A deep learning-based prediction method for three-dimensional dislocation interaction forces

Abstract

The application discloses a kind of based on deep learning's three-dimensional dislocation interaction force prediction method, belongs to nuclear material irradiation damage calculation simulation application technical field;The application proposes a kind of based on deep learning's three-dimensional dislocation interaction force prediction method, based on open source software generation available data set, the standardization method of data preprocessing is designed, effectively eliminates the dimensional difference in data set;After data preprocessing, training, the regression model generated by prediction dislocation segment interaction force is a kind of flexible, accurate, higher computational efficiency method, will effectively accelerate the prediction three-dimensional dislocation interaction force, can greatly improve the simulation efficiency of discrete dislocation dynamics (DDD) when three-dimensional dislocation modeling.

Description

Technical Field

[0001] The present invention relates to the technical field of computational simulation applications of nuclear material radiation damage, and in particular to a method for predicting three-dimensional dislocation interaction forces based on deep learning. Background Art

[0002] Dislocations are linear defects that evolve in reactor structural materials under extreme conditions such as high temperature, high pressure, and intense irradiation, and they determine the plastic deformation capacity of metals in most cases. Therefore, to investigate the physical connection between collective dislocation motion and interaction and the failure of the macroscopic mechanical properties of nuclear materials, discrete dislocation dynamics (DDD), a mesoscopic simulation method, has become a valuable computational tool for studying the plastic behavior of metals at the micro and submicro scales. The first two-dimensional DDD can simulate the motion of infinitely long straight edge dislocations parallel to each other within a simplified two-dimensional plane with high computational efficiency. While simplified two-dimensional modeling can provide valuable insights into many aspects of dislocation mechanisms, three-dimensional DDD is needed to address and account for more complex dislocation reaction mechanisms and microscale effects, such as dislocation loops and mixed dislocations.

[0003] Discrete dislocation dynamics (DDD) discretizes dislocation lines into dislocation segments of nanometer length connected by a series of dislocation nodes. The positions of the dislocation nodes are updated by solving the dynamic equations and using a time integration strategy, resulting in displacements that evolve over time. Since dislocation motion is the response of material stress to the node driving force, and all dislocation lines interact elastically with each other, N 2 The computational scale of the system is enormous, so the calculation of the nodal forces required by the system is often the most expensive stage in the simulation. Under three-mode modeling, the classic solution for dislocation elastic interaction forces involves solving a multi-variable continuous double integral equation related to local stresses, which is more difficult and requires a longer timeframe.

[0004]

[0005] Dislocation segment s 12 Dislocation segment s 34 The interaction force generated, where σ 12 Dislocation segment s 12 exist s 34 The local stress at is a single integral function. It is specifically expressed as follows under the isotropic assumption:

[0006]

[0007]

[0008]

[0009]

[0010] In the formula x 3. x 4 are s 34 The starting and ending positions of b yes s 34 The Burger vector of L 、 t Are s 34 The length of the tangent vector, a , μ , v represent the material property parameters - dislocation core diffusion radius, shear modulus and Poisson's ratio, respectively.

[0011] Dislocation types and physical reactions in 3D modeling are diverse, and dislocation density increases dramatically by several orders of magnitude with increasing strain. Although the fast multipole method (FMM), fast Fourier transform (FFT), and finite element method (FEM) can effectively reduce the computational cost of dislocation elastic interaction forces, simulating total strains exceeding 1% in a reasonable volume is still very time-consuming.

[0012] In recent years, the development of artificial intelligence (AI) has ushered in a new paradigm in scientific computing. For computationally intensive tasks such as numerical material simulations, the universal approximation theory, through deep learning techniques, enables neural networks to approximate multidimensional continuous functions with arbitrary precision. Consequently, the regression models generated by trained neural networks have the potential to replace classical numerical solutions to the equations of motion for three-dimensional dislocation modeling and accelerate the calculation of interdislocation interaction forces.

[0013] In view of the above background, the present invention proposes a prediction method for three-dimensional dislocation interaction forces based on deep learning. Summary of the Invention

[0014] The purpose of the present invention is to propose a prediction method for three-dimensional dislocation interaction forces based on deep learning to solve the problems raised in the background technology.

[0015] In order to achieve the above object, the present invention adopts the following technical solutions:

[0016] A deep learning-based prediction method for three-dimensional dislocation interaction forces includes the following:

[0017] (1) Dataset generation: Generate available original datasets based on open source simulation software, and randomly sample multiple data as training datasets and validation test sets;

[0018] (2) Data preprocessing: scaling the data of each indicator in the original data set, removing the unit restriction of the data, and converting it into dimensionless pure numerical values;

[0019] (3) Feature extraction and representation learning: Build the input layer and hidden layer of the neural network, determine the input features and dimensions of the input layer, the dimensions and number of hidden layers, and improve the complexity and learning expression ability of the neural network; in addition, use nonlinear activation functions to achieve nonlinear mapping of data and map the input data to a more advanced feature representation;

[0020] (4) Regression prediction: Build the output layer of the neural network, and use the feature representation learned by the hidden layer as the predicted output value of the neural network after a linear transformation of a fully connected layer;

[0021] (5) Back propagation: Determine the loss function and optimization algorithm, calculate the loss of the neural network based on the output value and the true value of the neural network, and recursively perform each layer from the output layer to the input layer based on the loss value and the optimization algorithm. Use the chain rule to calculate the partial derivative of the weight parameters to achieve the update of the weight parameters. Finally, a back propagation neural network model suitable for accelerating the prediction of the interaction force between dislocations under three-dimensional dislocation modeling is constructed, which is recorded as DD-BPNN.

[0022] Preferably, the original data set in step (1) is generated by simulating the strain hardening model and simulation system in the three-dimensional discrete dislocation dynamics simulation open source software, and a number of prismatic dislocation loops are randomly generated inside the simulation system, and the material property coefficients are a 、 μ 、 v Randomly generated with uniform distribution, where a represents the dislocation core radius, μ represents the shear modulus, v represents Poisson's ratio.

[0023] Preferably, the step (2) specifically includes the following contents:

[0024] Z-Score standardization is used to limit the preprocessed data to the range of [-1,1] to eliminate the adverse effects caused by singular sample data; the mean and standard deviation of the original data are given to standardize the data. The processed data conforms to the standard normal distribution with a mean of 0 and a standard deviation of 1, that is:

[0025]

[0026] in, Xis the original sample data, μ is the mean of all original samples, σ is the variance of all original samples.

[0027] Preferably, the step (3) specifically includes the following contents:

[0028] A multi-layer neural network consisting of an input layer and four hidden layers is constructed to achieve feature extraction and representation learning of the neural network model. A linear rectified unit activation function is used to introduce nonlinear transformation and feature combination to handle the complex data relationship and nonlinear pattern between input features and target values ​​in the three-dimensional discrete dislocation dynamics simulation, capturing the hierarchy and abstraction in the data. The input layer is specifically represented as:

[0029] V ={ x 1, x 2, x 3, x 4, b 1, b 2, a , μ , v}

[0030] y 0= W 0× V + b 0

[0031] in, V represents the input feature vector of the back-propagation neural network model, y 0 represents the input of the hidden layer, W 0 and b 0 represents the weight matrix and bias of the input layer respectively;

[0032] The action process of the hidden layer is specifically expressed as follows:

[0033] = Relu ( W 1× y 0+ b 1) → = Relu ( W 2× + b 2)

[0034] = Relu ( W 3× + b 3) → = Relu ( W4× + b 4)

[0035] in, W i , b i Respectively represent i The weight matrix and bias of the hidden layer, as input to the output layer.

[0036] Preferably, the step (4) specifically includes the following contents:

[0037] Use one fully connected layer as the output layer of the neural network model, and use the output of the last hidden layer obtained in step (3) as the output layer of the neural network model. As input features, namely:

[0038] W 5× + b 5

[0039] U = { f 1x , f 1y , f 1z , f 2x , f 2y , f 2z}

[0040] in, U Represents the regression prediction output value, f ij Indicates the dislocation segment i Nodes in j Force in direction.

[0041] Preferably, the step (5) specifically includes the following contents:

[0042] The value predicted by regression U Establish a mean square error loss function between the target value, that is:

[0043]

[0044] in, N represents the number of training samples passed through the neural network model, YRepresents the target value of the sample data; select the adaptive learning algorithm Adam starting from the output layer, use the chain rule to calculate the gradient of the loss function for each parameter and update the parameter value; repeat steps (3) and (4), calculate the loss, backpropagate and update the parameters until the stopping condition is reached.

[0045] Compared with the existing technology, the present invention provides a method for predicting three-dimensional dislocation interaction forces based on deep learning, which has the following beneficial effects:

[0046] During the simulation of three-dimensional discrete dislocation dynamics, the computational complexity of the elastic interaction forces between dislocations increases dramatically, as dislocation density increases by several orders of magnitude with the accumulation of plastic strain. This paper proposes a deep learning-based method for predicting three-dimensional dislocation interaction forces and constructs a back-propagation neural network (DD-BPNN) model suitable for accelerating the prediction of inter-dislocation interaction forces in three-dimensional dislocation modeling. Based on open-source software to generate a usable dataset, this paper designs a standardized data preprocessing method, effectively eliminating dimensional differences in the dataset. After data preprocessing and training, the generated regression model predicts the interaction forces between dislocation segments. This is a flexible, accurate, and computationally efficient method that will effectively accelerate the prediction of three-dimensional dislocation interaction forces and significantly improve the simulation efficiency of discrete dislocation dynamics (DDD) in three-dimensional dislocation modeling.

[0047] Compared with the existing technology, the present invention is based on the universal approximation theory of artificial intelligence and uses the back-propagation neural network to provide a more flexible, accurate and fast calculation paradigm, replacing the complex and computationally inefficient classical numerical solution, effectively reducing the force calculation time, and improving the simulation efficiency of discrete dislocation dynamics (DDD) under three-dimensional modeling. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 This is a flowchart of predicting dislocation interaction forces based on deep learning technology mentioned in Example 1 of the present invention;

[0049] Figure 2 This is a network structure diagram of the back propagation neural network model (DD-BPNN) mentioned in Example 1 of the present invention. DETAILED DESCRIPTION

[0050] The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments.

[0051] Example 1:

[0052] See also Figure 1-2The present invention proposes a method for predicting three-dimensional dislocation interaction forces based on deep learning. The present invention designs and constructs a back propagation neural network model (DD-BPNN) for predicting three-dimensional dislocation interaction forces. The process is as follows: Figure 1 As shown, first, the raw data is generated through open source software and the rough data is preprocessed; then the zero-score standardization operation is used to scale the raw data to the interval [-1,1]; then the network input layer, hidden layer, and output layer are built to realize feature extraction and representation learning. The output layer passes through a fully connected layer to obtain the initial prediction value of the network, and then the gradient is calculated based on the error between the prediction value and the true target value to update the network weight parameters; finally, it is determined whether the number of iterations is met. If the conditions are not met, iterative training will continue, otherwise the training process will be exited and the network model parameters will be saved. The grid structure of the back propagation neural network model (DD-BPNN) constructed through the above steps is as follows: Figure 2 As shown, it includes an input layer (1 layer), hidden layers (4 layers) and an output layer (1 layer); data transmission and feature extraction are achieved between each layer through full connection; the input features of the input layer include the node coordinates of the two segments x 1, x 2, x 3, x 4, and the two-bit mismatched burges vector b 1, b 2 and material property coefficients dislocation core diffusion radius a , material shear modulus μ and the material Poisson's ratio v Therefore, the input layer has a dimension of 4*3+2*3+3=21. There are four hidden layers, each containing 128, 128, 64, and 32 neurons, respectively. Each neural network uses the ReLU activation function to achieve nonlinear activation of input and hidden features, mapping the input features into a multidimensional feature space. The output layer consists of a fully connected layer with an output dimension of 6, representing the forces acting on the two nodes of the dislocation segment in the x, y, and z directions.

[0053] Based on the above description, this embodiment specifically includes the following contents:

[0054] Step 1: Dataset Generation:

[0055] Using ParaDiS, an open-source software for 3D discrete dislocation dynamics simulation developed by Lawrence Livermore National Laboratory in the United States, a strain hardening model and simulation system are considered. 10,000 prismatic dislocation loops are randomly generated within the simulation system, and the material property coefficient dislocation core diffusion radius a , material shear modulus μ and the material Poisson's ratio vA total of 400,000 data sets were generated using uniform random distribution, and 200,000 data sets were randomly sampled as training data and test data for the back propagation neural network.

[0056] Step 2: Data preprocessing:

[0057] In the field of machine learning, different evaluation indicators (i.e., different features in the feature vector are the different evaluation indicators) often have different dimensions and dimensional units. The input features of three-dimensional discrete dislocation dynamics (DDD) include coordinate information x , Burgers vector b and the material property coefficient dislocation core radius a , material shear modulus μ and the material Poisson's ratio v , and the distance between the input value and the dislocation segment R Inversely proportional to the value of the feature, and accompanied by a sharp gradient. These features have different dimensions and dimensional units, and the numerical range spans multiple orders of magnitude, which will affect the results of data analysis. In order to eliminate the dimensional influence between indicators, data standardization is required to solve the comparability between data indicators. Z-Score standardization is used to limit the preprocessed data to the range of [-1,1], eliminating the adverse effects caused by singular sample data. The mean and standard deviation of the original data are given to standardize the data. The processed data conforms to the standard normal distribution with a mean of 0 and a standard deviation of 1, that is:

[0058]

[0059] in, X is the original sample data, μ is the mean of all original samples, σ is the variance of all original samples.

[0060] Step 3: Feature extraction and representation learning:

[0061] A multi-layer neural network consisting of an input layer and four hidden layers (with layer dimensions of 21, 128, 128, 64, and 32, respectively) was constructed to implement feature extraction and representation learning for DD-BPNN. The rectified linear unit (ReLU) activation function was used to introduce nonlinear transformations and feature combinations to handle the complex data relationships and nonlinear patterns between input features and target values ​​in three-dimensional discrete dislocation dynamics (DDD) simulations, capturing the hierarchical and abstract nature of the data. The input layer is specifically represented as:

[0062] V ={ x 1, x 2,x 3, x 4, b 1, b 2, a , μ , v}

[0063] y 0= W 0× V + b 0

[0064] in, V is the input feature vector of DD-BPNN, y 0 is the input of the hidden layer, W 0 and b 0 are the weight matrix and bias of the input layer respectively. The specific process of the hidden layer is expressed as follows:

[0065] = Relu ( W 1× y 0+ b 1) → = Relu ( W 2× + b 2)

[0066] = Relu ( W 3× + b 3) → = Relu ( W 4× + b 4)

[0067] in, W i , b i They are i The weight matrix and bias of the hidden layer, as input to the output layer.

[0068] Step 4: Regression prediction:

[0069] Use one fully connected layer as the output layer of DD-BPNN, and the input feature is the output of the last hidden layer ,Right now:

[0070] W 5× + b 5

[0071] U = { f 1x , f 1y , f 1z , f 2x , f 2y , f 2z}

[0072] in U Represents the regression prediction output value, f ij Indicates the dislocation segment i Nodes in j Force in direction.

[0073] Step 5: Backward Propagation:

[0074] The value predicted by regression U The mean square error (MSE) loss function is established between the target value, that is:

[0075]

[0076] in, N is the number of training samples through DD-BPNN, Y is the target value for the sample data. The adaptive learning algorithm Adam is selected, starting from the output layer. Using the chain rule, the gradient of the loss function with respect to each parameter is calculated and the parameter values ​​are updated. The forward propagation (steps 3 and 4), loss calculation, backpropagation, and parameter update process are repeated until a stopping condition is met (e.g., reaching the maximum number of iterations, loss function convergence, etc.).

[0077] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. The method for predicting three-dimensional dislocation interaction forces based on deep learning involved in the present invention, including the hybrid grid region decomposition algorithm, parallel spectral element grid generation method, node number synchronization algorithm, and subgrid merging and spectral element grid data output method provided in the invention, are all considered to be within the scope of protection of the present invention. It should be noted that the above description is a preferred embodiment of the present invention. For those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and such improvements and modifications should also be considered to be within the scope of protection of the present invention.

Claims

1. A method for predicting three-dimensional dislocation interaction forces based on deep learning, characterized in that: Includes the following: (1) Dataset generation: Generate available original datasets based on open source simulation software, and randomly sample multiple data as training datasets and validation test sets; The original data set is generated by the strain hardening model and simulation system in the three-dimensional discrete dislocation dynamics simulation open source software. Several prismatic dislocation loops are randomly generated inside the simulation system, and the material property coefficients a 、 μ 、 v Randomly generated with uniform distribution, where a represents the dislocation core radius, μ represents the shear modulus, v represents Poisson's ratio; (2) Data preprocessing: scaling the data of each indicator in the original data set, removing the unit restriction of the data, and converting it into dimensionless pure numerical values; (3) Feature extraction and representation learning: Build the input layer and hidden layer of the neural network, determine the input features and dimensions of the input layer, the dimensions and number of hidden layers, and improve the complexity and learning expression ability of the neural network; in addition, use nonlinear activation functions to achieve nonlinear mapping of data and map the input data to a more advanced feature representation; the input features of the input layer include the node coordinates of the two segments x 1, x 2, x 3, x 4. Two-bit staggered burges vector b 1, b 2. Material property coefficient Dislocation core diffusion radius a , material shear modulus μ and the material Poisson's ratio v ; (4) Regression prediction: Build the output layer of the neural network, and use the feature representation learned by the hidden layer as the predicted output value of the neural network after a linear transformation of a fully connected layer; specifically, it includes the following: Use one fully connected layer as the output layer of the neural network model, and use the output of the last hidden layer obtained in step (3) as the output layer of the neural network model. As input features, namely: W 5× + b 5 U = { f 1x , f 1y , f 1z , f 2x , f 2y , f 2z} in, U Represents the regression prediction output value, f ij Indicates the dislocation segment i Nodes in j Directional force; (5) Back propagation: Determine the loss function and optimization algorithm, calculate the loss of the neural network based on the output value and the true value of the neural network, and recursively perform each layer from the output layer to the input layer based on the loss value and the optimization algorithm. Use the chain rule to calculate the partial derivative of the weight parameters to achieve the update of the weight parameters. Finally, construct a back propagation neural network model suitable for accelerating the prediction of the interaction force between dislocations under three-dimensional dislocation modeling, which is recorded as DD-BPNN.

2. The method for predicting three-dimensional dislocation interaction forces based on deep learning according to claim 1, characterized in that: The step (2) specifically includes the following contents: Z-Score standardization is used to limit the preprocessed data to the range of [-1,1] to eliminate the adverse effects caused by singular sample data; the mean and standard deviation of the original data are given to standardize the data. The processed data conforms to the standard normal distribution with a mean of 0 and a standard deviation of 1, that is: in, X is the original sample data, μ is the mean of all original samples, σ is the variance of all original samples.

3. The method for predicting three-dimensional dislocation interaction forces based on deep learning according to claim 2, characterized in that: The step (3) specifically includes the following contents: A multi-layer neural network consisting of an input layer and four hidden layers is constructed to achieve feature extraction and representation learning of the neural network model. A linear rectified unit activation function is used to introduce nonlinear transformation and feature combination to handle the complex data relationship and nonlinear pattern between input features and target values ​​in the three-dimensional discrete dislocation dynamics simulation, capturing the hierarchy and abstraction in the data. The input layer is specifically represented as: V ={ x 1, x 2, x 3, x 4, b 1, b 2, a , μ , v} y 0= W 0× V + b 0 in, V represents the input feature vector of the back-propagation neural network model, y 0 represents the input of the hidden layer, W 0 and b 0 represents the weight matrix and bias of the input layer respectively; The action process of the hidden layer is specifically expressed as follows: = Relu ( W 1× y 0+ b 1)→ = Relu ( W 2× + b 2) = Relu ( W 3× + b 3)→ = Relu ( W 4× + b 4) in, W i , b i Respectively represent i The weight matrix and bias of the hidden layer, as input to the output layer.

4. The method for predicting three-dimensional dislocation interaction forces based on deep learning according to claim 3, characterized in that: The step (5) specifically includes the following contents: The value predicted by regression U Establish a mean square error loss function between the target value, that is: in, N represents the number of training samples passed through the neural network model, Y Represents the target value of the sample data; select the adaptive learning algorithm Adam starting from the output layer, use the chain rule to calculate the gradient of the loss function for each parameter and update the parameter value; repeat steps (3) and (4), calculate the loss, backpropagate and update the parameters until the stopping condition is reached.

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