Prediction method, device, storage medium and product for rotational equivariant physical quantity

Abstract

The present application discloses a prediction method, device, medium and product for rotational equivariant physical quantities, and relates to the technical field of electrical digital data processing. Among them, the prediction method for rotational equivariant physical quantities includes: constructing and training a nonlinear equivariant deep learning model, the nonlinear equivariant deep learning model includes a graph neural network and a decoder with linear computational complexity; when the training of the nonlinear equivariant deep learning model is completed, the physical system model of the material structure to be tested is input into the nonlinear equivariant deep learning model; the graph neural network is used to extract rotational equivariant features; the nonlinear rotational invariant features corresponding to the rotational equivariant features are converted according to the gradient induction mechanism to obtain nonlinear rotational equivariant features; the decoder is used to decode the nonlinear rotational equivariant features to obtain the rotational equivariant physical quantities of the material structure to be tested. The present application can solve the technical problem that the prior art is difficult to simultaneously ensure the prediction accuracy and computational efficiency of rotational equivariant physical quantities, which limits the application of material structures.

Description

Technical Field

[0001] The present application relates to the technical field of electrical digital data processing, and in particular to a prediction method, device and product for a rotational or other variable physical quantity. Background Art

[0002] In the field of electrical digital data processing, a large number of important physical quantities, such as the Hamiltonian of electronic structure, angular momentum and force field, are rotational equivariant physical quantities. The accurate prediction of these rotational equivariant physical quantities plays a key role in understanding and predicting the electrical, magnetic and thermal properties of related physical systems, and is an indispensable part of materials science, chemistry and biomedicine research. For example, the Hamiltonian of a crystalline material can be used to derive complete information about the electronic structure of the crystal, and then the physical and chemical properties of the crystalline material can be derived based on the crystal electronic structure.

[0003] For the prediction of rotational equivariant physical quantities, the algorithm is required to follow the intrinsic properties of rotational equivariance while accurately capturing the complex mapping relationship from input features to target physical quantities, so as to obtain accurate prediction results of rotational equivariant physical quantities. In addition, the corresponding prediction algorithm is also required to have high computational efficiency to support the needs of large-scale physical system research. Most traditional prediction algorithms for rotational equivariant physical quantities use prediction algorithms based on classical density functional theory or prediction algorithms for rotational equivariant physical quantities based on deep learning. The classical density functional theory is limited by the computational complexity of the cubic growth of the relative atomic number, resulting in too low computational efficiency and unable to complete the computational tasks for large-scale physical systems under limited and acceptable hardware resources and time costs. However, although the computational efficiency of the prediction algorithm based on deep learning has been significantly improved compared with the classical density functional theory, there is a situation where the nonlinear expression ability is incompatible with rotational equivariance, so there is an obvious bottleneck in the prediction accuracy.

[0004] For the above reasons, it is difficult for both prediction algorithms to simultaneously guarantee the prediction accuracy and computational efficiency of rotational and other variable physical quantities, resulting in difficulty in accurately calculating large-scale physical systems under limited hardware resources and time costs, and difficulty in accurately predicting the physical and chemical properties of related material structures, which limits the application of material structures and further limits their research and expansion in materials science, chemistry and biomedicine.

[0005] The above contents are only used to assist in understanding the technical solution of the present application and do not constitute an admission that the above contents are prior art. Summary of the invention

[0006] The main purpose of this application is to provide a prediction method, equipment medium and product based on rotational and other variable physical quantities, aiming to solve the technical problem that the existing technical solutions are difficult to simultaneously ensure the prediction accuracy and calculation efficiency of rotational and other variable physical quantities, and are difficult to accurately predict the physical and chemical properties of related material structures, which limits the application of related material structures and further limits their research and expansion in materials science, chemistry and biomedicine.

[0007] In view of the above technical shortcomings, the main purpose of the present invention is to provide a prediction method for rotational equivariant physical quantities, comprising:

[0008] Constructing and training a nonlinear equivariant deep learning model, wherein the nonlinear equivariant deep learning model includes a graph neural network and a decoder with linear computational complexity;

[0009] When the training of the nonlinear equivariant deep learning model is completed, the physical system model of the material structure to be tested is input into the nonlinear equivariant deep learning model;

[0010] Extract rotational equivariant features of physical system models using graph neural networks;

[0011] According to the gradient induced mechanism, the nonlinear rotation invariant feature corresponding to the rotation equivariant feature is converted to obtain the nonlinear rotation equivariant feature;

[0012] The decoder is used to decode the nonlinear rotational equivariant characteristics and predict the rotational equivariant physical quantities of the material structure to be tested.

[0013] Preferably, the above-mentioned prediction method of rotational equivariant physical quantity, before the step of converting the nonlinear rotational invariant feature corresponding to the rotational equivariant feature according to the gradient induction mechanism, further comprises:

[0014] Perform direct product operation on the rotational equivariant features to obtain the direct product operation result;

[0015] Perform Clebsch-Gordan decomposition on the direct product operation result to obtain the rotation invariant component corresponding to the rotation equivariant feature;

[0016] A nonlinear neural network of a nonlinear equivariant deep learning model is used to perform nonlinear encoding on the rotation invariant component to obtain nonlinear rotation invariant features.

[0017] Preferably, in the above-mentioned prediction method of rotational equivariant physical quantity, the step of converting the nonlinear rotational invariant feature corresponding to the rotational equivariant feature according to the gradient induction mechanism to obtain the nonlinear rotational equivariant feature comprises:

[0018] Using rotational equivariant features, according to the gradient-induced mechanism:

[0019]

[0020] The nonlinear rotation invariant features are transformed to obtain nonlinear rotation equivariant features, where represents the rotational equivariant feature, represents the nonlinear rotation invariant feature, Represents nonlinear rotational equivariant characteristics.

[0021] Preferably, in the above-mentioned method for predicting rotational equivariant physical quantities, the steps of constructing and training a nonlinear equivariant deep learning model include:

[0022] Use multiple equivariant function operators to construct a graph neural network with linear computational complexity;

[0023] Construct nonlinear neural networks for nonlinear coding;

[0024] Connecting the graph neural network and the nonlinear neural network to obtain an encoder, wherein the encoder is used to output nonlinear rotation equivariant features;

[0025] The encoders are stacked in series multiple times to obtain a deep encoding network with multiple layers of encoders;

[0026] Construct a decoder for decoding nonlinear rotation-equivariant features;

[0027] The deep encoding network and the decoder are connected to construct a nonlinear equivariant deep learning model.

[0028] Preferably, in the above-mentioned prediction method of rotational equivariant physical quantities, the step of constructing and training a nonlinear equivariant deep learning model includes:

[0029] Constructing a training sample data set of the material structure to be tested, wherein each training sample in the training sample data set includes a physical system model of the material structure to be tested and a physical quantity true value label;

[0030] Use training samples to train the nonlinear equivariant deep learning model to obtain the rotational equivariant physical quantities corresponding to the physical system model;

[0031] Use physical quantity truth labels to verify rotational equivariant physical quantities;

[0032] For other training samples in the training sample data set, the steps of training the nonlinear equivariant deep learning model using the training samples and subsequent steps are repeated until the loss function of the nonlinear equivariant deep learning model converges.

[0033] Preferably, in the above-mentioned prediction method of rotational equivariant physical quantities, the step of using training samples to train a nonlinear equivariant deep learning model to obtain rotational equivariant physical quantities corresponding to the physical system model includes:

[0034] Starting from the first encoder layer of the deep encoding network, the encoder’s graph neural network is used to extract the rotational equivariant features of the physical system model.

[0035] According to the gradient induced mechanism, the nonlinear rotation invariant feature corresponding to the rotation equivariant feature is converted to obtain the nonlinear rotation equivariant feature;

[0036] The nonlinear rotation equivariant features are input to the next layer of encoder of the deep encoding network for operation until the nonlinear rotation equivariant features output by the last layer of encoder are obtained;

[0037] The nonlinear rotational equivariant features output by the last layer encoder are input into the decoder for decoding to obtain the rotational equivariant physical quantity.

[0038] Preferably, in the above-mentioned prediction method of rotational equivariant physical quantities, the step of constructing a training sample data set of the material structure to be tested includes:

[0039] Compute equivariant truth labels for verifying rotational equivariant quantities;

[0040] Use the equivariant truth value label to calculate the formula based on the rotationally invariant physical quantity:

[0041]

[0042] Calculate the invariant truth value label used to verify the rotation invariant physical quantity, where B represents the rotation invariant physical quantity, D represents the rotation equivariant physical quantity, T represents the trace operation, represents the conjugate transpose operation;

[0043] After the decoder outputs the rotational equivariant physical quantity and the rotational invariant physical quantity, the rotational equivariant physical quantity and the rotational invariant physical quantity are verified using the equivariant truth value label and the invariant truth value label, respectively.

[0044] To achieve the above-mentioned objectives, the present application also provides a prediction device for rotational equivariant physical quantities, which includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program is configured to implement the steps of a prediction method for rotational equivariant physical quantities as provided in any of the above-mentioned technical solutions.

[0045] To achieve the above-mentioned purpose, the present application also provides a storage medium, which is a computer-readable storage medium, and a computer program is stored on the storage medium. When the computer program is executed by a processor, the steps of the method for predicting rotational equivariant physical quantities provided by any of the above-mentioned technical solutions are implemented.

[0046] To achieve the above objectives, the present application also provides a computer program product, which includes a computer program. When the computer program is executed by a processor, it implements the steps of the method for predicting rotational and equivariant physical quantities provided by any of the above technical solutions.

[0047] One or more technical solutions proposed in this application have at least the following technical effects:

[0048] Construct and train a nonlinear equivariant deep learning model, which includes a graph neural network and a decoder with linear computational complexity; when the training of the nonlinear equivariant deep learning model is completed, the physical system model of the material structure to be tested is input into the nonlinear equivariant deep learning model, and the rotational equivariant features of the physical system model can be extracted using the graph neural network. Since the graph neural network has linear computational complexity, the graph neural network is limited to the computational complexity of the cubic growth of the number of atoms compared to the traditional classical density functional theory, and its computational complexity is greatly reduced, thereby reducing the calculation steps of the rotational equivariant features and improving the technical efficiency of subsequent rotational equivariant physical quantities. After the rotational equivariant features of the physical system model are obtained using the graph neural network, the nonlinear rotational invariant features of the rotational equivariant features are converted according to the gradient induction mechanism. The present application uses a gradient induction mechanism to convert the rotational invariant features compatible with nonlinearity, thereby obtaining rotational equivariant features compatible with nonlinearity, that is, nonlinear rotational equivariant features. This method can solve the problem that the nonlinear expression of the existing prediction algorithm based on deep learning is incompatible with rotational equivariance, and greatly improves the prediction accuracy of subsequent rotational equivariant physical quantities. Finally, by using a decoder to decode the nonlinear rotational equivariant feature, the rotational equivariant physical quantity of the material structure to be tested can be obtained, thereby using a graph neural network and gradient induction mechanism with linear computational complexity, while ensuring the prediction accuracy and computational efficiency of the rotational equivariant physical quantity, thereby achieving accurate calculation of large-scale physical systems under limited hardware resources and time costs, and expanding the research and application of related material structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and, together with the description, serve to explain the principles of the present application.

[0050] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0051] Figure 1A schematic flow chart of a method for predicting rotational equivariant physical quantities provided in an embodiment of the present application;

[0052] Figure 2 A schematic flow chart of a method for generating a nonlinear rotationally invariant physical quantity provided in an embodiment of the present application;

[0053] Figure 3 For this application Figure 1 A schematic diagram of a flow chart of a method for constructing a nonlinear equivariant deep learning model provided in the illustrated embodiment;

[0054] Figure 4 For this application Figure 1 A schematic diagram of a flow chart of a training method for a nonlinear equivariant deep learning model provided in the illustrated embodiment;

[0055] Figure 5 for Figure 4 A flowchart of a method for training a nonlinear equivariant deep learning model using training samples provided by the illustrated embodiment;

[0056] Figure 6 yes Figure 4 A schematic diagram of a flow chart of a method for constructing a training sample data set provided in the illustrated embodiment;

[0057] Figure 7 It is a structural schematic diagram of a nonlinear equivariant deep learning model provided in an embodiment of the present application;

[0058] Figure 8 It is a structural schematic diagram of a prediction device for rotational equivariant physical quantities provided in an embodiment of the present application.

[0059] The purpose, features and advantages of this application will be further described in conjunction with the embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0060] It should be understood that the specific embodiments described herein are only used to explain the technical solutions of the present application and are not used to limit the present application.

[0061] In order to better understand the technical solution of the present application, a detailed description will be given below in conjunction with the accompanying drawings and specific implementation methods.

[0062] The technical problems existing in the prior art are as follows:

[0063] Most of the existing prediction algorithms for rotational equivariant physical quantities use prediction algorithms based on classical density functional theory or prediction algorithms based on deep learning.

[0064] Classical density functional theory is limited by its computational complexity, which grows at a cubic rate with respect to the number of atoms. This results in low computational efficiency and makes it impossible to complete computational tasks for large-scale physical systems within limited and acceptable hardware resources and time costs.

[0065] Although the computational efficiency of the prediction algorithm based on deep learning has been significantly improved compared with the classical density functional theory, there is a situation where the nonlinear expression ability is incompatible with rotation and equivariance. This is because the classic nonlinear activation functions in deep learning, such as Sigmoid, Tanh, Softmax, ReLU, and SiLU, are applied to the features of equivariant operators, which will destroy their equivariance. Therefore, the use of these activation functions can only be limited, resulting in insufficient expression of the encoded features, affecting the generalization performance of the model, and thus leading to an obvious bottleneck in prediction accuracy.

[0066] For the above reasons, it is difficult for both prediction algorithms to simultaneously guarantee the prediction accuracy and computational efficiency of rotational and other variable physical quantities, resulting in difficulty in accurately calculating large-scale physical systems under limited hardware resources and time costs, and difficulty in accurately predicting the physical and chemical properties of related material structures, which limits the application of material structures and further limits their research and expansion in materials science, chemistry and biomedicine.

[0067] To solve the above technical problems, the present application provides a solution by inducing and calculating rotationally invariant physical quantities using a graph neural network with linear computational complexity and a gradient induction mechanism, thereby achieving accurate prediction of rotationally invariant physical quantities while ensuring the prediction accuracy and computational efficiency of rotationally invariant physical quantities, thereby achieving accurate calculation of large-scale physical systems with limited hardware resources and time costs, and expanding the research and application of related material structures.

[0068] It should be noted that the execution subject of this embodiment can be a computing service device with data processing, network communication and program running functions, such as a tablet computer, a personal computer, a mobile phone, etc., or an electronic device that can realize the above functions, a computer-readable storage medium, etc.

[0069] In order to better understand the above technical solution, the exemplary embodiments of the present application will be described in more detail with reference to the accompanying drawings. Although the exemplary embodiments of the present application are shown in the accompanying drawings, it should be understood that the present application can be implemented in various forms and should not be limited by the embodiments shown here. On the contrary, these embodiments are provided to enable a more thorough understanding of the present application and to fully convey the scope of the present application to those skilled in the art.

[0070] To achieve the above technical objectives, see Figure 1 , Figure 1A flowchart of a method for predicting rotational equivariant physical quantities is provided for the present application embodiment. Figure 1 As shown, the prediction method of the rotational equivariant physical quantity includes:

[0071] S110: Construct and train a nonlinear equivariant deep learning model, wherein the nonlinear equivariant deep learning model includes a graph neural network and a decoder with linear computational complexity.

[0072] The nonlinear equivariant deep learning model is essentially a deep convolutional neural network model. By using a neural convolutional neural network to predict rotational equivariant physical quantities, it has a smaller amount of computation and higher computational efficiency than the traditional classical density functional theory. In addition, the nonlinear equivariant deep learning model includes a graph neural network with linear computational complexity, so that when training and predicting the structure of the material to be tested, operations with linear computational complexity can be performed. Compared with the classical density functional theory, which is limited by the computational complexity of the cubic growth of the number of atoms, the amount of computation is greatly reduced and the computational efficiency is greatly improved. And by converting the relevant features of the material structure into a form of graph vector representation, the rotational equivariant features of its physical system model can be extracted simply and quickly.

[0073] S120: When the training of the nonlinear equivariant deep learning model is completed, the physical system model of the material structure to be tested is input into the nonlinear equivariant deep learning model.

[0074] When the training of the nonlinear equivariant deep learning model is completed, that is, when the loss function of the nonlinear equivariant deep learning model converges, the prediction accuracy of the model can meet the standard. At this time, inputting the physical system model of the material structure to be tested into the nonlinear equivariant deep learning model can accurately predict the rotational equivariant physical quantities of the material structure to be tested.

[0075] The physical system models here include microscopic structural models with quantum effects, such as atomic system models, molecular system models and crystal models. The atomic system model is a physical system composed of multiple atoms, and these systems all contain quantum mechanical effects. In this atomic system, the interaction between different atoms determines the values ​​of physical quantities such as energy, force and Hamiltonian. Here, the physical system model is input into the nonlinear equivariant deep learning model, specifically, the type of each atom in the atomic system and their initial features such as position are input into the nonlinear equivariant deep learning model. Two types of features can be further extracted through position: 1. The distance between atoms; 2. The relative orientation of atoms, represented by the direction vector after the relative position vector modulus is normalized. The initial features are processed by the neural network to obtain a more advanced feature representation.

[0076] For example, the 3D atomic structure of a magnetic material is converted into a standard 3D graph format, where each atom is modeled as a vertex of the graph, and each atomic pair within the truncation radius is modeled as an edge of the graph. Features such as atomic properties, bond properties, bond lengths, bond angles, relative positions and orientations between atoms are used as the initial representation of the 3D graph.

[0077] S130: Extracting rotational equivariant features of the physical system model using a graph neural network.

[0078] As mentioned above, graph neural networks have linear computational complexity. Compared with the traditional classical functional density theory calculation method in which the number of atoms grows cubically, the computational complexity of graph neural networks is greatly reduced and the computational efficiency is greatly improved. This makes it possible to quickly extract the initial rotational equivariant features from the physical system model.

[0079] S140: Convert the nonlinear rotation invariant feature corresponding to the rotation equivariant feature according to the gradient induction mechanism to obtain the nonlinear rotation equivariant feature. The nonlinear expression capability can be transferred to the rotation equivariant feature through the gradient induction mechanism, so that the rotation equivariant feature can obtain the nonlinear expression capability while maintaining the equivariant property.

[0080] In order to solve the problem that the nonlinear expression ability and rotation equivariance of the existing prediction algorithms based on deep learning are incompatible, the technical solution of the present application first processes the rotation equivariant features and converts them into nonlinear rotation invariant features. The nonlinear rotation invariant features are compatible with the nonlinear expression ability and rotation invariance, and the nonlinear rotation invariant features are converted using a gradient induction mechanism, and the obtained rotation equivariant features also have nonlinearity, so that the nonlinear expression ability and rotation equivariance are compatible, solving the problem that the nonlinear expression ability and rotation equivariance of the existing prediction algorithms based on deep learning are incompatible. In addition, since the nonlinear rotation invariant features are extracted from the rotation equivariant features, the converted nonlinear rotation equivariant features can also correspond to the initial rotation equivariant features.

[0081] S150: Using a decoder to decode the nonlinear rotational equivariant characteristics, and predicting the rotational equivariant physical quantity of the material structure to be tested.

[0082] The above-mentioned graph neural network extracts rotational equivariant features and converts them into nonlinear rotational equivariant features according to the gradient induced mechanism, which is a coding behavior. Therefore, a decoder is required to decode the nonlinear rotational equivariant features so as to accurately predict the rotational equivariant physical quantities of the material structure to be tested.

[0083] The technical solution provided by the embodiment of the present application is to construct and train a nonlinear equivariant deep learning model, which includes a graph neural network and a decoder with linear computational complexity; when the training of the nonlinear equivariant deep learning model is completed, the physical system model of the material structure to be tested is input into the nonlinear equivariant deep learning model, and the rotational equivariant features of the physical system model can be extracted using the graph neural network. Since the graph neural network has linear computational complexity, the graph neural network is limited to the computational complexity of the cubic growth of the number of atoms compared to the traditional classical density functional theory, and its computational complexity is greatly reduced, thereby reducing the calculation steps of the rotational equivariant features and improving the technical efficiency of subsequent rotational equivariant physical quantities. After the rotational equivariant features of the physical system model are obtained using the graph neural network, the nonlinear rotational invariant features of the rotational equivariant features are converted according to the gradient induction mechanism. The present application uses a gradient induction mechanism to convert the rotational invariant features compatible with nonlinearity, thereby obtaining rotational equivariant features compatible with nonlinearity, that is, nonlinear rotational equivariant features. This method can solve the problem of incompatibility between nonlinear expression and rotational equivariance in existing prediction algorithms based on deep learning, greatly improving the prediction accuracy of subsequent rotational equivariant physical quantities. Finally, by using a decoder to decode the nonlinear rotational equivariant feature, the rotational equivariant physical quantity of the material structure to be tested can be obtained, thereby using linear computational complexity and gradient induction mechanism, while ensuring the prediction accuracy and computational efficiency of rotational equivariant physical quantities, thereby achieving accurate calculation of large-scale physical systems under limited hardware resources and time costs, and expanding the research and application of related material structures.

[0084] In order to realize the conversion of the nonlinear rotation invariant features corresponding to the rotation equivariant features by the gradient induced mechanism, it is necessary to first extract the rotation invariant components from the rotation equivariant features. The rotation invariant components are compatible with the nonlinearity. Therefore, by processing the rotation invariant components, the nonlinear rotation invariant features corresponding to the rotation equivariant features can be obtained.

[0085] Because rotational invariance means that a physical quantity or feature remains completely unchanged after rotation; rotational equivariance means that a physical quantity or feature changes according to physical and mathematical laws (in a manner prescribed by group theory) after rotation, not "weakened". Both are extremely strict in mathematics. Under certain specific conditions, rotational equivariant physical quantities and rotational invariant physical quantities can be converted into each other. This is also the reason why this application can convert rotational equivariant features and rotational invariant features.

[0086] Specifically, as a preferred embodiment, Figure 2 As shown, the above-mentioned prediction method of rotation equivariant physical quantity, before the step S140: converting the nonlinear rotation invariant feature corresponding to the rotation equivariant feature according to the gradient induction mechanism, further includes:

[0087] S201: Perform a direct product operation on the rotational equivariant features to obtain a direct product operation result.

[0088] Direct product, also known as Cartesian product, is often used in set theory. The rotational equivariant feature extracted here is likely to be a collection of features. Therefore, by performing a direct product operation on the rotational equivariant feature with itself, a direct product operation result containing ordered pairs of features can be obtained. Specifically, in mathematical notation, if the initial rotational equivariant feature is , then the direct product operation result is the new rotational equivariant feature f The calculation formula is as follows:

[0089] .

[0090] S202: Perform Clebsch-Gordan decomposition on the direct product operation result to obtain the rotation invariant component corresponding to the rotation equivariant feature.

[0091] Clebsch-Gordan decomposition is an important concept in quantum mechanics and group theory, especially when dealing with angular momentum coupling. It describes how the possible values ​​of their total angular momentum and the corresponding states are represented when two systems with a certain angular momentum are combined. Specifically, if the two systems have angular momentum l1 and l2, respectively, and the corresponding magnetic quantum numbers (or z-component angular momentum) m1 and m2, then the possible values ​​of their total angular momentum L and total magnetic quantum number M and the corresponding states can be determined by the Clebsch-Gordan coefficients. Specifically, the Clebsch-Gordan decomposition is used to deal with the coupling of two angular momentum states and extract the eigenstates of the total angular momentum. The present application performs a direct product operation on the rotationally equivariant features, so that it can be used to decompose the coupling between the rotationally equivariant features. Since some eigenstates of this coupling are rotationally invariant, it means that they remain unchanged under spatial rotation. Therefore, the Clebsch-Gordan decomposition can indeed be used to extract the rotationally invariant components. Mathematically, this can be achieved by projecting the direct product of the two rotationally equivariant features into the eigenspace of the total angular momentum. This projection is done via the Clebsch-Gordan coefficients, which give how to combine two rotationally equivariant features into a state with a certain total angular momentum. Therefore, through the above Clebsch-Gordan decomposition, the rotationally invariant component corresponding to the rotationally equivariant feature can be obtained.

[0092] S203: Using a nonlinear neural network of a nonlinear equivariant deep learning model, nonlinearly encode the rotation invariant component to obtain a nonlinear rotation invariant feature. The nonlinear neural network has a nonlinear activation function, such as a ReLU function, and can therefore perform nonlinear encoding on the rotation invariant component.

[0093] A nonlinear neural network is needed here. Figure 7 By performing nonlinear encoding on the rotation invariant feature through the nonlinear neural network, a nonlinear characteristic can be given to the rotation invariant component, thereby obtaining a nonlinear rotation invariant feature that is compatible with sub-linearity and rotation invariance. Because the nonlinear rotation invariant feature is obtained by operating on the rotation equivariant feature, the nonlinear rotation invariant feature can be reversed to obtain a nonlinear rotation equivariant feature that is compatible with nonlinearity.

[0094] In order to realize the transformation from nonlinear rotation invariant features to nonlinear rotation equivariant features, the present application introduces a gradient induction mechanism to obtain nonlinear rotation equivariant features.

[0095] Specifically, as a preferred embodiment, combined with Figure 7 It can be seen from the structure shown that in the above-mentioned prediction method of rotation equivariant physical quantity, step S140: converting the nonlinear rotation invariant feature corresponding to the rotation equivariant feature according to the gradient induction mechanism to obtain the nonlinear rotation equivariant feature, specifically includes:

[0096] Using rotational equivariant features, according to the gradient-induced mechanism:

[0097]

[0098] The nonlinear rotation invariant features are transformed to obtain nonlinear rotation equivariant features, where represents the rotational equivariant feature, represents the nonlinear rotation invariant feature, Represents nonlinear rotational equivariant characteristics.

[0099] In the technical solution provided by the embodiment of the present application, as described above, the nonlinear rotation invariant feature is obtained by nonlinearly encoding the rotation invariant component, and the rotation invariant component is obtained by performing Clebsch-Gordan decomposition on the direct product operation result of the rotation equivariant feature, so the nonlinear rotation invariant feature corresponds to the rotation equivariant feature, so that the nonlinear rotation invariant feature can be inversely transformed using the gradient induction mechanism to obtain the nonlinear rotation equivariant feature. In addition, since the nonlinear rotation invariant feature can be well compatible with nonlinearity, the nonlinear rotation equivariant feature obtained by the gradient induction mechanism can be well compatible with nonlinearity and rotation equivariant features.

[0100] The technical solution provided in the embodiment of the present application requires the construction and training of the nonlinear equivariant deep learning model before using the nonlinear equivariant deep learning model to predict the rotational equivariant physical quantities of the material structure.

[0101] Specifically, as a preferred embodiment, Figure 3 As shown, in the above-mentioned prediction method of rotational equivariant physical quantities, step S110: the step of constructing and training a nonlinear equivariant deep learning model includes:

[0102] S111: Use multiple equivariant function operators to construct a graph neural network with linear computational complexity.

[0103] Specifically, the present application can construct an efficient graph neural network with linear computational complexity relative to the number of input atoms through spherical harmonics, tensor addition, tensor direct sum, tensor direct product, Clebsch-Gordan decomposition, equivariant Dropout, equivariant Layernorm and equivariant gated activation function and other equivariant function operators. The efficient graph neural network can transform the physical system model into a 3D graph form. For example, the 3D structure of each atom in the atomic system is converted into a standard 3D grid format, where each atom is modeled as a vertex of the graph, and each atomic pair within the truncation radius is modeled as an edge of the graph, and atomic properties, bond properties, bond lengths, bond angles, relative positions and orientations between atoms are used as the initial representation of the 3D graph, so that the rotational equivariant features of the physical system model can be quickly and easily extracted. Since graph neural networks are relatively mature prior art, the specific scheme of using multiple equivariant function operators to construct graph neural networks will not be repeated.

[0104] S112: Construct a nonlinear neural network for nonlinear coding. Figure 7 As can be seen from the structural diagram of the nonlinear equivariant deep learning model shown, the embodiment of the present application constructs a nonlinear neural network in the model and connects it with the graph neural network, so that nonlinearity can be added to the rotational invariant components corresponding to the rotational equivariant features.

[0105] S113: Connect the graph neural network and the nonlinear neural network to obtain an encoder, wherein the encoder is used to output nonlinear rotational equivariant features. After the nonlinear rotational invariant features are output through the nonlinear neural network, a gradient induction mechanism needs to be used to generate and output nonlinear rotational equivariant features. The specific method is as described above and will not be repeated here.

[0106] Combination Figure 7 It can be seen from the nonlinear equivariant deep learning model shown that the embodiment of the present application extracts the initial features of the input physical system through an efficient graph neural network, extracts rotational equivariant features, then performs direct product operations on the initial rotational equivariant features and returns the rotational invariant components to obtain rotational invariant features, which are input into the nonlinear neural network module to add nonlinearity, thereby obtaining nonlinear rotational invariant features. This constitutes an encoder, i.e. Figure 7The kth encoding module shown in Figure 1. Taking the atomic system as an example, the initial features include the type of each atom in the system and their positions. Two types of features can be further extracted through the position: 1. The distance between atoms; 2. The relative orientation of atoms, represented by the direction vector after the relative position vector modulus is normalized. The initial features are processed by the neural network to obtain a more advanced feature representation.

[0107] S114: The encoders are stacked in series multiple times to obtain a deep encoding network with multiple layers of encoders.

[0108] Combination Figure 7 It can be seen from the nonlinear equivariant deep learning model shown that the embodiment of the present application stacks k coding modules in series to obtain a deep coding network with k layers of coding modules.

[0109] S115: Construct a decoder for decoding nonlinear rotation equivariant features.

[0110] Combination Figure 7 It can be seen from the nonlinear equivariant deep learning model provided by the illustrated embodiment that the decoder provided by the embodiment of the present application includes a rotational equivariant decoder and a rotational invariant decoder. Among them, the rotational equivariant decoder is a linear scaling function; the rotational invariant decoder is a shallow fully connected feedforward network module. The rotational equivariant decoder is connected to the operator of the gradient induction mechanism of the above-mentioned k-th encoding module, and the rotational equivariant physical quantity is obtained by processing the nonlinear rotational equivariant features. The rotational invariant decoder is connected to the nonlinear equivariant neural network module and outputs the rotational invariant physical quantity.

[0111] S116: Connect the deep encoding network and the decoder to construct a nonlinear equivariant deep learning model.

[0112] The technical solution provided in the embodiment of the present application is combined with Figure 7It can be seen from the nonlinear equivariant deep learning model shown that the present application constructs a graph neural network with linear computational complexity by using multiple equivariant function operators. These equivariant function operators can extract rotational equivariant features in the physical system model and enable the constructed graph neural network to have linear computational complexity. Compared with the characteristics of the cubic computational complexity of the input atomic number in the classical functional density theory, the graph neural network can greatly improve the computational efficiency. After the graph neural network is applied to extract the rotational equivariant features, the rotational equivariant features are subjected to direct product operations and Clebsch-Gordan decomposition to obtain the rotational invariant components, and then the rotational invariant components are encoded by the constructed nonlinear neural network to obtain nonlinear rotational invariant features, and then the nonlinear rotational equivariant features can be obtained through gradient induction. The graph neural network and the nonlinear neural network and the related operators constitute an encoder, so that the encoder is stacked in series to obtain a deep encoding network with multiple layers of encoders, so that more accurate nonlinear rotational equivariant features can be obtained after multiple processing. In addition, the present application also constructs a decoder, and the decoder is used to decode the nonlinear rotational equivariant features, so that the rotational equivariant physical quantity can be output. A complete nonlinear deep learning model is constructed in the above manner.

[0113] After building a nonlinear equivariant deep learning model, it is necessary to train and test the nonlinear equivariant deep learning model. Neural networks have training and testing phases. In the training phase, the model outputs a predicted value, compares it with the true value label, and back-propagates the error to train the network parameters to obtain better network parameters. In the testing phase, the trained model is directly used for prediction. When a prediction result is obtained for an input sample, the true value label may be compared with the prediction result to evaluate the performance of the neural network.

[0114] Specifically, as a preferred embodiment, Figure 4 As shown, in the above-mentioned prediction method of rotational equivariant physical quantities, step S110: the step of constructing and training a nonlinear equivariant deep learning model includes:

[0115] S117: Constructing a training sample data set for the material structure to be tested, wherein each training sample in the training sample data set includes a physical system model of the material structure to be tested and a physical quantity true value label.

[0116] Here, a training sample dataset of the material structure to be tested is constructed. The dataset contains N training samples. Each training sample consists of the input atomic system X and the corresponding true value labels of the rotationally invariant physical quantity B and the rotationally equivariant physical quantity D. The true value labels of B and D are represented by B* and D*, respectively. Among them, the true value label D* of the rotationally equivariant physical quantity D can be calculated by classical functional density theory to facilitate subsequent verification. The true value label B* of the rotationally invariant physical quantity B can be calculated by D* through relevant algorithms. For specific algorithms, see Figure 6 The embodiment shown.

[0117] S118: Use the training samples to train the nonlinear equivariant deep learning model to obtain the rotational equivariant physical quantities corresponding to the physical system model.

[0118] The training samples include a physical system model, which contains the 3D structure of atoms, including atomic properties, bond properties, bond lengths, bond angles, relative positions and orientations between atoms, etc. After obtaining the physical system model, the rotational equivariant physical quantity can be obtained by training the graph neural network, nonlinear neural network and decoder of the equivariant deep learning model. The steps of using the equivariant deep learning model to predict the rotational equivariant physical quantity corresponding to the physical system model are as follows: Figure 1 The prediction steps shown are the same and will not be described in detail.

[0119] S119: Use physical quantity truth labels to verify rotational equivariant physical quantities.

[0120] The truth value label D* of the rotational equivariant physical quantity and the truth value label B* of the rotational invariant physical quantity are obtained above. In this way, the truth value labels of the above physical quantities can be used to verify the rotational equivariant physical quantity and the rotational invariant physical quantity. Specifically, Figure 7 The nonlinear equivariant deep learning model shown in Figure 2 is shown in Figure 2. After verification, the loss function of the model can be gradually converged.

[0121] Specifically, the loss function of the model in the embodiment of the present application is as follows:

[0122]

[0123] in and is a hyperparameter.

[0124] For other training samples in the training sample data set, the nonlinear equivariant deep learning model is trained using the training samples and subsequent steps until the loss function of the nonlinear equivariant deep learning model converges. The embodiment of the present application constructs a nonlinear equivariant deep learning model and uses other training samples in the training sample data set to repeatedly perform the training and verification process of the nonlinear equivariant deep learning model until the loss function of the nonlinear equivariant deep learning model converges, so as to obtain a nonlinear equivariant deep learning model that has been trained and has achieved prediction accuracy.

[0125] Combination Figure 7 As shown in the nonlinear equivariant deep learning model, the model includes graph neural network, nonlinear neural network, gradient induction mechanism and decoder modules. For specific training methods, see Figures 4 to 6 The embodiment shown.

[0126] Specifically, Figure 5 As shown, as a preferred embodiment, in the above-mentioned prediction method of rotational equivariant physical quantities, step S118: using training samples to train a nonlinear equivariant deep learning model to obtain rotational equivariant physical quantities corresponding to the physical system model, comprises:

[0127] S1181: Starting from the first encoder layer of the deep encoding network, use the encoder's graph neural network to extract rotational equivariant features of the physical system model.

[0128] Graph neural networks have linear computational complexity, which greatly reduces the computational complexity and greatly improves the computational efficiency compared to the traditional classical functional density theory calculation method in which the number of atoms grows cubically. This makes it possible to quickly extract initial rotational equivariant features from training samples.

[0129] S1182: Convert the nonlinear rotational invariant feature corresponding to the rotational equivariant feature according to the gradient induced mechanism to obtain the nonlinear rotational equivariant feature.

[0130] It should be noted that in microscopic physical systems, physical quantities can be divided into rotationally invariant quantities and rotationally equivariant quantities. The two can be converted into each other. Here, the true value label of the rotationally invariant quantity is used as a supervisory signal to promote the learning of rotationally invariant features and obtain higher quality rotationally invariant features. In the gradient induction mechanism, rotationally invariant features are converted into rotationally equivariant features, which in turn improves the quality of rotationally equivariant features and enhances their expressiveness.

[0131] In order to solve the problem that the nonlinear expression ability and rotation equivariance of existing deep learning-based prediction algorithms are incompatible, it is necessary to first process the rotation equivariant features and convert them into nonlinear rotation invariant features. The nonlinear rotation invariant features are compatible with nonlinear expression ability and rotation invariance, and the nonlinear rotation invariant features are converted using the gradient induction mechanism. The obtained rotation equivariant features also have nonlinearity, so that the converted nonlinear rotation equivariant features have both nonlinear expression ability and rotation equivariance, which solves the problem that the nonlinear expression ability and rotation equivariance of existing deep learning-based prediction algorithms are incompatible.

[0132] S1183: Input the nonlinear rotation equivariant features to the next layer of encoder of the deep coding network for calculation until the nonlinear rotation equivariant features output by the last layer of encoder are obtained. The present application performs k serial replication and stacking of the encoding process of the above steps to form a deep coding network with k basic units, and uses the nonlinear rotation equivariant features of the previous layer as the input of the next layer of encoder. This is repeated k times to obtain the nonlinear rotation equivariant features output by the last layer of encoder. In this way, the value of the nonlinear rotation equivariant features is more accurate.

[0133] S1184: Input the nonlinear rotational equivariant features output by the last layer encoder into the decoder for decoding to obtain rotational equivariant physical quantities.

[0134] The technical solution provided in the embodiment of the present application repeatedly performs the above operations on other training samples in the training sample data set until the loss function of the nonlinear equivariant deep learning model converges, thereby obtaining a trained nonlinear equivariant deep learning model with high prediction accuracy.

[0135] In addition, it should be noted that in order to predict the rotational equivariant physical quantities and rotational invariant physical quantities output by the nonlinear equivariant deep learning model, in addition to constructing the equivariant truth value labels of the rotational equivariant physical quantities in the embodiments of the present application, it is also necessary to construct the invariant truth value labels of the rotational invariant physical quantities, and the truth value labels of the rotational invariant physical quantities are calculated from the truth value labels of the rotational equivariant physical quantities.

[0136] Specifically, as a preferred embodiment, Figure 6 As shown, in the above-mentioned prediction method of rotational equivariant physical quantities, step S117: the step of constructing a training sample data set of the material structure to be tested, comprises:

[0137] S1171: Calculate equivariant truth labels for verifying rotational equivariant physical quantities.

[0138] The technical solution provided in the embodiment of the present application can use the traditional density functional theory method to calculate the rotational equivariant physical quantity D corresponding to the material structure in the sample training data set to obtain its equivariant true value label D*.

[0139] S1172: Use the equivariant truth value label and calculate the formula based on the rotationally invariant physical quantity:

[0140]

[0141] Calculate the invariant truth value label used to verify the rotation invariant physical quantity, where B represents the rotation invariant physical quantity, D represents the rotation equivariant physical quantity, T represents the trace operation, represents the conjugate transpose operation;

[0142] After the decoder outputs the rotational equivariant physical quantity D and the rotational invariant physical quantity B, the equivariant truth label D* and the invariant truth label B* are used to verify the rotational equivariant physical quantity and the rotational invariant physical quantity respectively.

[0143] In deep learning, true value labels are used for supervised training of neural network parameters, the purpose of which is to optimize the neural network parameters. The neural network parameters are trained through paired data (input samples, true value labels) to make the neural network have stronger and stronger predictive performance.

[0144] Specifically, if the application needs to predict the rotational equivariant physical quantities of crystal materials, it is necessary to construct a crystal material dataset containing rich 3D structures and element categories for the training and verification of nonlinear equivariant deep learning models. First, the Hamiltonian matrix D corresponding to the crystal structure in the dataset is calculated using the traditional density functional theory method to obtain its true value label D*. Then, according to

[0145] Obtain the corresponding rotationally invariant physical quantity B from the Hamiltonian and calculate its true value label B*;

[0146] Also, see Figure 7 , Figure 7 A schematic diagram of the structure of a nonlinear equivariant deep learning model provided in an embodiment of the present application. In combination with the nonlinear equivariant deep learning model, an embodiment of the present application provides the following method for predicting rotational equivariant physical quantities, and the specific steps are as follows:

[0147] Step 310: Rotate the equivariant physical quantity for the prediction target , construct a rotationally invariant physical quantity related to it ,in represents the trace operation, Represents the conjugate transpose operation.

[0148] Step 320: Construct a training data set, including N training samples, each of which consists of an input atomic system X and a corresponding rotationally invariant physical quantity. and rotational equivariant quantities The true value label of . and The true value labels are respectively and To express.

[0149] Step 330: Build an atomic system As input, the rotationally invariant physical quantity and rotational equivariant quantities Deep learning neural network model for prediction, including extraction of nonlinear rotation invariant features and nonlinear rotational equivariant features The encoding network and the decoded and The decoding network. The encoding and decoding process is as follows:

[0150] Step 331: construct an efficient graph neural network with linear computational complexity relative to the number of input atoms through operators such as spherical harmonics, tensor addition, tensor direct sum, tensor direct product, Clebsch-Gordan decomposition, equivariant Dropout, equivariant Layernorm, and equivariant gated activation function, and quickly extract initial rotation equivariant features from the input object. ;

[0151] Step 332: Initial rotation equivariant feature With itself direct product operation; specifically, in mathematical symbols, if the initial rotation equivariant characteristic is , then the direct product operation result, that is, the calculation formula of the new rotational equivariant feature f is as follows:

[0152]

[0153] Step 333, perform Clebsch-Gordan decomposition on the direct product operation result of step 332, and obtain the rotation invariant component;

[0154] Step 334: Encode the result of step 333 (rotation invariant component) through a nonlinear neural network module to obtain a nonlinear rotation invariant feature. ;

[0155] Step 335: Introduce the gradient induction mechanism to obtain nonlinear rotational equivariant features , the specific calculation formula of the gradient induction mechanism is as follows:

[0156]

[0157] Step 336: perform K serial replications and stacking of the encoding process described in steps 331 to 335 to form a deep encoding network with K basic units; Figure 7 shown.

[0158] Step 337: extract the rotation invariant features of the last layer of the encoding network described in step 336 respectively and rotational equivariant features , through the rotation invariant decoder and the rotation equivariant decoder, the predicted target is obtained respectively and ;

[0159] Step 340: and As supervisory signals, the deep learning neural network model described in step 3 is trained respectively, and a large number of samples are trained until the model converges; specifically, in the embodiment of the present application, the loss function of the deep learning neural network model is as follows:

[0160]

[0161] in and is the hyperparameter of the model. Through continuous training, the loss function of the model convergence.

[0162] Step 350: After the nonlinear equivariant deep learning model is trained, for new input samples, the predicted target is inferred based on the trained parameters. The numerical value of .

[0163] The technical solution provided in the above-mentioned embodiments of the present application aims to solve the deficiencies in the computational accuracy and efficiency of the existing methods for predicting rotational and equivariant physical quantities, and can combine the advantages of high computational efficiency, nonlinear expression capability and strict rotational equivariance, thereby achieving a harmonious unity of computational efficiency and prediction accuracy, making it possible to perform precise calculations of large-scale physical systems under limited hardware resources and time costs, and effectively enabling the development of downstream industries such as materials science, chemistry and biomedicine.

[0164] Specifically, regarding computational efficiency: since the computational complexity is linear in the number of atoms, it has obvious computational efficiency advantages compared to the traditional density functional theory which requires a complexity of the cubic order of the number of atoms.

[0165] Regarding nonlinear expression ability: Due to the source of the nonlinear expression ability of rotational equivariant features: first construct rotational invariant features through rotational equivariant features; apply nonlinear operations to rotational invariant features to obtain nonlinear expression ability; transfer the nonlinear expression ability to rotational equivariant features through the gradient induction mechanism, so that rotational equivariant features can obtain nonlinear expression ability while maintaining equivariant properties.

[0166] About strict rotational equivariance: Because of the gradient induction mechanism, mathematical methods are used to transform the rotational invariant features, thus achieving strict rotational equivariance.

[0167] In addition, in combination with the atomic system of the crystal structure, the present application provides a method for predicting the Hamiltonian of the crystal structure. Specifically, in this embodiment, the method is used to predict the electronic structure and physical and chemical properties of the crystal. The specific implementation scheme and steps are as follows:

[0168] Step 410: Construct a crystal material dataset containing rich 3D structures and element categories for training and validating a nonlinear equivariant deep learning model.

[0169] Step 420: Training and validation, using traditional density functional theory methods to train the Hamiltonian matrix corresponding to the crystal structure in the data set Calculate and get its true value label Then, according to From the Hamiltonian, we get the corresponding rotationally invariant physical quantity B and calculate its true value label .

[0170] Step 430: Convert each 3D structure in the data set constructed in step 410 into a standard 3D graph format, model each atom as a vertex of the graph, and model each atom pair within the truncation radius as an edge of the graph. Use features such as atomic properties, bond properties, bond lengths, bond angles, relative positions and orientations between atoms as initial representations of the 3D graph.

[0171] Step 440: Send the features in step 420 to the nonlinear equivariant deep learning model proposed in the present invention, and train the entire model until convergence through the true value labels of the Hamiltonian D and its corresponding rotationally invariant physical quantity B.

[0172] Step 450: For the new crystal structure whose electronic structure Hamiltonian is to be predicted, convert it into a 3D image and extract initial features in the manner described in step 420, and then send it to the trained deep learning model described in step 430 for reasoning to obtain the corresponding Hamiltonian prediction value D;

[0173] Step 460: Calculate the charge density and band structure of the crystal from the Hamiltonian matrix D predicted in step 450, thereby obtaining complete information on the electronic structure of the crystal, and derive the physical and chemical properties of the crystal based on the electronic structure.

[0174] Compared with the prior art, the present invention has the following advantages and positive effects:

[0175] By constructing rotationally invariant physical quantities from rotationally equivariant physical quantities as supervisory signals, the nonlinear equivariant deep learning model's ability to model and encode the intrinsic mathematical structure of the target physical quantity is improved.

[0176] Taking rotation invariant features as a bridge, the nonlinear expression ability of rotation invariant features is transformed into rotation equivariant features through the gradient induction mechanism, so that rotation equivariant features have sufficient nonlinear expression ability, which is helpful to accurately predict rotation equivariant targets.

[0177] The computational complexity of this technical solution is linear in the number of atoms, achieving a harmonious unity of computational efficiency and prediction accuracy, making it possible to perform precise calculations of large-scale physical systems with limited hardware resources and time costs.

[0178] In addition, it should be noted that the above examples are only used to understand the present application and do not constitute a limitation on the prediction method of rotational equivariant physical quantities of the present application. More forms of simple transformations based on this technical concept are all within the scope of protection of the present application.

[0179] In addition, the prediction device of rotational equivariant physical quantities provided in the present application includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the prediction method of rotational equivariant physical quantities of any of the above-mentioned embodiments.

[0180] Reference below Figure 8 , which shows a schematic diagram of the structure of a prediction device for rotational equivariant physical quantities suitable for implementing the embodiment of the present application. The prediction device for rotational equivariant physical quantities in the embodiment of the present application can include but is not limited to mobile terminals such as mobile phones, laptop computers, digital broadcast receivers, PDAs (Personal Digital Assistants), PADs (Portable Application Descriptions), PMPs (Portable Media Players), vehicle-mounted terminals (such as vehicle-mounted navigation terminals), etc., and fixed terminals such as digital TVs, desktop computers, etc. Figure 8The prediction device for rotational and other variable physical quantities shown is merely an example and should not bring any limitation to the functions and scope of use of the embodiments of the present application.

[0181] like Figure 8 As shown, the prediction device of rotational equivariant physical quantity can include a processing device 1001 (such as a central processing unit, a graphics processing unit, etc.), which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM: Read Only Memory) 1002 or a program loaded from a storage device 1003 to a random access memory (RAM: Random Access Memory) 1004. Various programs and data required for the operation of the prediction device of rotational equivariant physical quantity are also stored in RAM1004. The processing device 1001, ROM1002 and RAM1004 are connected to each other via a bus 1005. An input / output (I / O) interface 1006 is also connected to the bus. Typically, the following systems can be connected to the I / O interface 1006: input devices 1007 including, for example, a touch screen, a touchpad, a keyboard, a mouse, an image sensor, a microphone, an accelerometer, a gyroscope, etc.; output devices 1008 including, for example, a liquid crystal display (LCD), a speaker, a vibrator, etc.; storage devices 1003 including, for example, a magnetic tape, a hard disk, etc.; and communication devices 1009. The communication device 1009 can enable the prediction device of variable physical quantities such as rotation to communicate wirelessly or wired with other devices to exchange data. Although the figure shows a model building device with various systems, it should be understood that it is not required to implement or have all the systems shown. More or fewer systems can be implemented or have instead.

[0182] In particular, according to the embodiments disclosed in the present application, the process described above with reference to the flowchart can be implemented as a computer software program. For example, the embodiments disclosed in the present application include a computer program product, which includes a computer program carried on a computer-readable medium, and the computer program includes a program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network through a communication device, or installed from a storage device 1003, or installed from a ROM 1002. When the computer program is executed by the processing device 1001, the above-mentioned functions defined in the method of the embodiment disclosed in the present application are executed.

[0183] The prediction device for rotational equivariant physical quantities provided by the present application adopts the prediction method for rotational equivariant physical quantities in the above-mentioned embodiment, which can solve the technical problem that the existing technical methods are difficult to take into account both the calculation efficiency and the calculation accuracy of rotational equivariant physical quantities. Compared with the prior art, the beneficial effects of the prediction device for rotational equivariant physical quantities provided by the present application are the same as the beneficial effects of the prediction method for rotational equivariant physical quantities provided by the above-mentioned embodiment, and other technical features in the prediction device for rotational equivariant physical quantities are the same as the features disclosed in the method of the previous embodiment, which will not be repeated here.

[0184] It should be understood that the various parts disclosed in this application can be implemented by hardware, software, firmware or a combination thereof. In the description of the above embodiments, specific features, structures, materials or characteristics can be combined in any one or more embodiments or examples in a suitable manner.

[0185] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

[0186] The present application provides a computer-readable storage medium having computer-readable program instructions (ie, computer programs) stored thereon, wherein the computer-readable program instructions are used to execute the method for predicting rotational equivariant physical quantities in the above-mentioned embodiment.

[0187] The computer-readable storage medium provided in the present application can be, for example, a USB flash drive, but is not limited to electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, systems or devices, or any combination of the above. More specific examples of computer-readable storage media can include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM: Random Access Memory), a read-only memory (ROM: Read Only Memory), an erasable programmable read-only memory (EPROM: Erasable Programmable Read Only Memory or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM: CD-Read Only Memory), an optical storage device, a magnetic storage device, or any suitable combination of the above. In this embodiment, the computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in combination with an instruction execution system, system or device. The program code contained on the computer-readable storage medium can be transmitted using any appropriate medium, including but not limited to: wires, optical cables, RF (Radio Frequency: Radio Frequency), etc., or any suitable combination of the above.

[0188] The computer-readable storage medium can be included in the prediction device of rotational equivariant physical quantity; or it can exist independently without being assembled into the prediction device of rotational equivariant physical quantity.

[0189] The computer-readable storage medium carries one or more programs, and when the one or more programs are executed by the model building device, the computer program code for performing the operation of the present application can be written in one or more programming languages ​​or a combination thereof, and the programming language includes an object-oriented programming language, such as Java, Smalltalk, C++, and a conventional procedural programming language, such as "C" language or a similar programming language. The program code can be executed completely on the user's computer, partially on the user's computer, as an independent software package, partially on the user's computer and partially on a remote computer, or completely on a remote computer or server. In the case of a remote computer, the remote computer can be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computer (for example, through the Internet using an Internet service provider).

[0190] The flow chart and block diagram in the accompanying drawings illustrate the possible architecture, function and operation of the system, method and computer program product according to various embodiments of the present application. In this regard, each square box in the flow chart or block diagram can represent a module, a program segment or a part of a code, and the module, the program segment or a part of the code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the square box can also occur in a sequence different from that marked in the accompanying drawings. For example, two square boxes represented in succession can actually be executed substantially in parallel, and they can sometimes also be executed in the opposite order, depending on the functions involved. It should also be noted that each square box in the block diagram and / or flow chart, and the combination of the square boxes in the block diagram and / or flow chart can be implemented by a dedicated hardware-based system that performs a specified function or operation, or can be implemented by a combination of dedicated hardware and computer instructions.

[0191] The modules involved in the embodiments of the present application can be implemented by software or hardware, wherein the name of the module does not limit the unit itself in some cases.

[0192] The readable storage medium provided in the present application is a computer-readable storage medium, which stores computer-readable program instructions (i.e., computer programs) for executing the above-mentioned method for predicting rotational equivariant physical quantities. Compared with the prior art, the beneficial effects of the computer-readable storage medium provided in the present application are the same as the beneficial effects of the method for predicting rotational equivariant physical quantities provided in the above-mentioned embodiments, which will not be elaborated here.

[0193] The present application also provides a computer program product, including a computer program, which implements the steps of the above-mentioned method for predicting rotational and other variable physical quantities when executed by a processor.

[0194] The computer program product provided by the present application can solve the technical problem that the existing methods are difficult to simultaneously ensure the prediction accuracy and calculation efficiency of rotational equivariant physical quantities. Compared with the prior art, the beneficial effects of the computer program product provided by the present application are the same as the beneficial effects of the prediction method of rotational equivariant physical quantities provided by the above-mentioned embodiment, and will not be described in detail here.

[0195] The above descriptions are only some embodiments of the present application, and are not intended to limit the patent scope of the present application. All equivalent structural changes made using the contents of the present application specification and drawings under the technical concept of the present application, or direct / indirect applications in other related technical fields are included in the patent protection scope of the present application.

Claims

1. A method for predicting rotational equivariant physical quantities, characterized in that: include: Constructing and training a nonlinear equivariant deep learning model, wherein the nonlinear equivariant deep learning model includes a graph neural network and a decoder with linear computational complexity; When the training of the nonlinear equivariant deep learning model is completed, the physical system model of the material structure to be tested is input into the nonlinear equivariant deep learning model; Extracting rotational equivariant features of the physical system model using the graph neural network; Converting the nonlinear rotational invariant feature corresponding to the rotational equivariant feature according to a gradient induction mechanism to obtain a nonlinear rotational equivariant feature; Decoding the nonlinear rotational equivariant characteristics using a decoder to predict the rotational equivariant physical quantity of the material structure to be tested; The step of converting the nonlinear rotational invariant feature corresponding to the rotational equivariant feature according to the gradient induction mechanism to obtain the nonlinear rotational equivariant feature comprises: Using the rotational equivariant feature, according to the gradient induction mechanism: The nonlinear rotation invariant feature is converted to obtain the nonlinear rotation equivariant feature, wherein: represents the rotational equivariant feature, represents the nonlinear rotation invariant feature, Represents nonlinear rotational equivariant characteristics; The steps of constructing and training a nonlinear equivariant deep learning model include: Using multiple equivariant function operators, constructing the graph neural network with linear computational complexity; Construct nonlinear neural networks for nonlinear coding; Connecting the graph neural network and the nonlinear neural network to obtain an encoder, wherein the encoder is used to output the nonlinear rotational equivariant feature; The encoders are stacked in series multiple times to obtain a deep encoding network with multiple layers of encoders; constructing a decoder for decoding the nonlinear rotational equivariant feature; The deep encoding network and the decoder are connected to construct the nonlinear equivariant deep learning model.

2. The method according to claim 1, characterized in that Before the step of converting the nonlinear rotation invariant feature corresponding to the rotation equivariant feature according to the gradient induction mechanism, the method further comprises: Performing a direct product operation on the rotational equivariant feature to obtain a direct product operation result; Performing Clebsch-Gordan decomposition on the direct product operation result to obtain a rotationally invariant component corresponding to the rotationally equivariant feature; The nonlinear neural network of the nonlinear equivariant deep learning model is used to perform nonlinear encoding on the rotation invariant component to obtain the nonlinear rotation invariant feature.

3. The method according to claim 1, characterized in that The steps of constructing and training a nonlinear equivariant deep learning model include: Constructing a training sample data set of the material structure to be tested, wherein each training sample in the training sample data set includes a physical system model of the material structure to be tested and a physical quantity true value label; Using the training samples to train the nonlinear equivariant deep learning model, to obtain rotational equivariant physical quantities corresponding to the physical system model; Verify the rotational equivariant physical quantity using the physical quantity truth label; For other training samples in the training sample data set, repeatedly perform the steps of training the nonlinear equivariant deep learning model using the training samples and subsequent steps until the loss function of the nonlinear equivariant deep learning model converges.

4. The method according to claim 3, characterized in that The step of using the training samples to train the nonlinear equivariant deep learning model to obtain rotational equivariant physical quantities corresponding to the physical system model includes: Starting from a first layer encoder of the deep encoding network, using a graph neural network of the encoder, extracting rotational equivariant features of the physical system model; Converting the nonlinear rotational invariant feature corresponding to the rotational equivariant feature according to a gradient induction mechanism to obtain a nonlinear rotational equivariant feature; Inputting the nonlinear rotation equivariant feature into the next layer of encoder of the deep coding network for operation until the nonlinear rotation equivariant feature output by the last layer of encoder is obtained; The nonlinear rotational equivariant features output by the last layer encoder are input into the decoder for decoding to obtain the rotational equivariant physical quantity.

5. The method according to claim 3, characterized in that The step of constructing a training sample data set of the material structure to be tested comprises: Calculating an equivariant truth label for verifying the rotational equivariant physical quantity; Using the equivariant truth value label, the formula for calculating the rotationally invariant physical quantity is: Calculate the invariant truth value label used to verify the rotation invariant physical quantity, where B represents the rotation invariant physical quantity, D represents the rotation equivariant physical quantity, T represents the trace operation, represents the conjugate transpose operation; After the decoder outputs the rotational equivariant physical quantity and the rotational invariant physical quantity, the rotational equivariant truth value label and the invariant truth value label are used respectively to verify the rotational equivariant physical quantity and the rotational invariant physical quantity.

6. A prediction device for rotational equivariant physical quantities, characterized in that: The device comprises: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program is configured to implement the steps of the method for predicting a rotational equivariant physical quantity according to any one of claims 1 to 5.

7. A storage medium, characterized in that: The storage medium is a computer-readable storage medium, and a computer program is stored on the storage medium. When the computer program is executed by a processor, the steps of the method for predicting rotational equivariant physical quantities according to any one of claims 1 to 5 are implemented.

8. A computer program product, characterized in that The computer program product comprises a computer program, and when the computer program is executed by a processor, the steps of the method for predicting a rotational equivariant physical quantity according to any one of claims 1 to 5 are implemented.

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