A lattice design and performance prediction method based on deep learning

Abstract

The present invention discloses a lattice design and performance prediction method based on deep learning, including: S1, constructing a lattice data set; S2, constructing a deep learning framework, and using the lattice data set to train it, to obtain a pseudo-physical enhanced neural network model, which includes a backbone network for preliminarily learning the relationship between input features and output features and a pseudo-physical information extraction network for extracting pseudo-physical information of input features and output features; S3, inputting the geometric parameters of the lattice structure of unknown performance into the physical enhancement model, outputting the corresponding mechanical properties and the manifested physical relationship, and then designing the lattice structure according to the physical relationship. The method of the present invention uses a deep learning model and algorithm to extract effective features from the geometric data of the lattice structure, and realizes efficient, accurate and reliable prediction of the mechanical properties of different structures.

Description

Technical Field

[0001] The present invention belongs to the field of mechanical superstructure materials, and specifically relates to a lattice design and performance prediction method based on deep learning. Background Art

[0002] Lattice structure is a key component of metamaterials. Its macroscopic properties are determined by its geometric shape, which provides a large design space. Establishing performance prediction and customized design models of lattice structures is the key to further improving mechanical properties, which is of great strategic significance to aerospace, transportation, building materials and other fields. There are currently two main methods, one is the traditional method based on finite element calculation or homogenization method, and the other is a data-driven machine learning method, such as neural networks (generative adversarial networks, variational autoencoders, graph networks...), random forests and vector machines.

[0003] Traditional methods rely on a large amount of simulation calculations and experimental data, which are costly and difficult to handle in complex working environments. Although machine learning (deep learning) methods can automatically learn and extract key geometric factors that affect the performance of lattice structures, they are still in their infancy, especially the application of models such as physical information neural networks and Kolmogorov–Arnold neural networks, which can only be applied through The extraction of physical laws using ten mathematical forms may lead to insufficient expression capabilities of the network. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, the deep learning-based lattice design and performance prediction method provided by the present invention solves the problems of low prediction performance accuracy and difficulty in giving corresponding physical relationship expressions in existing related methods.

[0005] In order to achieve the above-mentioned invention object, the technical solution adopted by the present invention is: A lattice design and performance prediction method based on deep learning, comprising the following steps:

[0006] S1, build lattice data set;

[0007] The data in the lattice data set include crystal structure geometric parameters as input features and lattice structure mechanical properties as corresponding output features;

[0008] S2. Build a deep learning framework and train it using the lattice dataset to obtain a pseudo-physics enhanced neural network model;

[0009] The pseudo-physics enhanced neural network model includes a backbone network and a pseudo-physics information extraction network; the backbone network is used to preliminarily learn the relationship between input features and output features; the pseudo-physics information extraction network is used to extract pseudo-physics information of input features and output features based on the learned relationship between input features and output features;

[0010] During the training of the deep learning framework, a pseudo-physical loss for extracting pseudo-physical information is embedded into the loss calculation of the backbone network, and the backbone network is back-propagated and optimized based on the pseudo-physical loss;

[0011] S3. Input the geometric parameters of the lattice structure with unknown performance into the physical enhancement model, output the corresponding mechanical properties and the manifested physical relationship, and then design the lattice structure according to the physical relationship.

[0012] Further, the step S1 comprises the following sub-steps:

[0013] S11, determining a unique model through independent geometric parameters of the lattice structure, and using the geometric parameters as input features;

[0014] S12, importing the unique model into the CAE model to calculate its corresponding mechanical properties as output features;

[0015] S13, performing maximum-minimum normalization processing on the input features and output features, and then constructing a lattice data set.

[0016] Furthermore, in step S2, the loss of the backbone network for:

[0017] ;

[0018] ;

[0019] ;

[0020] ;

[0021] In the formula, For data loss in the backbone network, Pseudo-physics loss for the pseudo-physics information extraction network, is the data loss weight, is the pseudo-physical loss weight, is the prediction result of the backbone network. Pseudo-physical information extracted by the pseudo-physical information extraction network, is the data pair sequence number, is the training data of the input features, is the training data of the output features, is the number of data loss, The number of physical losses.

[0022] Furthermore, the pseudo-physical information extraction network It is expressed as:

[0023] ;

[0024] In the formula, is the n initial input value of the first layer, the activation function θ α,β :[0,1]→ R , activation function , is the number of input values ​​for the first layer, is the number of input values ​​for the second layer, is the total number of data, is the set of real numbers, Represents the second layer input value.

[0025] Furthermore, the activation function and It is a learnable unary function, whose activation value is added after fitting and passed to the next neuron, which is expressed as:

[0026] ;

[0027] In the formula, is the sum of activation values, is the output value of the activation function, represents the activation function, is the input value of the activation function, is the neuron index, Extracting pseudo-physical information from the network The number of neurons in the layer, is the index of the neuron input, is the total number of neuron inputs.

[0028] Furthermore, the output of the pseudo-physical information extraction network It is expressed as:

[0029] ;

[0030] In the formula, , , …, , The pseudo-physical information extraction network is ~The neuron index in layer 1, is the layer number of the pseudo-physical information extraction network, , …, , The pseudo-physical information extraction network is ~1 layer activation function, Extract the input feature values ​​of the first layer in the network for pseudo-physical information, , , , The pseudo-physical information extraction network is ~The number of neurons in layer 1.

[0031] Furthermore, in step S2, the deep learning framework is trained using a stacking optimization strategy, and the training method is specifically as follows:

[0032] S21, dividing the lattice data set into a plurality of subsets;

[0033] S22, taking the backbone network, the pseudo-physical information extraction network, and the PINN obtained by embedding the pseudo-physical information extraction network as physical information as three basic models;

[0034] S23, using a cross-validation method, using each subset to train the basic model respectively, outputting the corresponding predicted value, and forming a predicted data set;

[0035] S24, using the new data set to further train the three basic models and generate new meta-feature combinations;

[0036] S25. All meta-features are combined to form a new training data set, and the deep learning framework is optimized to minimize its loss function to obtain a pseudo-physics enhanced neural network model.

[0037] Furthermore, in step S25, the obtained pseudo-physics enhanced neural network model is expressed as:

[0038] ;

[0039] In the formula, is the optimal pseudo-physics enhanced neural network model, is the predicted value vector, is the actual value, To form a new training data set, is the predicted value, is the loss function.

[0040] Furthermore, in step S25, the hyperparameters optimized for the deep learning framework include the number of layers in the backbone network. , the number of neurons in the mth layer and learning rate , the number of layers in the pseudo-physical information extraction network and the number of neurons in the uth layer , and the data loss weight in the backbone network loss and pseudo-physical loss weight .

[0041] The beneficial effects of the present invention are:

[0042] The method of the present invention uses deep learning models and algorithms to extract effective features from the geometric data of the lattice structure, and realizes efficient, accurate and reliable prediction of the mechanical properties of different structures. Compared with traditional finite element simulation methods or other basic networks, the technical solution of the present invention has the following advantages:

[0043] (1) Once the constructed Pseudo-PINN model is trained, its prediction speed for lattice structure performance is at least five orders of magnitude lower than that of finite element or homogenization methods, greatly reducing computational cost and time.

[0044] (2) It can handle complex working environments and improve the versatility and adaptability of predictions.

[0045] (3) Compared with other networks, Pseudo-PINN requires less data and has lower training costs.

[0046] (4) It can provide explicit physical information, which to a certain extent solves the “black box problem” of neural networks.

[0047] (5) Due to the existence of explicit physical information, a well-trained Pseudo-PINN can simultaneously achieve the functions of performance prediction and customized design. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 Flowchart of the lattice design and performance prediction method based on deep learning provided by the present invention. DETAILED DESCRIPTION

[0049] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0050] The present invention provides a lattice design and performance prediction method based on deep learning, such as Figure 1 As shown, the following steps are included:

[0051] S1, build lattice data set;

[0052] The data in the lattice data set include crystal structure geometric parameters as input features and lattice structure mechanical properties as corresponding output features;

[0053] S2. Build a deep learning framework and train it using the lattice dataset to obtain a pseudo-physics enhanced neural network model;

[0054] The pseudo-physics enhanced neural network model includes a backbone network and a pseudo-physics information extraction network; the backbone network is used to preliminarily learn the relationship between input features and output features; the pseudo-physics information extraction network is used to extract pseudo-physics information of input features and output features based on the learned relationship between input features and output features;

[0055] During the training of the deep learning framework, a pseudo-physical loss for extracting pseudo-physical information is embedded into the loss calculation of the backbone network, and the backbone network is back-propagated and optimized based on the pseudo-physical loss;

[0056] S3. Input the geometric parameters of the lattice structure with unknown performance into the physical enhancement model, output the corresponding mechanical properties and the manifested physical relationship, and then design the lattice structure according to the physical relationship.

[0057] Step S1 of the embodiment of the present invention includes the following sub-steps:

[0058] S11, determining a unique model through independent geometric parameters of the lattice structure, and using the geometric parameters as input features;

[0059] S12, importing the unique model into the CAE model to calculate its corresponding mechanical properties as output features;

[0060] S13, performing maximum-minimum normalization processing on the input features and output features, and then constructing a lattice data set.

[0061] In this embodiment, the input features and output features are integrated into a csv file. By performing maximum-minimum normalization processing, considering that there are no negative values, the normalization range is [0,1], which helps to improve the convergence speed of the algorithm and avoid the deviation caused by data of different dimensions during calculation. The formula for maximum-minimum normalization processing is:

[0062] ;

[0063] In the formula, is the value before normalization, is the normalized value, is the minimum value in the same feature, is the maximum value in the same data.

[0064] In step S2 of the embodiment of the present invention, a pseudo-physical enhanced neural network model based on a deep learning framework is called Pseudo-PINN (pseudo-physical informed neural network), which is obtained by embedding pseudo-physical information extracted by a microphysical information extraction network (KAN network) into the physical loss calculation module of PINN. When realizing performance prediction, the model uses the geometric parameters of the lattice structure as one-dimensional input features and the required mechanical properties as output features. The output result is a quantitative physical relationship between the neural network and the parameters that can achieve rapid prediction, and then when performing structural customization design, it is directly obtained according to the given physical relationship without retraining the network.

[0065] The Pseudo-PINN in this invention adopts the core concept of PINN. First, an optional NN is used as the backbone network to preliminarily learn the relationship between input features and output features, including stress-strain relationship and energy information. Then, the same data is loaded into KAN for training to extract explicit pseudo-physical information. The prediction results of NN are used to calculate the data loss and pseudo-physical loss respectively. Based on this, the loss of the backbone network is for:

[0066] ;

[0067] ;

[0068] ;

[0069] ;

[0070] In the formula, For data loss in the backbone network, Pseudo-physics loss for the pseudo-physics information extraction network, is the data loss weight, is the pseudo-physical loss weight, is the prediction result of the backbone network. Pseudo-physical information extracted by the pseudo-physical information extraction network, is the data pair sequence number, is the training data of the input features, is the training data of the output features, is the number of data loss, The number of physical losses.

[0071] Preferably, the backbone network in this embodiment is a multi-layer perceptron MLP. During the back-propagation optimization process of the multi-layer perceptron MLP, feed-forward propagation including linear combination and nonlinear transformation is first performed, and then back-propagation is performed;

[0072] Among them, the linear combination includes:

[0073] ;

[0074] In the formula, is the first Tier The linear output of a neuron, For the Tier neurons and Tier The weights between neurons, For the Tier The activation value of a neuron, For the The subscript q is the bias term of a neuron, p is the neuron index, and s is the total number of neurons.

[0075] The output result of the linear combination is transformed nonlinearly by introducing a nonlinear activation function. Among them, the nonlinear activation functions include Sigmoid, tanh, ReLU, etc. Choosing a suitable activation function is the key to training the network.

[0076] In the back propagation process, the weights and biases are updated by calculating the loss function of the backbone neural network. The weight update formula is:

[0077] ;

[0078] In the formula, is the learning rate, MSE is the loss function, and MSE is usually used as the loss function in pseudo-PINN.

[0079] In the pseudo-physics enhanced neural network model of this embodiment, embedding KAN as a physical information extractor into PINN is the key to Pseudo-PINN. KAN relies on the Kolmogorov-Arnold representation theorem, that is, for a smooth function, the pseudo-physical information extraction network It is expressed as:

[0080] ;

[0081] In the formula, is the n initial input value of the first layer, the activation function θ α,β :[0,1]→ R , activation function , is the number of input values ​​for the first layer, is the number of input values ​​for the second layer, is the total number of data, is the set of real numbers, Represents the second layer input value.

[0082] In this embodiment, for the KAN network, each activation function and It is a learnable univariate function (such as spline function, Fourier function), which is set on the "edge" of the network. After its activation value is fitted, it is summed and passed to the next neuron. It is expressed as:

[0083] ;

[0084] In the formula, is the sum of activation values, is the output value of the activation function, represents the activation function, is the input value of the activation function, is the neuron index, Extracting pseudo-physical information from the network The number of neurons in the layer, is the index of the neuron input, is the total number of neuron inputs.

[0085] Based on the above formula, the output of the pseudo-physical information extraction network is It is expressed as:

[0086] ;

[0087] In the formula, , , …, , The pseudo-physical information extraction network is ~The neuron index in layer 1, is the layer number of the pseudo-physical information extraction network, , …, , The pseudo-physical information extraction network is ~1 layer activation function, Extract the input feature values ​​of the first layer in the network for pseudo-physical information, , , , The pseudo-physical information extraction network is ~The number of neurons in layer 1; among them, the first layer of the pseudo-physical information extraction network is defined as the input layer of the pseudo-physical information extraction network.

[0088] In step S2 of the embodiment of the present invention, the deep learning framework is trained using a stacking optimization strategy to improve the overall prediction accuracy and generalization ability by combining the prediction results of multiple models. The specific training method is:

[0089] S21, dividing the lattice data set into a plurality of subsets;

[0090] The partitioned subset is represented as ,in is the feature vector, is the target vector, is the dimension;

[0091] S22, the backbone network , Pseudo-Physical Information Extraction Network And the PINN obtained by embedding the pseudo-physical information extraction network as physical information As three basic models;

[0092] S23, using a cross-validation method, using each subset to train the basic model respectively, outputting the corresponding predicted value, and forming a predicted data set;

[0093] Among them, the predicted value is represented as a vector:

[0094] ;

[0095] In the formula, The prediction vector generated for this round of prediction is used to evaluate the expressiveness of the current model;

[0096] S24, using the new data set to further train the three basic models and generate new meta-feature combinations;

[0097] Among them, the new meta-feature combination It is expressed as:

[0098] ;

[0099] In the formula, The three basic models are new predicted values ​​for the input pairs;

[0100] S25. All meta-features are combined to form a new training data set, and the deep learning framework is optimized to minimize its loss function to obtain a pseudo-physics enhanced neural network model.

[0101] Among them, the obtained pseudo-physics enhanced neural network model is expressed as:

[0102] ;

[0103] In the formula, is the optimal pseudo-physics enhanced neural network model, is the predicted value vector, is the actual value, To form a new training data set, is the predicted value, is the loss function.

[0104] In this embodiment, the hyperparameters optimized for the deep learning framework include the number of layers in the backbone network. , the number of neurons in the mth layer and learning rate , the number of layers in the pseudo-physical information extraction network and the number of neurons in the uth layer , and the data loss weight in the backbone network loss and pseudo-physical loss weight .

[0105] Among them, for the backbone network, the number of hyperparameters will be increased or decreased according to the specific network type. The hyperparameters of the pseudo-physical information extraction network will greatly affect its physical information extraction ability and further affect the accuracy of the model. The selection of weights in the backbone network loss is crucial for the effective expression of PINN, and it changes dynamically during the model training process.

[0106] In the embodiment of the present invention, the application of the stacking optimization strategy can greatly improve the performance of Pseudo-PINN, which is specifically embodied in: by combining the prediction results of multiple models, data reuse is achieved, and better prediction performance can be obtained than that of a single model; the flexibility of the model is improved, and different types of basic models can be combined to adapt to different problems; and PINN is prevented from overfitting due to the constraints of KAN.

[0107] The present invention uses specific embodiments to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

[0108] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A lattice design and performance prediction method based on deep learning, characterized in that: The following steps are involved: S1, build lattice data set; The data in the lattice data set include crystal structure geometric parameters as input features and lattice structure mechanical properties as corresponding output features; S2. Build a deep learning framework and train it using the lattice dataset to obtain a pseudo-physics enhanced neural network model; The pseudo-physics enhanced neural network model includes a backbone network and a pseudo-physics information extraction network; the backbone network is used to preliminarily learn the relationship between input features and output features; the pseudo-physics information extraction network is used to extract pseudo-physics information of input features and output features based on the learned relationship between input features and output features; During the training of the deep learning framework, a pseudo-physical loss for extracting pseudo-physical information is embedded into the loss calculation of the backbone network, and the backbone network is back-propagated and optimized based on the pseudo-physical loss; S3, inputting the geometric parameters of the lattice structure with unknown performance into the physical enhancement model, outputting the corresponding mechanical properties and the manifested physical relationship, and then designing the lattice structure according to the physical relationship; In step S2, the deep learning framework is trained using a stacking optimization strategy, and the training method is specifically as follows: S21, dividing the lattice data set into a plurality of subsets; S22, taking the backbone network, the pseudo-physical information extraction network and the PINN obtained by embedding the pseudo-physical information extraction network as physical information as three basic models; S23, using a cross-validation method, using each subset to train the basic model respectively, outputting the corresponding predicted value, and forming a predicted data set; S24, using the new data set to further train the three basic models and generate new meta-feature combinations; S25, combining all meta-features to form a new training data set, optimizing the deep learning framework to minimize its loss function, and obtaining a pseudo-physics enhanced neural network model; In step S25, the obtained pseudo-physics enhanced neural network model is expressed as: ； In the formula, is the optimal pseudo-physics enhanced neural network model, is the predicted value vector, is the actual value, To form a new training data set, is the predicted value, is the loss function.

2. The lattice design and performance prediction method based on deep learning according to claim 1, characterized in that: Described step S1 comprises the following sub-steps: S11, determining a unique model through independent geometric parameters of the lattice structure, and using the geometric parameters as input features; S12, importing the unique model into the CAE model to calculate its corresponding mechanical properties as output features; S13, performing maximum-minimum normalization processing on the input features and output features, and then constructing a lattice data set.

3. The lattice design and performance prediction method based on deep learning according to claim 1, characterized in that: In step S2, the loss of the backbone network for: ； ； ； ； In the formula, For data loss in the backbone network, Pseudo-physics loss for the pseudo-physics information extraction network, is the data loss weight, is the pseudo-physical loss weight, is the prediction result of the backbone network. Pseudo-physical information extracted by the pseudo-physical information extraction network, is the data pair sequence number, is the training data of the input features, is the training data of the output features, is the number of data loss, The number of physical losses.

4. The lattice design and performance prediction method based on deep learning according to claim 1, characterized in that: The pseudo-physical information extraction network It is expressed as: ； In the formula, is the n initial input value of the first layer, the activation function , activation function , is the number of input values ​​for the first layer, is the number of input values ​​for the second layer, is the total number of data, is the set of real numbers, Represents the second layer input value.

5. The lattice design and performance prediction method based on deep learning according to claim 4, characterized in that: The activation function and It is a learnable unary function, whose activation value is added after fitting and passed to the next neuron, which is expressed as: ； In the formula, is the sum of activation values, is the output value of the activation function, represents the activation function, is the input value of the activation function, is the neuron index, Extracting pseudo-physical information from the network The number of neurons in the layer, is the index of the neuron input, is the total number of neuron inputs.

6. The lattice design and performance prediction method based on deep learning according to claim 5, characterized in that: The output of the pseudo-physical information extraction network It is expressed as: ； In the formula, , , …, , The pseudo-physical information extraction network is ~The neuron index in layer 1, is the layer number of the pseudo-physical information extraction network, , …, , The pseudo-physical information extraction network is ~1 layer activation function, Extract the input feature values ​​of the first layer in the network for pseudo-physical information, , , , The pseudo-physical information extraction network is ~The number of neurons in layer 1.

7. The lattice design and performance prediction method based on deep learning according to claim 1, characterized in that: In step S25, the hyperparameters optimized for the deep learning framework include the number of layers in the backbone network , the number of neurons in the mth layer and learning rate , the number of layers in the pseudo-physical information extraction network and the number of neurons in the uth layer , and the data loss weight in the backbone network loss and pseudo-physical loss weight .

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