Device for optimal design of nonlinear structure using topological optimization framework with embedded convolutional neural network, and method therefor

Abstract

A method for optimal design, according to a preferred embodiment of the present invention for achieving the above-described objective, comprises: a step in which a numerical analysis unit performs numerical analysis to derive a sensitivity satisfying minimization of an objective function from a density at a material point constituting an analysis subject until a predetermined first branching condition is satisfied; a step in which, if the first branching condition is satisfied, a data processing unit configures learning data including a density tensor and an objective vector from the density at the material point of the analysis subject derived through the numerical analysis and the sensitivity derived corresponding to the density; and a step in which a model learning unit trains a neural network model by using the learning data to derive a sensitivity vector predicting the sensitivity at the material point from the density vector representing the density at the material point of the analysis subject.

Description

Device for optimal design of nonlinear structures using a topology optimization framework with an inherent convolutional neural network and a method therefor

[0001] The present invention relates to optimal design of nonlinear structures, and more particularly, to a device for optimal design of nonlinear structures using a topology optimization framework incorporating a convolutional neural network, and a method therefor.

[0002] Research in topology optimization (TOO) technology aims to develop topology optimization algorithms that achieve rapid convergence and efficient computation. However, the inherent iterative nature of topology optimization techniques based on the finite element method (FEM) significantly limits overall efficiency improvements.

[0003] The purpose of the present invention is to provide a device and method for optimal design of a nonlinear structure using a topology optimization framework incorporating a convolutional neural network (CNN).

[0004] In order to achieve the above-described object, a method for optimal design according to a preferred embodiment of the present invention includes a step of performing a numerical analysis to derive a sensitivity that satisfies minimization of an objective function from a density at a material point constituting an analysis target until a predetermined first branching condition is satisfied by a numerical analysis unit; a step of configuring learning data including a density tensor and an objective vector from the density at the material point of the analysis target derived through the numerical analysis and the sensitivity derived in response to the density when the first branching condition is satisfied by a data processing unit; and a step of performing learning on a neural network model using the learning data so that a model learning unit derives a sensitivity vector that predicts the sensitivity at the material point of the analysis target from the density vector representing the density at the material point of the analysis target.

[0005] The method further includes a step of stopping the learning when the model learning unit satisfies a predetermined second branch condition, and a step of re-performing the numerical analysis until the numerical analysis unit satisfies the first branch condition.

[0006] The method further includes a step of reconstructing learning data including density and sensitivity at a material point derived according to the re-performed numerical analysis when the data processing unit satisfies the first branch condition, and a step of performing learning on a neural network model by the model learning unit using the reconstructed learning data.

[0007] The above second branch condition is characterized by whether, when the neural network model derives a sensitivity vector that predicts the sensitivity at a point of interest from a density vector representing the density at the point of interest of the analysis target, the loss representing the difference between the target vector of the learning data and the derived sensitivity vector exceeds a threshold.

[0008] The step of performing the above learning includes a step in which the model learning unit inputs the density vector of the learning data into a neural network model, a step in which the neural network model performs a plurality of operations to which weights for which learning has not yet been completed are applied to the density vector to derive a sensitivity vector for predicting sensitivity at the material point, a step in which the model learning unit derives a loss representing the difference between the sensitivity vector and the target vector of the learning data through a loss function, and a step in which the model learning unit performs optimization to update the weights of the neural network model so that the loss is minimized.

[0009] The step of deriving the sensitivity vector includes a step of deriving a latent vector by performing encoding that compresses the features of a density tensor by an encoder of the neural network model, and a step of deriving a sensitivity vector by performing decoding that restores the latent vector to the size of a density tensor by a decoder of the neural network model.

[0010] The step of deriving the sensitivity vector includes: a step in which, when a density tensor is input to the input layer of the neural network model, the first pooling layer of the neural network model performs a pooling operation on the density tensor to derive a first feature map; a step in which the first convolutional layer of the neural network model performs a convolution operation and an operation by an activation function on the first feature map to derive a second feature map; a step in which the second pooling layer of the neural network model performs a pooling operation on the second feature map to derive a third feature map; a step in which the second convolutional layer of the neural network model performs a convolution operation and an operation by an activation function on the third feature map to derive a fourth feature map; a step in which the third convolutional layer of the neural network model performs a convolution operation and an operation by an activation function on the fourth feature map (FM4) to derive a fifth feature map; and a step in which the first upsampling layer of the neural network model performs an operation by an activation function on the fifth feature map. The method includes: a step of performing an upconvolution operation to derive a sixth feature map; a step of allowing a first convolution layer of the neural network model to combine the third feature map and the sixth feature map to form a seventh feature map; a step of allowing a fourth convolution layer of the neural network model to perform a convolution operation and an operation using an activation function on the seventh feature map to derive an eighth feature map; a step of allowing a second upsampling layer of the neural network model to perform an upconvolution operation on the eighth feature map to derive a ninth feature map; a step of allowing a second convolution layer of the neural network model to combine the input tensor and the ninth feature map to form a tenth feature map; a step of allowing a fifth convolution layer of the neural network model to perform a convolution operation and an operation using an activation function on the tenth feature map to derive an eleventh feature map; and a step of allowing an output layer of the neural network model to perform an operation using an activation function on the eleventh feature map to derive a sensitivity vector.

[0011] The above loss function is a mathematical formula

[0012]

[0013] , and the above θ is a loss, and the above is the target vector, and the above is the transpose matrix of the target vector, and is a sensitivity vector, and i is characterized by being an index of learning data.

[0014] The density tensor includes a plurality of three-channel images divided into the same standard, and each of the plurality of three-channel images is characterized by including a first channel that expresses the density in the current order iteration as an image, a second channel that expresses the difference in density in the current order and the previous order iteration as an image, and a third channel that is a position map indicating the position of the three-channel image.

[0015] The above target vector is characterized by including multiple images that are divided into the same standard and represent sensitivity.

[0016] In order to achieve the above-described object, a device for optimal design according to a preferred embodiment of the present invention includes a numerical analysis unit that performs a numerical analysis to derive a sensitivity that satisfies the minimization of an objective function from a density at a material point constituting an analysis target until a predetermined first branching condition is satisfied; a data processing unit that, when the first branching condition is satisfied, constructs learning data including a density tensor and an objective vector from the density at the material point of the analysis target derived through the numerical analysis and the sensitivity derived corresponding to the density; and a model learning unit that performs learning on the neural network model using the learning data so that the neural network model derives a sensitivity vector that predicts the sensitivity at the material point from the density vector representing the density at the material point of the analysis target.

[0017] The above model learning unit is characterized in that, when a predetermined second branch condition is satisfied, the learning is stopped, and the numerical analysis unit re-performs the numerical analysis until the first branch condition is satisfied.

[0018] The above data processing unit is characterized in that, when the first branch condition is satisfied, the learning data including the density and sensitivity at the material point derived according to the re-performed numerical analysis is reconstructed, and the model learning unit performs learning on a neural network model using the reconstructed learning data.

[0019] The above second branch condition is characterized by whether, when the neural network model derives a sensitivity vector that predicts the sensitivity at a point of interest from a density vector representing the density at the point of interest of the analysis target, the loss representing the difference between the target vector of the learning data and the derived sensitivity vector exceeds a threshold.

[0020] The above model learning unit inputs the density vector of the learning data into a neural network model, and the neural network model performs a plurality of operations to which weights that have not yet been learned are applied to the density vector to derive a sensitivity vector that predicts sensitivity at the material point, and then derives a loss representing the difference between the sensitivity vector and the target vector of the learning data through a loss function, and performs optimization to update the weights of the neural network model so that the loss is minimized.

[0021] The above neural network model includes an encoder that performs encoding to compress the features of a density tensor to derive a latent vector, and a decoder that performs decoding to restore the latent vector to the size of the density tensor to derive a sensitivity vector.

[0022] The neural network model comprises: an input layer in which, when a density tensor is input, a first pooling layer of the neural network model performs a pooling operation on the density tensor to derive a first feature map; a first convolution layer in which a convolution operation and an operation by an activation function are performed on the first feature map to derive a second feature map; a second pooling layer in which a pooling operation is performed on the second feature map to derive a third feature map; a second convolution layer in which a convolution operation and an operation by an activation function are performed on the third feature map to derive a fourth feature map; a third convolution layer in which a convolution operation and an operation by an activation function are performed on the fourth feature map (FM4) to derive a fifth feature map; a first upsampling layer in which an upconvolution operation is performed on the fifth feature map to derive a sixth feature map; and a seventh feature map is formed by combining the third feature map and the sixth feature map. It includes a first combination layer, a fourth convolution layer that performs a convolution operation and an operation using an activation function on the seventh feature map to derive an eighth feature map, a second upsampling layer that performs an upconvolution operation on the eighth feature map to derive a ninth feature map, a second combination layer that combines the input tensor and the ninth feature map to form a tenth feature map, a fifth convolution layer that performs a convolution operation and an operation using an activation function on the tenth feature map to derive an eleventh feature map, and an output layer that performs an operation using an activation function on the eleventh feature map to derive a sensitivity vector.

[0023] The above loss function is a mathematical formula

[0024]

[0025] , and the above θ is a loss, and the above is the target vector, and the above is the transpose matrix of the target vector, and is a sensitivity vector, and i is characterized by being an index of learning data.

[0026] The density tensor includes a plurality of three-channel images divided into the same standard, and each of the plurality of three-channel images is characterized by including a first channel that expresses the density in the current order iteration as an image, a second channel that expresses the difference in density in the current order and the previous order iteration as an image, and a third channel that is a position map indicating the position of the three-channel image.

[0027] The above target vector is characterized by including multiple images that are divided into the same standard and represent sensitivity.

[0028] According to the present invention, by iterating a numerical analysis operation for a predetermined number of times in turn depending on branching conditions and iterating a neural network model (NNM) learning for a predetermined number of times using learning data derived from the numerical analysis, the speed and load of learning for topology optimization can be significantly reduced.

[0029] FIG. 1 is a diagram for explaining the configuration of a device for optimal design of a nonlinear structure using a phase optimization framework incorporating a convolutional neural network according to an embodiment of the present invention.

[0030] FIG. 2 is a diagram for explaining learning data for a neural network model (NNM) according to an embodiment of the present invention.

[0031] FIG. 3 is a diagram for explaining the configuration of a neural network model (NNM) according to an embodiment of the present invention.

[0032] FIG. 4 is a flowchart illustrating a method for optimal design of a nonlinear structure using a topology optimization framework incorporating a convolutional neural network according to an embodiment of the present invention.

[0033] Figure 5 is a flowchart for explaining a learning method of a neural network model (NNM) according to an embodiment of the present invention.

[0034] FIG. 6 is a drawing showing a computing device according to an embodiment of the present invention.

[0035] Before going into a detailed description of the present invention, it should be understood that the embodiments described in this specification and the configurations illustrated in the drawings are merely the most preferred embodiments of the present invention and do not represent all of the technical ideas of the present invention, and therefore, there may be various equivalents and modified examples that can replace them at the time of filing this application.

[0036] Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the attached drawings. It should be noted that, where possible, identical components are represented by identical reference numerals throughout the drawings. Furthermore, detailed descriptions of well-known functions and structures that may obscure the gist of the present invention will be omitted. For the same reason, some components in the attached drawings are exaggerated, omitted, or schematically depicted, and the sizes of each component do not fully reflect their actual sizes.

[0037] In addition, the terms and words used in the present specification and claims described below should not be interpreted as limited to their usual or dictionary meanings, but should be interpreted as meanings and concepts that conform to the technical idea of ​​the present invention based on the principle that the inventor can appropriately define the concept of the term to explain his or her own invention in the best way.

[0038] First, the configuration of a device for optimal design of a nonlinear structure using a topology optimization framework with a built-in convolutional neural network according to an embodiment of the present invention will be described. Fig. 1 is a diagram for explaining the configuration of a device for optimal design of a nonlinear structure using a topology optimization framework with a built-in convolutional neural network according to an embodiment of the present invention. Referring to Fig. 1, the optimal design device (10) of the present invention includes a numerical analysis unit (100), a data processing unit (200), and a model learning unit (300).

[0039] The numerical analysis unit (100) performs a numerical analysis to derive a sensitivity that satisfies the minimization of the objective function from the density at the particle point constituting the analysis target until a predetermined first branch condition is satisfied. This numerical analysis is based on the finite element method (FEM) and is for topology optimization. The numerical analysis iterates the calculation of the state variables so that the objective function satisfies the minimization from the calculation results for the state variables corresponding to the density at the particle point.

[0040] The data processing unit (200) is for constructing learning data. The data processing unit (200) is for constructing learning data including a density tensor and a target vector from the density at the mass point of the analysis target derived through numerical analysis and the sensitivity derived in response to the density.

[0041] The model learning unit (300) is for performing learning (deep learning) on ​​a neural network model (NNM) using the learning data configured by the data processing unit (200). In particular, according to an embodiment of the present invention, the model learning unit (300) performs learning in real time (on line) using the learning data configured by the data processing unit (200). At this time, the model learning unit (300) performs learning on the neural network model so that the neural network model (NNM) derives a sensitivity vector that predicts the sensitivity at a material point of the analysis target from a density vector representing the density at the material point.

[0042] The specific operation of the optimal design device (10), including the numerical analysis unit (100), data processing unit (200), and model learning unit (300) described above, will be described in more detail below.

[0043] Next, the configuration of a neural network model (NNM) according to an embodiment of the present invention will be described in more detail. Fig. 2 is a diagram illustrating training data for a neural network model (NNM) according to an embodiment of the present invention. Fig. 3 is a diagram illustrating the configuration of a neural network model (NNM) according to an embodiment of the present invention.

[0044] First, referring to FIG. 2, the density tensor includes multiple 3-channel images segmented into the same standard. Each of the multiple 3-channel images includes a first channel (CH1) that represents the density in the current iteration as an image, a second channel (CH2) that represents the difference in density between the current iteration and the previous iteration as an image, and a third channel (CH3) that is a position map indicating the position of the 3-channel image. The density tensor is configured in a tensor format by connecting the first channel (CH1), the second channel (CH2), and the third channel (CH3), and the density tensor in the tensor format is used as input data for a neural network model (NNM).

[0045] Meanwhile, the target vector contains multiple images of a single channel, each of which is divided into the same specifications and represents a sensitivity.

[0046] Referring to FIG. 3, a neural network model (NNM) according to an embodiment of the present invention includes multiple layers. The neural network model (NNM) includes an encoder (EN) and a decoder (DE). That is, the neural network model (NNM) includes multiple layers, and the multiple layers can be divided into an encoder (EN) and a decoder (DE).

[0047] The encoder (EN) includes an input layer (IL), multiple convolutional layers (CL), and multiple pooling layers (PL).

[0048] The decoder (DE) includes multiple concatenated layers (NL), multiple convolutional layers (CL), multiple upsampling layers (UL), and an output layer (OL).

[0049] Multiple layers of a neural network model (NNM) generate feature maps (FMs) through multiple operations where weights are applied between the multiple layers. In Figure 3, the hexahedrons represent the feature maps (FMs) of each layer.

[0050] The convolutional layer (CL) performs convolution operations and operations using an activation function. Activation functions include, but are not limited to, sigmoid, hyperbolic tangent (tanh), exponential linear unit (ELU), rectified linear unit (ReLU), leaky ReLU, maxout, minout, and softmax. In the embodiment of the present invention, it is preferable to use rectified linear unit (ReLU) for operations using an activation function.

[0051] The pooling layer (PL) is for down-sampling and performs a pooling (max pooling) operation.

[0052] The upsampling layer (UL) is used for upsampling and can perform up-convolution operations.

[0053] The concatenation layer (NL) combines the feature map (FM) of the convolutional layer (CL) of the encoder (EN) and the feature map (FM) of the upsampling layer (UL) of the decoder (DE) to form a feature map (FM).

[0054] When there are multiple layers with , a concatenation operation is performed to combine the feature map (FM) of the first half with the feature map (FM) of the second half.

[0055] As mentioned above, a neural network model (NNM) comprises multiple layers, each of which involves multiple operations. Furthermore, the layers are connected by weights (W). The computational results of one layer are weighted and then fed into the next layer. In other words, each layer of a neural network model (NNM) receives a weighted value from the previous layer, performs an operation on it, and then passes the result of that operation as input to the next layer.

[0056] As illustrated in Figure 3, when a density tensor is input, the encoder (EN) performs encoding that compresses the features of the density tensor to derive a latent vector. This latent vector can become the feature map (FM) of the second convolutional layer of the encoder (EN). The decoder (DE) performs decoding that restores the latent vector to the size of the density tensor, thereby deriving a sensitivity vector.

[0057] The more specific weight calculation procedures for these neural network models (NNMs) are listed sequentially as follows. In the explanation below, the feature map, which is the output of the previous layer, is weighted and input to the calculations of the next layer.

[0058] When a density tensor is input to the input layer (IL), the first pooling layer (PL1) of the encoder (EN) performs a pooling operation on the density tensor to derive a first feature map (FM1).

[0059] The first convolutional layer (CL1) performs a convolution operation and an operation using an activation function on the first feature map (FM1) to derive the second feature map (FM2).

[0060] The second pooling layer (PL2) performs a pooling operation on the second feature map (FM2) to derive the third feature map (FM3).

[0061] The second convolutional layer (CL2) performs a convolution operation and an operation using an activation function on the third feature map (FM3) to derive the fourth feature map (FM4).

[0062] Next, the third convolutional layer (CL3) of the decoder (DE) performs a convolution operation and an operation using an activation function on the fourth feature map (FM4) to derive a fifth feature map (FM5).

[0063] The first upsampling layer (UL1) performs an upconvolution operation on the fifth feature map (FM5) to derive the sixth feature map (FM6).

[0064] The first concatenated layer (NL1) combines the third feature map (FM3) and the sixth feature map (FM6) to form the seventh feature map (FM7).

[0065] The fourth convolutional layer (CL4) performs a convolution operation and an activation function operation on the seventh feature map (FM7) to derive the eighth feature map (FM8).

[0066] The second upsampling layer (UL2) performs an upconvolution operation on the eighth feature map (FM8) to derive the ninth feature map (FM9).

[0067] The second concatenated layer (NL2) combines the input tensor and the ninth feature map (FM9) to form the tenth feature map (FM10).

[0068] The fifth convolutional layer (CL5) performs a convolution operation and an operation using an activation function on the tenth feature map (FM10) to derive the eleventh feature map (FM11).

[0069] The output layer (OL) performs an operation using an activation function on the 11th feature map (FM11) to derive a sensitivity vector.

[0070] Next, a method for optimal design of a nonlinear structure using a topology optimization framework incorporating a convolutional neural network according to an embodiment of the present invention will be described. Figure 4 is a flowchart illustrating a method for optimal design of a nonlinear structure using a topology optimization framework incorporating a convolutional neural network according to an embodiment of the present invention.

[0071] The numerical analysis unit (100) performs a numerical analysis to derive a sensitivity that satisfies the minimization of the objective function from the density at the material point constituting the analysis target in step S110. This numerical analysis is based on the finite element method (FEM) and is for topology optimization. The numerical analysis iterates the calculation of the state variables so that the objective function satisfies the minimization from the calculation results for the state variables corresponding to the density at the material point.

[0072] At this time, the numerical analysis unit (100) determines whether the first branch condition is satisfied at step S120, and if the first branch condition is satisfied, the numerical analysis is stopped. On the other hand, if the first branch condition is not satisfied at step S120, the numerical analysis unit (100) proceeds to step S110 and repeats the operation for numerical analysis. Here, the first branch condition may be a predetermined number of iterations of the operation for numerical analysis.

[0073] If the first branch condition is satisfied, the data processing unit (200) constructs learning data from the data derived through numerical analysis in step S130, i.e., density and sensitivity. That is, the data processing unit (200) constructs learning data including a density tensor and a target vector from the density at the mass point of the analysis target derived through numerical analysis and the sensitivity derived in response to the density.

[0074] As illustrated in FIG. 2, the density tensor includes multiple 3-channel images segmented into the same standard. Each of the multiple 3-channel images includes a first channel (CH1) that represents the density in the current iteration as an image, a second channel (CH2) that represents the difference in density between the current iteration and the previous iteration as an image, and a third channel (CH3) that is a position map indicating the position of the 3-channel image. The density tensor is configured in a tensor format by connecting the first channel (CH1), the second channel (CH2), and the third channel (CH3), and the density tensor in the tensor format is used as input data for a neural network model (NNM).

[0075] Meanwhile, the target vector contains multiple images of a single channel, each of which is divided into the same specifications and represents a sensitivity.

[0076] Next, the model learning unit (300) performs learning on the neural network model (NNM) using learning data in step S140, such that the neural network model derives a sensitivity vector that predicts the sensitivity at a point of interest from a density vector representing the density at that point of interest. This learning method will be described in more detail below.

[0077] Meanwhile, the model learning unit (300) determines whether the second branch condition is satisfied in step S150. Here, the second branch condition may be whether, when the neural network model derives a sensitivity vector that predicts the sensitivity at a point of interest from a density vector representing the density at the point of interest of the analysis target, the loss representing the difference between the target vector of the learning data and the sensitivity vector exceeds a preset threshold.

[0078] If the second branch condition is satisfied as a result of the determination at step S150, the model learning unit (300) stops learning, returns to step S110, and repeats steps S110 to S150 described above.

[0079] That is, the numerical analysis unit (100) re-performs the numerical analysis until the first branch condition described above in step S110 is satisfied.

[0080] Accordingly, in step S120, after determining whether the first branch condition is satisfied again, if the first branch condition is satisfied, the data processing unit (200) reconstructs the learning data including the density and sensitivity at the material point derived according to the numerical analysis re-performed in step S130. Subsequently, the model learning unit (300) performs learning on the neural network model using the reconstructed learning data in step S140.

[0081] On the other hand, if the determination result of step S150 does not satisfy the second branch condition, the model learning unit (300) determines whether the learning termination condition is satisfied in step S160. If the determination result of step S150 does not satisfy the predetermined learning termination condition, the process returns to step S140. On the other hand, if the determination result of step S150 satisfies the predetermined learning termination condition, the model learning unit (300) terminates learning in step S170.

[0082] Here, the learning termination condition may be when the loss representing the difference between the target vector of the learning data and the sensitivity vector converges and becomes less than a preset reference value when the neural network model derives a sensitivity vector that predicts the sensitivity at a point of interest from a density vector representing the density at the point of interest of the analysis target.

[0083] Next, the learning method for the aforementioned neural network model (NNM) will be described. Figure 5 is a flowchart illustrating the learning method for a neural network model (NNM) according to an embodiment of the present invention. In other words, Figure 5 provides a detailed description of step S140.

[0084] Referring to FIG. 5, the model learning unit (300) receives learning data for learning a neural network model (NNM) from the data processing unit (200) at step S210. The learning data includes a density tensor derived from the density at the material point of the analysis target derived through numerical analysis, a sensitivity derived in response to the density, and a target vector corresponding to the density tensor.

[0085] As illustrated in Figure 2, the density tensor is a tensor comprising multiple three-channel images to represent density characteristics. Furthermore, the target vector comprises multiple single-channel images, each divided into identical dimensions, representing sensitivity.

[0086] Once the learning data is prepared, the model learning unit (300) inputs the density tensor into the neural network model (NNM) whose learning has not been completed in step S220.

[0087] Then, in step S230, the neural network model (NNM) performs multiple operations on the density tensor, assigning weights that have not yet been learned across multiple layers, to derive a sensitivity vector. The specific procedure for deriving the sensitivity vector is as previously described with reference to Figure 3. The sensitivity vector contains a value that predicts the sensitivity at a particle point from the density vector.

[0088] Accordingly, the model learning unit (300) can calculate a loss representing the difference between the target vector and the sensitivity vector through a loss function in step S240. At this time, the model learning unit (300) can calculate the loss through a loss function according to the following mathematical expression 1.

[0089]

[0090] Here, θ represents loss. is the target vector, and the above represents the transpose matrix of the target vector. Also, represents the sensitivity vector. And i is the index of the training data.

[0091] Next, the model learning unit (300) performs optimization to modify the weights of the neural network model (NNM) so that the loss derived through the loss function is minimized in step S250.

[0092] The above-described steps S220 to S250 are repeated using different learning data until the second branch condition (S150) is satisfied or the learning end condition (S160) is satisfied.

[0093] Fig. 6 is a diagram illustrating a computing device according to an embodiment of the present invention. The computing device (TN100) of Fig. 6 may be a device described in this specification, for example, an optimal design device (10).

[0094] In the embodiment of FIG. 6, the computing device (TN100) may include at least one processor (TN110), a transceiver (TN120), and a memory (TN130). In addition, the computing device (TN100) may further include a storage device (TN140), an input interface device (TN150), an output interface device (TN160), and the like. The components included in the computing device (TN100) may be connected by a bus (TN170) to communicate with each other.

[0095] The processor (TN110) can execute program commands stored in at least one of the memory (TN130) and the storage device (TN140). The processor (TN110) may refer to a central processing unit (CPU), a graphics processing unit (GPU), or a dedicated processor in which methods according to embodiments of the present invention are performed. The processor (TN110) may be configured to implement procedures, functions, methods, etc. described in relation to embodiments of the present invention. The processor (TN110) may control each component of the computing device (TN100).

[0096] The memory (TN130) and the storage device (TN140) can each store various information related to the operation of the processor (TN110). The memory (TN130) and the storage device (TN140) can each be configured with at least one of a volatile storage medium and a non-volatile storage medium. For example, the memory (TN130) can be configured with at least one of a read-only memory (ROM) and a random access memory (RAM).

[0097] The transceiver (TN120) can transmit or receive wired or wireless signals. The transceiver (TN120) can be connected to a network to perform communication.

[0098] In particular, the numerical analysis unit (100), data processing unit (200), and model learning unit (300) according to an embodiment of the present invention may be implemented in the form of a program readable by a computing device, stored in a memory (TN130), and then executed by a processor (TN110), or implemented as a lower module of the processor (TN110).

[0099] Meanwhile, the method according to the embodiment of the present invention described above may be implemented in the form of a program readable by various computer means and recorded on a computer-readable recording medium. Here, the recording medium may include program commands, data files, data structures, etc., singly or in combination. The program commands recorded on the recording medium may be those specially designed and configured for the present invention, or may be those known and usable by those skilled in the art of computer software. For example, the recording medium includes magnetic media such as hard disks, floppy disks, and magnetic tapes, optical media such as CD-ROMs and DVDs, magneto-optical media such as floptical disks, and hardware devices specially configured to store and execute program commands, such as ROMs, RAMs, and flash memories. Examples of program commands may include not only machine language wires generated by a compiler, but also high-level language wires that can be executed by a computer using an interpreter, etc. These hardware devices may be configured to operate as one or more software modules to perform the operations of the present invention, and vice versa.

[0100] While the present invention has been described using several preferred embodiments, these embodiments are illustrative and not limiting. As such, those skilled in the art will appreciate that various changes and modifications can be made in accordance with the doctrine of equivalents without departing from the spirit of the invention and the scope of the claims.

Claims

1. In the method for optimal design, A step of performing a numerical analysis to derive a sensitivity that satisfies the minimization of the objective function from the density at the mass point constituting the analysis target until the numerical analysis section satisfies a predetermined first branch condition; If the data processing unit satisfies the first branch condition, a step of configuring learning data including a density tensor and an objective vector from the density at the mass point of the analysis target derived through the numerical analysis and the sensitivity derived in response to the density; and A step in which a model learning unit performs learning on the neural network model using the learning data so that the neural network model derives a sensitivity vector that predicts sensitivity at a mass point from a density vector representing density at the mass point of the analysis target; characterized by including Methods for optimal design.

2. In paragraph 1, A step of stopping the learning when the above model learning unit satisfies a predetermined second branch condition; and A step of re-performing the numerical analysis until the numerical analysis unit satisfies the first branch condition; characterized by further including Methods for optimal design.

3. In paragraph 2, If the above data processing unit satisfies the first branch condition, a step of reconstructing learning data including density and sensitivity at the mass point derived according to the re-performed numerical analysis; and A step in which the above model learning unit performs learning on a neural network model using the above reconstructed learning data; characterized by further including Methods for optimal design.

4. In paragraph 2, The above second quarter conditions are When a neural network model derives a sensitivity vector that predicts the sensitivity at a point of interest from a density vector that represents the density at the point of interest of the analysis target, It is characterized by whether the loss representing the difference between the target vector of the learning data and the derived sensitivity vector exceeds the threshold. Methods for optimal design.

5. In paragraph 1, The steps to perform the above learning are: A step in which the above model learning unit inputs the density vector of the above learning data into the neural network model; A step of the neural network model performing multiple operations to which weights that have not yet been learned are applied to the density vector to derive a sensitivity vector that predicts the sensitivity at the mass point; A step in which the above model learning unit derives a loss representing the difference between the sensitivity vector and the target vector of the learning data through a loss function; and A step in which the model learning unit performs optimization to update the weights of the neural network model so that the loss is minimized; characterized by including Methods for optimal design.

6. In paragraph 5, The steps for deriving the above sensitivity vector are A step in which the encoder of the above neural network model performs encoding to compress the features of the density tensor to derive a latent vector; and A step of decoding the decoder of the above neural network model to restore the latent vector to the size of the density tensor, thereby deriving a sensitivity vector; characterized by including Methods for optimal design.

7. In paragraph 5, The steps for deriving the above sensitivity vector are A step of deriving a first feature map by performing a pooling operation on the density tensor by a first pooling layer of the neural network model when a density tensor is input to the input layer of the neural network model; A step of deriving a second feature map by performing a convolution operation and an operation using an activation function on the first feature map by the first convolutional layer of the neural network model; A step of the second pooling layer of the above neural network model performing a pooling operation on the second feature map to derive a third feature map; A step of deriving a fourth feature map by performing a convolution operation and an operation using an activation function on the third feature map by the second convolutional layer of the above neural network model; A step of deriving a fifth feature map by performing a convolution operation and an operation using an activation function on the fourth feature map (FM4) by the third convolutional layer of the above neural network model; A step of the first upsampling layer of the above neural network model performing an upconvolution operation on the fifth feature map to derive a sixth feature map; A step of combining the third feature map and the sixth feature map in the first combination layer of the neural network model to form a seventh feature map; A step of deriving an 8th feature map by performing a convolution operation and an operation using an activation function on the 7th feature map by the 4th convolution layer of the above neural network model; A step of the second upsampling layer of the above neural network model performing an upconvolution operation on the above eighth feature map to derive a ninth feature map; A step of combining the second concatenated layer of the above neural network model to form a tenth feature map by combining the input tensor and the ninth feature map; A step of the fifth convolutional layer of the neural network model performing a convolution operation and an operation using an activation function on the tenth feature map to derive an eleventh feature map; and A step of deriving a sensitivity vector by performing an operation using an activation function on the 11th feature map by the output layer of the above neural network model; characterized by including Methods for optimal design.

8. In paragraph 5, The above loss function is Mathematical formula And, The above θ is the loss, Above is the target vector, Above is the transpose of the target vector, Above is the sensitivity vector, The above i is characterized as being an index of learning data. Methods for optimal design.

9. In paragraph 1, The above density tensor is Contains multiple 3-channel images divided into the same specifications, Each of the multiple 3-channel images The first channel, which represents the density in the current iteration as an image, A second channel that represents the difference in density between the current and previous iterations as an image. The third channel is a location map that shows the location of the three-channel image. characterized by including Methods for optimal design.

10. In paragraph 1, The above target vector is characterized by including multiple images divided into the same standard and representing the sensitivity; Methods for optimal design.

11. In a device for optimal design, A numerical analysis unit that performs a numerical analysis to derive a sensitivity that satisfies the minimization of the objective function from the density at the mass points constituting the analysis target until a predetermined first-quarter condition is satisfied; If the above first branch condition is satisfied, a data processing unit that configures learning data including a density tensor and an objective vector from the density at the mass point of the analysis target derived through the numerical analysis and the sensitivity derived corresponding to the density; and A model learning unit that performs learning on the neural network model using the above learning data so that the neural network model derives a sensitivity vector that predicts sensitivity at a particle point from a density vector representing density at the particle point of the analysis target; characterized by including Device for optimal design.

12. In paragraph 11, The above model learning section If the second quarter conditions are met, the above learning is stopped. The above numerical analysis section characterized in that the numerical analysis is re-performed until the above first quarter condition is satisfied. Device for optimal design.

13. In paragraph 12, The above data processing unit If the above first branch condition is satisfied, the learning data including the density and sensitivity at the mass point derived from the re-performed numerical analysis is reconstructed, The above model learning section It is characterized by performing learning on a neural network model using the above reconstructed learning data. Device for optimal design.

14. In paragraph 12, The above second quarter conditions are When a neural network model derives a sensitivity vector that predicts the sensitivity at a point of interest from a density vector that represents the density at the point of interest of the analysis target, It is characterized by whether the loss representing the difference between the target vector of the learning data and the derived sensitivity vector exceeds the threshold. Device for optimal design.

15. In paragraph 11, The above model learning section Input the density vector of the above learning data into the neural network model, If the above neural network model performs multiple operations to which weights that have not yet been learned are applied to the above density vector, and derives a sensitivity vector that predicts the sensitivity at the above mass point, A loss function is used to derive a loss that represents the difference between the sensitivity vector and the target vector of the learning data. It is characterized by performing optimization to update the weights of the neural network model so that the loss is minimized. Device for optimal design.

16. In paragraph 15, The above neural network model An encoder that derives a latent vector by performing encoding that compresses the features of a density tensor; and A decoder that derives a sensitivity vector by performing decoding that restores the latent vector to the size of the density tensor; characterized by including Device for optimal design.

17. In paragraph 15, The above neural network model An input layer in which, when a density tensor is input, the first pooling layer of the neural network model performs a pooling operation on the density tensor to derive a first feature map; A first convolutional layer that performs a convolution operation and an operation using an activation function on the first feature map to derive a second feature map; A second pooling layer that performs a pooling operation on the second feature map to derive a third feature map; A second convolutional layer that performs a convolution operation and an operation using an activation function on the third feature map to derive a fourth feature map; A third convolutional layer that performs a convolution operation and an operation using an activation function on the fourth feature map (FM4) to derive a fifth feature map; A first upsampling layer that performs an upconvolution operation on the fifth feature map to derive a sixth feature map; A first combining layer that combines the third feature map and the sixth feature map to form a seventh feature map; A fourth convolutional layer that performs a convolution operation and an operation using an activation function on the seventh feature map to derive an eighth feature map; A second upsampling layer that performs an upconvolution operation on the above-mentioned eighth feature map to derive a ninth feature map; A second combining layer that combines the above input tensor and the ninth feature map to form a tenth feature map; A fifth convolutional layer that performs a convolution operation and an operation using an activation function on the above-mentioned tenth feature map to derive an eleventh feature map; and An output layer that derives a sensitivity vector by performing an operation using an activation function on the above 11th feature map; characterized by including Device for optimal design.

18. In paragraph 15, The above loss function is Mathematical formula And, The above θ is the loss, Above is the target vector, Above is the transpose of the target vector, Above is the sensitivity vector, The above i is characterized as being an index of learning data. Device for optimal design.

19. In paragraph 11, The above density tensor is Contains multiple 3-channel images divided into the same specifications, Each of the multiple 3-channel images The first channel, which represents the density in the current iteration as an image, A second channel that represents the difference in density between the current and previous iterations as an image. The third channel is a location map that shows the location of the three-channel image. characterized by including Device for optimal design.

20. In paragraph 11, The above target vector is characterized by including multiple images divided into the same standard and representing the sensitivity; Device for optimal design.

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