling rate of amorphization reveals the complex physical mechanisms involved in the formation of amorphous materials, and this relationship aligns with existing research on the formation mechanisms of amorphous materials. This provides a theoretical basis for further research on amorphous materials and plays a key role in the prediction accuracy of the target network.

[0139] S530: Input a portion of the K descriptors corresponding to each sample material into the target network for prediction to obtain the predicted value corresponding to the amorphization critical cooling rate of the sample material. Wherein: the target network includes multiple sub-networks with the same structure and arranged hierarchically. Each sub-network includes N input nodes and 1 output node. The output node of the sub-network in the i-th level serves as the input node of the sub-network in the (i+1)-th level. Each sub-network in the first level is input with the N1 core descriptors and N2 non-core descriptors. The N2 non-core descriptors are a portion of the K1 non-core descriptors, and the non-core descriptors input to different sub-networks are not completely identical, where N2 = N - N1.

[0140] Where X, K, K1, N1, N2, Y, and N are all integers greater than 1, and i is an integer greater than or equal to 1. Using a target network can avoid the overfitting problem during target network training when there are many descriptors but insufficient sample data. It should be noted that each sub-network can have different weighting factors during training.

[0141] In some embodiments, see Figure 7 The training system 100 generates m1 sets of descriptors based on the K descriptors, each set including the N1 core descriptors and N-N1 non-core descriptors; the m1 sets of descriptors are input into the m1 sub-networks of the first layer of the target network to obtain m1 intermediate predicted values ​​of the amorphization critical cooling rate; according to the order of i from 2 to F, the m1 sub-networks of the (i-1)th layer of the target network are... i-1 The critical cooling rate of amorphization obtained from the subnetwork is m i-1 The intermediate predicted values ​​are divided into m i Group input of m of the i-th layer of the target network i A sub-network was used to obtain the m-critical cooling rate for amorphization. i The intermediate predicted values ​​are then used as the final predicted values ​​for the amorphization critical cooling rate output by the sub-network of layer F. Where m1, F, and m are... i-1 All are integers greater than 1, m i It is an integer greater than or equal to 1.

[0142] In this embodiment, dividing the K descriptors into multiple groups and inputting them into multiple sub-networks avoids the problem of overfitting caused by too many descriptors inputting into a single sub-network, which would result in an excessive number of hyperparameters required for training due to insufficient sample data. Figure 7 The hierarchical structure of the target network shown allows descriptors to be distributed across multiple subnetworks, avoiding overfitting and expanding the number of descriptors to 909, thus enriching the dimensions of material characterization. For each subnetwork, the number of input descriptors is relatively small, resolving the machine learning contradiction arising from a large number of descriptors but a small number of sample materials. Furthermore, testing (see below for the testing process) demonstrates that the target network can fully utilize the information from a large number of descriptors, achieving higher prediction accuracy than other neural networks, which is beneficial for the study of amorphous materials.

[0143] For example, when K is 909, the training system 100 can obtain the following from 909-6=903 non-core descriptors through random combination. There are 6 non-core descriptor groups, and each non-core descriptor group plus 6 core descriptors can be obtained. There are 10 descriptor groups. In other words, the number of subnetworks in the first level can reach 100,000. However, this specification does not limit the number of subnetworks in the first level.

[0144] Different descriptor sets contribute to the prediction of the critical cooling rate of amorphization to varying degrees. This degree can be determined during the training of the target network. Using different input descriptor sets for each sub-network in the first layer can improve the generalization ability of the target network and reduce the possibility of overfitting. Compared to traditional methods that train a network using a single descriptor combination, the training method described in this specification considers various descriptor combinations, capturing or exploring the potential impact of different descriptor combinations on the prediction of the critical cooling rate of amorphization, thereby training a target network with higher prediction accuracy. Traditional algorithms, such as XGBoost and CNN, do not consider the differences in the contribution of different descriptor sets to the prediction of the critical cooling rate of amorphization, nor do they consider the differences in the performance of different descriptor sets on the target network.

[0145] For the first level of the target network, the input of each subnetwork is a descriptor set, and each descriptor set includes N (e.g., 25) descriptors; that is, one input node of each subnetwork in the first level corresponds to one descriptor. For example... The input is descriptor group 1, and so on. Each descriptor group includes N1 (e.g., 6) core descriptors and N2 (e.g., 19) non-core descriptors. At least one of the N2 non-core descriptors in different descriptor groups must be different. For the second level, the input to each sub-network is N intermediate predictions from the outputs of the sub-networks in the first level, such as... For the third level, the input for each subnetwork is the output of N subnetworks from the second level. to The N intermediate predicted values ​​output are respectively to The intermediate predicted values, and so on. For the F-th level, the subnetwork F The input is the intermediate prediction values ​​of the output of the N sub-networks at the F-1 level.

[0146] During training, the target network can learn iterative knowledge from different sub-networks. This knowledge can include overlapping information as well as unique knowledge from each sub-network, thus improving prediction accuracy. When the amount of sample material is limited, training a single neural network with only 909 descriptors avoids an excessive number of hyperparameters, which could negatively impact training accuracy. As the number of layers in the target network increases, the predicted value for the critical cooling rate of amorphization gradually converges.

[0147] For example, in the process of training the target network, the core descriptors input to each sub-network in the first layer are, for example, MD1 to MD6, and the outputs of each sub-network after the first layer are predicted values ​​about the critical cooling rate of amorphization.

[0148] S540: The parameters of the target network are updated with the training objective of minimizing the difference between the predicted and experimental values ​​of the critical cooling rate for amorphization of the sample material.

[0149] For example, this specification may use the coefficient of determination (R²). 2 The mean absolute percentage error (MAPE) and R are used as evaluation metrics for the target network. 2 The calculation formula is as follows:

[0150]

[0151]

[0152] Where n represents the number of sample materials in the current training round, y i This represents the experimental value of the critical cooling rate for amorphization of the i-th sample material. F(x) represents the average experimental value of the critical cooling rate for amorphization of the sample material. i R represents the predicted value of the i-th sample material regarding the critical cooling rate for amorphization, as predicted by the target network. 2 A higher MAPE value and a lower MAPE value indicate better performance of the target network, meaning more accurate prediction results.

[0153] For example, the training system 100 divides the Y sample materials into a training set and a test set, and trains the following network models, including the target network: 145-XGBoost, 909-XGBoost, 145-CNN, 909-CNN, 145-HNN, and 909-HNN. Here, the numbers represent the number of descriptors in the input network model, and HNN represents the target network.

[0154] For example, "145-XGBoost" indicates that the network to be trained is XGBoost and the input of XGBoost is the 145 descriptors used by other current machine learning models; "909-XGBoost" indicates that the network to be trained is XGBoost and the input of XGBoost is the 909 descriptors provided in this specification; "145-CNN" indicates that the network to be trained is CNN and the input of CNN is the 145 descriptors; "909-CNN" indicates that the network to be trained is CNN and the input of CNN is the 909 descriptors; "145-HNN" indicates that the network to be trained is the target network and the input of the target network is the 145 descriptors; "909-HNN" indicates that the network to be trained is the target network and the input of the target network is the 909 descriptors.

[0155] Figure 8 The learning results of the above network models are shown.

[0156] For example, in a), the horizontal axis represents different network models, and the left vertical axis represents the test R. 2 b) represents the training and testing results of "909-CNN". c) represents the training and testing results of "909-HNN". Wherein, training R... 2 This indicates the R-value of the network model on the training set sample material. c The relationship between predicted and experimental values; testing R 2 This indicates the R-value of the network model for the sample materials in the test set. c The relationship between predicted and experimental values.

[0157] See Figure 8 It can be seen that when the traditional CNN model uses 909 descriptors, the test set R... 2 The score is only 0.58, while the HNN model performs better on the test set R under the same descriptor. 2 Achieving a score of 0.942, the prediction performance is significantly better than other models. Furthermore, CNN models are prone to overfitting with high-dimensional descriptors (e.g., 909 descriptors), while the target network provided in this specification introduces a hierarchical structure, decomposing the complex neural network into multiple sub-networks, effectively avoiding overfitting. Optimization can be performed layer by layer during training, significantly improving prediction accuracy. Moreover, while maintaining prediction accuracy, the number of descriptors input to each sub-network is greatly reduced. Compared to training a traditional network model with 909 descriptors, the hierarchical parallel training fully utilizes the computational resources of each sub-model, reducing training time by 30%-40% and improving prediction efficiency.

[0158] The target network trained in this manual can be applied to interpolation prediction of multi-element systems included in sample materials. Taking the multi-element system Zr-Cu-Al as an example, the target network can predict the critical cooling rate for amorphization of different materials with different proportions of Zr, Cu, and Al in the Zr-Cu-Al system.

[0159] In addition, the target network trained in this manual can also be used for extrapolation prediction of multi-element systems that do not appear in the sample materials in the experimental data. For example, if the Ge-Sb-Te system does not appear in the sample materials, the target network can predict the critical cooling rate of amorphization for different materials with different proportions of elements Ge, Sb, and Te in the Ge-Sb-Te system.

[0160] See Figure 9Figures a), c), and d) show the predicted critical cooling rates for amorphization under different elemental proportions in the Zr-Cu-Al system. Figure b) shows the predicted critical cooling rates for amorphization under different elemental proportions in the Ge-Sb-Te system. From the prediction results shown in a), the region with the lowest predicted critical cooling rate for amorphization (circled in the figure) and the proportions of each element in the corresponding material can be identified. The critical cooling rate for amorphization can quantitatively characterize glass forming ability (GFA), and the GFA of a material is inversely correlated with its critical cooling rate. The elemental proportions in the material corresponding to the region in a) are highly consistent with existing research on the elemental proportions in materials with high GFA in the Zr-Cu-Al system, verifying the accuracy and broad applicability of the target network's predictions.

[0161] In addition, this manual also uses multi-element systems (such as Mg-Zn-Ca and Ca-Cu-Mg) not found in the training and test sets for extrapolation prediction verification. Table 3 shows the comparison results between the experimental values ​​and the predicted values ​​of the target network. It can be seen that the deviation between the predicted values ​​of the target network and the experimental values ​​is extremely small, with prediction errors all less than 5%. Therefore, the accuracy of the extrapolation prediction results of the target network is also relatively high, proving the reliability of the target network.

[0162] Table 3

[0163] Materials Experimental value R c (K / s)] Predicted value R c (K / s) Error Mg 68 Zn 25 Ca7]]> 3708.0 3480.3 4.9％ Ca 50 Cu 25 Mg 25 ]]> 2509.8 2480.1 1.2％ Ge2Sb2Te5 1.9 x 10 9 ]]> 2.5 x 10 9 ]]> 3.2％ Ca 50 Cu 27.5 Mg 22.5 ]]> 2923.1 3028.8 3.6％

[0164] In summary, the training method and system for the target network provided in this specification expand the number of descriptors describing the sample materials, enrich the descriptive dimensions of the sample materials, and allow for parallel training of subnetworks by grouping K descriptors into multiple levels of the target network, avoiding the contradiction caused by an excessive number of descriptors and insufficient training samples. First, the significant increase in the number of descriptors, combined with the target network, can improve the prediction accuracy of the critical cooling rate of amorphization. Even with a small number of training samples, the predictive ability of the target network can be significantly enhanced, reducing experimental costs in the research of amorphous materials. Second, when grouping the descriptors, each group includes the same core descriptor and some non-core descriptors, taking into account both the importance of the core descriptor and exploring the potential impact of different combinations of non-core descriptors on the critical cooling rate of amorphization. Combined with the prediction performance data given above, the prediction accuracy of the target network is higher than that of other networks, which is conducive to accelerating the process of innovative research on amorphous materials.

[0165] Figure 10 A flowchart of a method P1000 for predicting the critical cooling rate of amorphization according to an embodiment of this specification is shown. The prediction system 200 can execute the method P1000 for predicting the critical cooling rate of amorphization.Figure 10 As shown, the prediction method P1000 for the critical cooling rate of amorphization includes the following steps.

[0166] S1010: Based on the proportion information of at least one element in the target material to be predicted and the attribute values ​​of X attributes corresponding to each of the at least one element, generate K descriptors to describe the target material.

[0167] In some embodiments, the X attributes include at least two of the following dimensions: periodic table dimension; thermodynamic dimension; physical dimension; and crystallographic dimension.

[0168] Specifically, the X attributes can be found in Table 1, and will not be repeated here.

[0169] In some embodiments, the K descriptors include at least one of the following:

[0170] The first set of descriptors is used to describe the statistical characteristics of the target material in the X properties;

[0171] The second set of descriptors is used to describe the valence electron occupation state of the target material;

[0172] The third set of descriptors is used to describe the ionicity of the target material; and

[0173] The fourth set of descriptors is used to describe the configuration entropy of the target material.

[0174] In some embodiments, the first set of descriptors is generated as follows:

[0175] For each of the X attributes, the prediction system 200 performs statistical analysis on the characteristics of the target material in the attribute from multiple statistical dimensions based on the proportion information of the at least one element in the target material and the attribute values ​​of the at least one element in the attribute respectively, and obtains P statistical values; and generates a first set of descriptors based on the P statistical values ​​of the target material in each of the X attributes, the number of the first set of descriptors being equal to X*P.

[0176] Specifically, the generation method of the first set of descriptors corresponding to the target material is similar to the generation method of the first set of descriptors corresponding to sample material #1. For details on the generation method, please refer to the above text, which will not be repeated here.

[0177] In some embodiments, the second set of descriptors includes: occupancy information of Q valence electrons in the target material, wherein the occupancy information of the z-th valence electron is obtained in the following manner:

[0178] For each of the at least one element, the prediction system 200 determines the number of each valence electron and the total number of valence electrons in the element based on the attribute values ​​of at least some of the X attributes corresponding to the element; for the z-th valence electron, the prediction system 200 determines the occupation information of the z-th valence electron based on the proportion information of the at least one element in the target material, the number of the z-th valence electrons corresponding to each of the at least one element, and the total number of valence electrons corresponding to each of the at least one element.

[0179] Specifically, the generation method of the second set of descriptors corresponding to the target material is similar to the generation method of the second set of descriptors corresponding to sample material #1. For details on the generation method, please refer to the above text, which will not be repeated here.

[0180] In some embodiments, the third set of descriptors is obtained based on the proportion information of the at least one element in the target material, the electronegativity of each of the at least one element, and any one of the following:

[0181] The maximum value of the electronegativity corresponding to each of the at least one element;

[0182] The average value of the electronegativity of each of the at least one element.

[0183] Specifically, the generation method of the third set of descriptors corresponding to the target material is similar to the generation method of the third set of descriptors corresponding to sample material #1. For details on the generation method, please refer to the above text, which will not be repeated here.

[0184] In some embodiments, the fourth set of descriptors is obtained based on the proportion of the at least one element in the target material, the Boltzmann constant, and room temperature.

[0185] Specifically, the generation method of the fourth set of descriptors corresponding to the target material is similar to the generation method of the fourth set of descriptors corresponding to sample material #1. For details on the generation method, please refer to the above text, which will not be repeated here.

[0186] S1020: N1 core descriptors and K1 non-core descriptors are determined from the K descriptors. The influence of the core descriptors on the critical cooling rate of amorphization is greater than that of the non-core descriptors.

[0187] In some embodiments, the N1 core descriptors include multiples of the following:

[0188] MD1, representing the average deviation of the different elements in the ground state atomic volume among the at least one element;

[0189] MD2 represents the maximum weighted deviation of the atomic numbers of the different elements in the at least one element;

[0190] MD3, representing the standard deviation of the attribute value of the at least one element on the work function;

[0191] MD4, representing the standard deviation of the property value of the at least one element at its melting point;

[0192] MD5 represents the range of weighted attribute values ​​for molar heat capacity of different elements among the at least one element; and

[0193] MD6 represents the average deviation of the different elements in the work function among the at least one element.

[0194] For example, after the prediction system 200 determines the N1 core descriptors from MD1 to MD6, it uses the remaining descriptors among the K descriptors as non-core descriptors.

[0195] S1030: Input at least some of the K descriptors into the target network for prediction to obtain the predicted value corresponding to the amorphization critical cooling rate of the target material. The target network is a network trained using Y sample materials. The target network includes multiple sub-networks with the same structure and arranged in a hierarchical manner. Each sub-network includes N input nodes and 1 output node. The output node of the sub-network in the i-th level serves as the input node of the sub-network in the (i+1)-th level. Each sub-network in the first level is input with the N1 core descriptors and N2 non-core descriptors. The N2 non-core descriptors are some of the K1 non-core descriptors, and the non-core descriptors input to different sub-networks are not completely the same.

[0196] In some embodiments, the prediction system 200 generates m1 sets of descriptors based on the K descriptors, each set including the N1 core descriptors and N-N1 non-core descriptors; the m1 sets of descriptors are input into the m1 sub-networks of the first layer of the target network to obtain m1 intermediate predicted values ​​of the amorphization critical cooling rate; according to the order of i from 2 to F, the m1 values ​​of the (i-1)th layer of the target network are... i-1 The critical cooling rate of amorphization obtained from the subnetwork is m i-1 The intermediate predicted values ​​are divided into m i Grouping inputs the m of the i-th layer of the target network i A sub-network was used to obtain the m-critical cooling rate for amorphization. i The intermediate predicted values; and the intermediate predicted value of the amorphization critical cooling rate output by the sub-network of the F layer as the final predicted value of the amorphization critical cooling rate.

[0197] For example, the prediction system 200 can input the m1 sets of descriptors respectively as follows: Figure 7The target network shown has m1 subnetworks in the first layer, from which m1 intermediate predicted values ​​of the critical cooling rate for amorphization are obtained; according to the order of i from 2 to F, the m1 subnetworks in the (i-1)th layer of the target network T are... i-1 The critical cooling rate of amorphization obtained from the subnetwork is m i-1 The intermediate predicted values ​​are divided into m i Group input to the target network T, layer m of the i-th layer i A sub-network was used to obtain the m-critical cooling rate for amorphization. i The intermediate predicted values ​​are then used as the final predicted values ​​of the amorphization critical cooling rate output by the sub-network of the F layer.

[0198] It is understood that some technical details involved in the prediction method P1000 for the critical cooling rate of amorphization can be referred to the description in the training method P500 for the target network, and will not be repeated here. The beneficial effects of the various embodiments in the above method P1000 can also be referred to the description of the beneficial effects of the embodiments in method P500, and will not be repeated here.

[0199] In summary, the prediction method and system for the critical cooling rate of amorphization provided in this specification expands the number of descriptors for the target material, enriches its descriptive dimensions, and allows for parallel prediction by grouping K descriptors into sub-networks through a multi-level target network. First, the significant increase in the number of descriptors, combined with the target network, improves the prediction accuracy of the critical cooling rate of amorphization for the target material, reducing experimental costs in amorphous material research. Second, when grouping descriptors, each group includes the same core descriptor and some non-core descriptors, considering both the importance of the core descriptor and exploring the potential impact of different non-core descriptor combinations on the critical cooling rate of amorphization for the target material. Combined with the prediction data presented above, the prediction accuracy of the target network is higher than other networks, which is beneficial for accelerating the innovative research process of amorphous materials.

[0200] Furthermore, this specification uses the P1000 method for predicting the critical cooling rate of amorphization to predict the critical cooling rate of amorphization for multiple materials in different multi-element systems. It was found that, for the same multi-element system, the material corresponding to the minimum predicted critical cooling rate of amorphization in that system is close to the eutectic point of that system. This provides an important direction for the design of amorphous materials (such as novel glass materials). Therefore, this specification also provides a method for predicting the eutectic point.

[0201] Figure 11 A flowchart of a eutectic point prediction method P1100 according to an embodiment of this specification is shown. The prediction system 200 can execute the eutectic point prediction method P1100. Figure 11 As shown, the method for predicting the eutectic point P1100 includes the following steps.

[0202] S1110: Using the amorphization critical cooling rate prediction method P1000, predict the amorphization critical cooling rate of multiple materials formed by multiple elements in a target multi-element system, wherein each of the multiple materials includes the multiple elements, and the proportion information of the multiple elements in different materials is different.

[0203] The multiple materials can cover various proportion information of the multiple elements in the target multi-element system. Theoretically, the more proportion information covered by the multiple materials, the more accurate the prediction result of the eutectic point will be.

[0204] For example, the target multi-element system is Zr-Cu-Al, where Zr i Cu j Al z The chemical formulas of multiple materials within a target multi-element system are given. Among these materials, at least one of the proportions of Zr, Cu, and Al (i, j, z) differs.

[0205] For each material in the target multi-element system, the prediction system uses the P1000 method to predict the critical cooling rate of amorphization, which is described above. The details are not repeated here.

[0206] S1120: The material with the smallest critical cooling rate for amorphization among the plurality of materials is identified as the target material, and the eutectic point of the target multi-element system is determined based on the target material.

[0207] For example, after the prediction system predicts the critical cooling rate for amorphization of all materials formed by elements Zr, Cu, and Al in the Zr-Cu-Al system using method P1000, it determines the critical cooling rate for Zr. 50 Cu 40 Al 10 The critical cooling rate for amorphization is the minimum among all materials in the Zr-Cu-Al system. Therefore, Zr... 50 Cu 40 Al 10 As the target material, the eutectic point of the Zr-Cu-Al system was determined to be Zr. 50 Cu 40 Al 10 .

[0208] Table 4 presents a comparison between the predicted and actual values ​​of the eutectic points of multiple multi-element systems predicted by the prediction system using the prediction method P1000.

[0209] Table 4

[0210]

[0211]

[0212] As shown in Table 4, for different multi-element systems, the error between the predicted and actual values ​​of the eutectic point obtained by the prediction system is basically less than 5%, indicating high accuracy.

[0213] In summary, the eutectic point prediction method and system provided in this specification improve upon the traditional method of determining the eutectic point through numerous experiments and thermodynamic simulations. This significantly enhances the prediction efficiency and accuracy of the eutectic point, reduces the time and cost of studying the eutectic point, and can promote the progress of materials research.

[0214] This specification, in another aspect, provides a computer-readable non-transitory storage medium storing at least one set of executable instructions for predicting amorphous critical cooling rates or amorphous points, or training a target network. When the executable instructions are executed by a processor, they instruct the processor to implement the steps of the amorphous critical cooling rate prediction method P1000 or P1100, or the target network training method P500, as described in this specification. In some possible embodiments, various aspects of this specification can also be implemented as a program product comprising program code. When the program product is run on system 400, the program code causes system 400 to perform the steps of the amorphous critical cooling rate or amorphous point prediction method P1000 or P1100, or the target network training method P500, as described in this specification. The program product for implementing the above methods may employ a portable compact disc read-only memory (CD-ROM) containing program code and may run on system 400. However, the program product described herein is not limited to this. In this specification, a readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system. The program product can take any combination of one or more readable media. A readable medium can be a readable signal medium or a readable storage medium. A readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of readable storage media include: an electrical connection having one or more wires, a portable disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. The computer-readable storage medium can include a data signal propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable storage medium can also be any readable medium other than a readable storage medium, which can be sent, propagated, or transmitted for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the readable storage medium can be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof. Program code for performing the operations of this specification can be written in any combination of one or more programming languages, including object-oriented programming languages—such as Java, C++, etc.—and conventional procedural programming languages—such as the "C" language or similar programming languages.The program code can be executed entirely on system 400, partially on system 400, as a standalone software package, partially on system 400 and partially on a remote computing device, or entirely on a remote computing device.

[0215] The term "and / or" in the embodiments of this specification describes the relationship between associated objects, indicating that three relationships can exist. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. The character " / " generally indicates that the preceding and following associated objects have an "or" relationship.

[0216] The terms “first”, “second”, etc., used in this specification are used to distinguish similar or related objects or entities, and do not necessarily imply a specific order or sequence.

[0217] Unless otherwise stated, the term "multiple" in this specification shall be understood as two or more.

[0218] The foregoing has described specific embodiments of this specification. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recited in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result. In some embodiments, multitasking and parallel processing are possible or may be advantageous.

[0219] In summary, after reading this detailed disclosure, those skilled in the art will understand that the foregoing detailed disclosure is presented by way of example only and is not restrictive. Although not explicitly stated herein, those skilled in the art will understand that this specification requires various reasonable changes, improvements, and modifications to the embodiments. These changes, improvements, and modifications are intended to be made by this specification and are within the spirit and scope of the exemplary embodiments described herein.

[0220] Furthermore, certain terms in this specification have been used to describe embodiments of this specification. For example, "an embodiment," "an embodiment," and / or "some embodiments" mean that a particular feature, structure, or characteristic described in connection with that embodiment may be included in at least one embodiment of this specification. Therefore, it is to be emphasized and understood that two or more references to "an embodiment" or "an embodiment" or "alternative embodiment" in various parts of this specification do not necessarily refer to the same embodiment. Moreover, specific features, structures, or characteristics may be suitably combined in one or more embodiments of this specification.

[0221] It should be understood that in the foregoing description of the embodiments in this specification, various features are combined in a single embodiment, drawing, or description for the purpose of simplifying the description and aiding in the understanding of a feature. However, this does not mean that the combination of these features is necessary, and those skilled in the art may readily identify some of the devices as separate embodiments when reading this specification. That is, the embodiments in this specification can also be understood as an integration of multiple secondary embodiments. It is also valid when each secondary embodiment contains fewer than all the features of a single foregoing disclosed embodiment.

[0222] Every patent, patent application, publication of a patent application, and other material, such as articles, books, specifications, publications, documents, and literature (excluding any related historical examination documents), cited in this disclosure is incorporated herein for all purposes, including, for example, in the specification and claims of this disclosure. However, in the event of any inconsistency or conflict between the descriptions, definitions, and / or terms used in the foregoing and those used in this disclosure, the descriptions, definitions, and / or terms used in this disclosure shall prevail.

[0223] Finally, it should be understood that the embodiments disclosed herein are illustrative of the principles of the embodiments described in this specification. Other modified embodiments are also within the scope of this specification. Therefore, the embodiments disclosed in this specification are merely examples and not limitations. Those skilled in the art can implement the applications described in this specification using alternative configurations based on the embodiments in this specification. Therefore, the embodiments in this specification are not limited to the embodiments precisely described in the applications.

Claims

1. A method for predicting the critical cooling rate of amorphization, comprising: Based on the proportion of at least one element in the target material to be predicted and the attribute values ​​of X attributes corresponding to each of the at least one element, K descriptors are generated to describe the target material. N1 core descriptors and K-N1 non-core descriptors are determined from the K descriptors. The core descriptors have a greater influence on the critical cooling rate of amorphization than the non-core descriptors. as well as At least a portion of the K descriptors are input into the target network for prediction to obtain the predicted value corresponding to the amorphization critical cooling rate of the target material, wherein... The target network is trained using Y sample materials. The target network comprises multiple sub-networks with identical structures arranged hierarchically. Each sub-network includes N input nodes and 1 output node. The output node of the sub-network in the i-th level serves as the input node of the sub-network in the (i+1)-th level. In the first level, each sub-network is input with the N1 core descriptors and N-N1 non-core descriptors. The N-N1 non-core descriptors are a subset of the K-N1 non-core descriptors, and the non-core descriptors input to different sub-networks are not exactly the same. Wherein, X, K, N1, Y, and N are all integers greater than 1, and i is an integer greater than or equal to 1; The N1 core descriptors include multiples of the following: a descriptor representing the average deviation of different elements in the ground-state atomic volume of the at least one element; a descriptor representing the maximum value of the weighted deviation of different elements in the atomic number of the at least one element; a descriptor representing the standard deviation of the attribute value of the at least one element in the work function; a descriptor representing the standard deviation of the attribute value of the at least one element in the melting point; a descriptor representing the range of the weighted attribute value of different elements in the molar heat capacity of the at least one element; and a descriptor representing the average deviation of different elements in the work function of the at least one element.

2. The method according to claim 1, wherein, The X attributes include at least two of the following dimensions: Dimensions of the periodic table; Thermodynamic dimension; Physical dimension; or Crystallographic dimension.

3. The method according to claim 1, wherein, The K descriptors include at least one of the following: The first set of descriptors is used to describe the statistical characteristics of the target material in the X properties; The second set of descriptors is used to describe the valence electron occupation state of the target material; The third set of descriptors is used to describe the ionicity of the target material; as well as The fourth set of descriptors is used to describe the configuration entropy of the target material.

4. The method according to claim 3, wherein, The first set of descriptors was generated in the following way: For each of the X attributes, based on the proportion information of the at least one element in the target material and the attribute value of the at least one element in the attribute, P statistical values ​​are obtained by statistically analyzing the characteristics of the target material in the attribute from multiple statistical dimensions. as well as Based on the P statistical values ​​corresponding to each of the X properties of the target material, a first set of descriptors is generated, and the number of descriptors in the first set is equal to X*P.

5. The method according to claim 3, wherein, The second set of descriptors includes: the occupancy information of Q valence electrons in the target material, wherein the occupancy information of the z-th valence electron is obtained in the following manner: For each of the at least one element, based on the attribute values ​​of at least some of the X attributes corresponding to the element, determine the number of each type of valence electron and the total number of valence electrons in the element; and For the z-th valence electron, the occupation information of the z-th valence electron is determined based on the proportion information of the at least one element in the target material, the number of the z-th valence electrons corresponding to each of the at least one element, and the total number of valence electrons corresponding to each of the at least one element.

6. The method according to claim 3, wherein, The third set of descriptors is obtained based on the proportion information of the at least one element in the target material, the electronegativity of each of the at least one element, and any one of the following: The maximum value of the electronegativity corresponding to each of the at least one element; or The average value of the electronegativity of each of the at least one element.

7. The method according to claim 3, wherein, The fourth set of descriptors is obtained based on the proportion of the at least one element in the target material, the Boltzmann constant, and room temperature.

8. The method according to claim 1, wherein, The target network comprises F levels. The step of inputting at least a portion of the K descriptors into the target network for prediction to obtain the predicted value corresponding to the amorphization critical cooling rate of the target material includes: Based on the K descriptors, generate m1 groups of descriptors, each group of descriptors including the N1 core descriptors and N-N1 non-core descriptors; The m1 sets of descriptors are respectively input into the m1 sub-networks of the first layer of the target network to obtain the m1 intermediate predicted values ​​of the amorphization critical cooling rate; Following the order of i values ​​from 2 to F, the m values ​​of the (i-1)th layer of the target network are... i-1 The critical cooling rate m of the amorphization obtained from the subnetwork i-1 The intermediate predicted values ​​are divided into m i The m-th layer of the target network is then input after the group. i A sub-network is used to obtain the m-value of the critical cooling rate for amorphization. i One intermediate predicted value; and The intermediate predicted value of the amorphization critical cooling rate output by the sub-network of layer F is used as the final predicted value of the amorphization critical cooling rate. Wherein, m1, F, and m i-1 All are integers greater than 1, and m i It is an integer greater than or equal to 1.

9. A method for training a target network, said target network being used to predict the critical cooling rate for amorphization of a material, the method comprising: Obtain experimental values ​​of Y sample materials at the critical cooling rate of amorphization, each sample material including at least one element; For each sample material, based on the proportion information of the at least one element in the sample material and the attribute values ​​of the X attributes corresponding to each of the at least one element, K descriptors are generated to describe the sample material, and N1 core descriptors and K-N1 non-core descriptors are determined from the K descriptors. The influence of the core descriptors on the critical cooling rate of amorphization is greater than that of the non-core descriptors on the critical cooling rate of amorphization. A portion of the K descriptors corresponding to each sample material are input into the target network for prediction, thereby obtaining the predicted value corresponding to the amorphization critical cooling rate of the sample material, wherein: The target network comprises multiple sub-networks with identical structures arranged hierarchically. Each sub-network includes N input nodes and 1 output node. The output node of the sub-network in the i-th level serves as the input node of the sub-network in the (i+1)-th level. In the first level, each sub-network is input with the N1 core descriptors and N-N1 non-core descriptors, where the N-N1 non-core descriptors are a subset of the K-N1 non-core descriptors, and the non-core descriptors input to different sub-networks are not entirely the same; and The parameters of the target network are updated with the training objective of minimizing the difference between the predicted value and the experimental value. Wherein, X, K, N1, Y, and N are all integers greater than 1, and i is an integer greater than or equal to 1; The N1 core descriptors include multiples of the following: a descriptor representing the average deviation of different elements in the ground-state atomic volume of the at least one element; a descriptor representing the maximum value of the weighted deviation of different elements in the atomic number of the at least one element; a descriptor representing the standard deviation of the attribute value of the at least one element in the work function; a descriptor representing the standard deviation of the attribute value of the at least one element in the melting point; a descriptor representing the range of the weighted attribute value of different elements in the molar heat capacity of the at least one element; and a descriptor representing the average deviation of different elements in the work function of the at least one element.

10. The method according to claim 9, wherein, The X attributes include at least two of the following dimensions: Dimensions of the periodic table; Thermodynamic dimension; Physical dimension; or Crystallographic dimension.

11. The method according to claim 9, wherein, The K descriptors include at least one of the following: The first set of descriptors is used to describe the statistical characteristics of the sample material on the X attributes; The second set of descriptors is used to describe the valence electron occupation state of the sample material; The third set of descriptors is used to describe the ionicity of the sample material; as well as The fourth set of descriptors is used to describe the configuration entropy of the sample material.

12. The method of claim 11, wherein, The first set of descriptors was generated in the following way: For each of the X attributes, based on the proportion of the at least one element in the sample material and the attribute value of the at least one element in the attribute, P statistical values ​​are obtained by statistically analyzing the characteristics of the sample material in the attribute from multiple statistical dimensions. as well as Based on the P statistical values ​​corresponding to each of the X attributes of the sample material, a first set of descriptors is generated, and the number of descriptors in the first set of descriptors is equal to X*P.

13. The method of claim 11, wherein, The second set of descriptors includes: the occupancy information of Q valence electrons in the sample material, wherein the occupancy information of the z-th valence electron is obtained in the following way: For each of the at least one element, based on the attribute values ​​of at least some of the X attributes corresponding to the element, determine the quantity of each type of valence electron and the total number of valence electrons in the element; and For the z-th valence electron, the occupation information of the z-th valence electron is determined based on the proportion information of the at least one element in the sample material, the number of z-th valence electrons corresponding to each of the at least one element, and the total number of valence electrons corresponding to each of the at least one element.

14. The method of claim 11, wherein, The third set of descriptors is obtained based on the proportion information of the at least one element in the sample material, the electronegativity of each of the at least one element, and any one of the following: The maximum value of the electronegativity corresponding to at least one element; or The average value of the electronegativity corresponding to at least one element.

15. The method according to claim 11, wherein, The fourth set of descriptors is obtained based on the proportion of the at least one element in the sample material, the Boltzmann constant, and room temperature.

16. The method according to claim 9, wherein, The target network comprises F levels. The step of inputting a portion of the K descriptors corresponding to each sample material into the target network for prediction, to obtain the predicted value corresponding to the amorphization critical cooling rate of the sample material, includes: Based on the K descriptors, generate m1 groups of descriptors, each group of descriptors including the N1 core descriptors and N-N1 non-core descriptors; The m1 sets of descriptors are respectively input into the m1 sub-networks of the first layer of the target network to obtain the m1 intermediate predicted values ​​of the amorphization critical cooling rate; Following the order of i from 2 to F, the m values ​​of the (i-1)th layer of the target network are... i-1 The critical cooling rate m of the amorphization obtained from the subnetwork i-1 The intermediate predicted values ​​are divided into m i After grouping, input the m of the i-th layer of the target network. i A sub-network is used to obtain the m-value of the critical cooling rate for amorphization. i One intermediate predicted value; and The intermediate predicted value of the critical cooling rate for amorphization output by the sub-network of layer F is used as the final predicted value of the critical cooling rate for amorphization of the sample material. Wherein, m1, F, and m i-1 All are integers greater than 1, and m i It is an integer greater than or equal to 1.

17. A method for predicting eutectic points, comprising: Based on the method of any one of claims 1-8, the amorphization critical cooling rate of multiple materials formed by multiple elements in a target multi-element system is predicted, wherein each of the multiple materials includes the multiple elements and the proportion information of the multiple elements in different materials is different; as well as The material with the lowest critical cooling rate for amorphization among the multiple materials is identified as the target material, and the eutectic point of the target multi-element system is determined based on the target material.

18. A prediction system, characterized in that, The parameters configured to predict the critical cooling rate for amorphization of the target material include: At least one storage medium storing at least one instruction set; and At least one processor is communicatively connected to the at least one storage medium. When the prediction system is running, the at least one processor reads the at least one instruction set and executes the method of any one of claims 1-8 according to the instructions of the at least one instruction set.

19. A training system, characterized in that, The target network configured to be trained for predicting the critical cooling rate of amorphization of materials includes: At least one storage medium storing at least one instruction set; and At least one processor is communicatively connected to the at least one storage medium. When the training system is running, the at least one processor reads the at least one instruction set and executes the method according to any one of claims 9-16 according to the instructions of the at least one instruction set.

20. A prediction system, characterized in that, Configured to predict the eutectic point of a multi-element system, including: At least one storage medium storing at least one instruction set; and At least one processor is communicatively connected to the at least one storage medium. When the prediction system is running, the at least one processor reads the at least one instruction set and executes the method of claim 17 according to the instructions of the at least one instruction set.

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