Graph generation adversarial learning estimation method for active distribution network topology under non-full measurement

Abstract

The application relates to the technical field of power systems and discloses a graph generation adversarial learning estimation method for an active distribution network topology under incomplete measurement, which comprises the following steps: distribution network topology transformation; transforming an original distribution network topology to obtain a line topology graph; graph convolution feature extraction; based on the line topology graph, a graph convolutional neural network transmits the dependency relationship between node features through a graph structure, extracts the spatial features of graph data, and constructs a generation adversarial topology estimation model; a generation adversarial network is constructed, the extracted spatial features are input into the generation adversarial network for training, wherein a generator function is trained by minimizing a logarithmic probability, and a discriminator function is trained by maximizing a logarithmic probability; a observability layout optimization design model is constructed; variational dropout regularization is added to an input layer of the GCN-GAN, and the observability layout optimization design model learns to reduce the dropout rate of important features of a GCN-GAN model for correctly predicting a topology.

Description

Technical Field

[0001] This invention relates to the field of power system technology, and in particular to a graph generative adversarial learning estimation method for active distribution network topology under incomplete measurement conditions. Background Technology

[0002] With the continuous advancement of new power system construction, the power grid scale is constantly expanding, and the integration of distributed energy resources is also increasing. Due to the volatility, randomness, and intermittency of distributed energy output, its power generation and stability are difficult to predict and control, posing a threat to power quality and the stability of distribution network operation. Furthermore, the operating characteristics of the distribution network will undergo profound changes. Features such as bidirectional power flow distribution, increasingly blurred source-load boundaries, more diverse operating modes, higher flexible resource demands, a shift from deterministic to probabilistic power balance, and the coupling of multiple energy sources bring new challenges to the safe operation of the distribution network. At the same time, the integration of new loads such as electric vehicles and energy storage systems, along with the comprehensive development of demand-side response, are causing a sharp increase in uncertainties faced by the distribution network, making its operation and management face a more complex and volatile environment. Correct identification and interpretation of the power topology is a key task for power systems, as accurate network topology knowledge is a prerequisite for system planning, operation, and control, laying the necessary foundation for its operation monitoring and management.

[0003] Topology identification is a key building block that provides valuable information for other applications such as state estimation, power flow calculation, fault analysis, network reconfiguration, economic dispatch, reactive power and voltage regulation, resilience enhancement, and demand response. The topology is determined by the states of sectionalizing switches and tie switches on a line. In actual operation, the system model relied upon by dispatchers is usually derived from planning documents. When maintenance, repairs, fault response, or the implementation of optimal control strategies are performed, the states of sectionalizing switches and tie switches change, resulting in dynamic adjustments to the system topology. These adjustments can lead to significant deviations between the actual topology and the recorded structure. To accurately capture these changes, topology identification is crucial. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a graph generation adversarial learning estimation method for active distribution network topology under incomplete measurement, aiming to solve the technical problems of poor adaptability and low learning efficiency of traditional topology identification methods.

[0005] The objective of this invention is achieved through the following technical solution: a graph generative adversarial learning estimation method for active distribution network topology under incomplete measurement, comprising the following steps:

[0006] Step S1: Distribution network topology transformation;

[0007] The original power distribution network topology is transformed to obtain a linear topology diagram;

[0008] Step S2: Graph convolution feature extraction;

[0009] Based on the line topology graph, the graph convolutional neural network (GCN) propagates the dependencies between node features through the graph structure, extracts the spatial features of the graph data, obtains hidden information, and thus updates its own line status.

[0010] Step S3: Construct a generative adversarial topology estimation model;

[0011] Generative Adversarial Networks (GANs) are constructed, and the extracted spatial features are input into the GANs for training. The generator function is trained by minimizing the log probability, and the discriminator function is trained by maximizing the log probability. In order to generate a topology corresponding to a specific operating scenario, additional information needs to be added to the model input, including the line status after the graph convolutional neural network is updated, the total active power, and the total reactive power.

[0012] Step S4: Construct an observability layout optimization design model;

[0013] Adding variational Dropout regularization to the input layer of GCN-GAN allows the observability layout optimization design model to reduce the dropout rate of topologically important features correctly predicted by the GCN-GAN model, while increasing the dropout rate of other unimportant features, thereby effectively filtering out important current features.

[0014] Specifically, in step S1, based on the Whitney isomorphism principle, for each branch in the original distribution network topology, a node is created in the line graph topology; for every two branches in the original distribution network topology that share a node, a branch is created between their corresponding line graph topology nodes to obtain the line topology graph.

[0015] Specifically, in step S2, the line topology graph is represented as an undirected connected graph. ,in, Represents a node. Edge representation, adjacency matrix The topology is represented as a binary matrix, where each element indicates whether nodes are connected; the node feature matrix. Includes available measurements for each node;

[0016] matrix Defined as:

[0017]

[0018] in, Indicates the amplitude of the current. This represents the phase angle of the current.

[0019] Specifically, the graph convolutional neural network uses an adjacency matrix. and node feature matrix binary pairs As input, its expression is:

[0020]

[0021] in, Indicates the first The hidden output feature matrix of the layer;

[0022] In the In the layer, the forward propagation rule of GCN is defined as:

[0023]

[0024] in, Indicates the first The learning weight matrix of the layer, express Activation function.

[0025] Specifically, in step S2, an identity matrix is ​​introduced:

[0026]

[0027] in, It is an adjacency matrix with a self-connected graph topology. It is the identity matrix;

[0028] For adjacency matrix Perform the following normalization:

[0029]

[0030] in, Let represent the degree absolute matrix of the self-loop adjacency matrix;

[0031] No. The layer-by-layer propagation rule is restated as follows:

[0032]

[0033] when At that time, there were:

[0034] .

[0035] Specifically, in step S3, the generative adversarial network trains both the generator function and the discriminator function simultaneously;

[0036] The training objective of the generator function is to minimize the following log probabilities:

[0037]

[0038] in, Represents the mathematical expectation. and This represents the generator function and the discriminator function. This represents the network parameters of the generator function. This represents random noise, while Indicate its probability distribution;

[0039] The discriminator function is trained by maximizing the following log probabilities:

[0040]

[0041] in, This represents the network parameters of the discriminator function. Representing the real topology The probability distribution;

[0042] Specifically, during the optimization process of the generative adversarial network, the generator function and the discriminator function compete with each other, forming a zero-sum game. The learning estimation model of the graph generative adversarial network is expressed as a minimax game in the following form:

[0043] .

[0044] Specifically, in step S3, in order to generate a topology suitable for a specific state, the following additional information is introduced:

[0045]

[0046] in, The current characteristics extracted in step 2, This represents the total active power of the system. The total reactive power of the system can be represented by the minimax game as follows:

[0047] .

[0048] Specifically, step S3 uses Wasserstein distance to define the loss function of the generator. The Wasserstein distance is defined as follows:

[0049]

[0050] The discriminator function needs to satisfy the 1-Lipschitz condition. A loss term is set in the topology estimation model, as shown below:

[0051]

[0052]

[0053] in, Indicates the penalty parameter. It is a random number that follows a uniform distribution in the interval [0,1]. This represents the pseudo-topology generated by the generator function. For the true topology, To be The L2 norm of the gradient after input to the discriminator. To pass The expected value obtained from sampling.

[0054] Specifically, in step S4, variational Dropout randomly discards a portion of neurons with a certain probability, thereby improving learning efficiency and reducing the risk of overfitting. The proportion of randomly discarded neurons in Dropout is obtained by minimizing the following logarithmic probability:

[0055]

[0056] in, Let represent a mask that follows a Bernoulli distribution and is obtained by sampling according to the above formula. Indicates the discard rate. Represents the Sigmoid function;

[0057] In this configuration, the loss functions for the generator function and the discriminator function are respectively expressed as:

[0058]

[0059]

[0060] The weight parameters of the generator function and the discriminator function are updated using stochastic gradient descent in the following ways:

[0061]

[0062]

[0063] in, This indicates noise or a small batch of topological samples.

[0064] The present invention has the following advantages:

[0065] 1. The adversarial learning estimation method of the present invention can effectively seek the minimum measurement configuration set that supports high-accuracy global topology identification, solve the problem of deploying a small number of line current sensors, ensure the practicality and economy of the above topology identification method, and provide an overall solution for engineering applications from measurement point deployment to topology identification.

[0066] 2. It can identify topology by learning the distribution characteristics of topology data closely related to current and load information, demonstrating superior identification performance compared to traditional supervised learning methods on unknown topology test sets. Furthermore, it significantly enhances the algorithm's robustness to noise by increasing the redundancy of topology identification-related data. Attached Figure Description

[0067] Figure 1 This is a flowchart of the graph generation adversarial learning estimation method for active distribution network topology under incomplete measurement according to the present invention.

[0068] Figure 2 This is a schematic diagram of the topology transformation of the present invention;

[0069] Figure 3 This is a model architecture diagram of the graph generation adversarial learning estimation method for active distribution network topology under incomplete measurement according to the present invention. Detailed Implementation

[0070] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention; that is, the described embodiments are merely some embodiments of the invention, and not all embodiments. The components of the embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0071] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0072] It should be noted that relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0073] The present invention will be further described below with reference to the accompanying drawings, but the scope of protection of the present invention is not limited to the following description.

[0074] like Figures 1 to 3 As shown, the graph generative adversarial learning estimation method for active distribution network topology under incomplete measurement includes the following steps:

[0075] Step S1: Distribution network topology transformation;

[0076] According to the Whitney isomorphism principle, a topology transformation of the distribution network is performed to obtain a topology graph with interchanged nodes and edges. According to the Whitney isomorphism principle, if graph G is connected, then except for one special case, graph G can always be restored from graph L(G) after topology transformation. Therefore, such transformation is equivalent. For each branch in the original distribution network topology, a node is created in the linear graph topology. For every two branches in the original distribution network topology that share a node, a branch is created between their corresponding linear graph topology nodes to obtain the linear topology graph.

[0077] Step S2: Graph convolution feature extraction;

[0078] Based on the line topology graph, the graph convolutional neural network (GCN) propagates the dependencies between node features through the graph structure, extracts the spatial features of the graph data, obtains hidden information, and thus updates its own line status.

[0079] The transformed line topology is represented as an undirected connected graph. ,in, Represents a node. Edge representation, adjacency matrix The topology is represented as a binary matrix, where each element indicates whether nodes are connected; the node feature matrix. Includes available measurements for each node;

[0080] matrix Defined as:

[0081]

[0082] in, Indicates the amplitude of the current. This represents the phase angle of the current; current measurement data is collected by a current transformer.

[0083] The graph convolutional neural network uses an adjacency matrix. and node feature matrix binary pairs As input, each graph node representing the bus performs a convolution operation to aggregate its own and neighboring nodes' current information to capture the topological or spatial connectivity in the current measurement data. For multi-layer GCNs, the graph convolutional layers are typically approximated as a nonlinear function, with the following expression:

[0084]

[0085] in, Indicates the first The hidden output feature matrix of the layer;

[0086] In the In the layer, the forward propagation rule of GCN is defined as:

[0087]

[0088] in, Indicates the first The learning weight matrix of the layer, express Activation function;

[0089] However, this propagation rule has two problems. First, there are no self-connected nodes, leading to an adjacency matrix... Since all diagonal elements are zero, the node's own current measurement data is ignored during feature extraction. To address this issue, an identity matrix is ​​introduced:

[0090]

[0091] in, It is an adjacency matrix with a self-connected graph topology. It is the identity matrix;

[0092] Another problem is the adjacency matrix. Since the adjacency matrix is ​​not normalized, multiple convolution operations can lead to asymmetrical distributions of current amplitude and phase angle due to varying node degrees. This can cause gradient vanishing or exploding problems during backpropagation. To address this issue, the adjacency matrix needs to be normalized. Perform the following normalization:

[0093]

[0094] in, Denote the degree absolute matrix of the self-loop adjacency matrix; then, the first... The layer-by-layer propagation rule is restated as follows:

[0095]

[0096] when At that time, there were:

[0097]

[0098] Hidden features extracted through propagation rules It contains current information and its topological or spatial connectivity;

[0099] Step S3: Construct a generative adversarial topology estimation model;

[0100] A generative adversarial network (GAN) is constructed. The extracted current features and load demand operation status information are input into the GAN to conditionally generate topology samples. Additional information is added to the model input to generate a topology corresponding to a specific operation scenario. The generator function is trained by minimizing the log probability, and the discriminator function is trained by maximizing the log probability. In order to generate a topology corresponding to a specific operation scenario, additional information needs to be added to the model input, including the line status updated by the graph convolutional neural network, total active power, and total reactive power.

[0101] To overcome the timeliness issues of traditional physical models and the generalization problems of supervised learning, we consider using Generative Adversarial Networks (GANs) for distribution network topology identification. Similar to supervised learning, GAN-driven distribution network topology identification relies on machine learning techniques, and its identification speed is superior to that of traditional physical model-driven models. However, unlike supervised learning, GANs do not directly learn the mapping relationship between measurement information and topology. Instead, they train two networks with opposing optimization objectives, indirectly uncovering the topology distribution and thus enhancing the algorithm's generalization ability.

[0102] Specifically, GAN trains both the generator function and the discriminator function simultaneously in a competitive manner. Both the generator function and the discriminator function are modeled by neural networks with strong expressive power. The generator function takes random noise as input and tries to approximate the real topological distribution, thereby "deceiving" the discriminator function.

[0103] The training objective of the generator function is to minimize the following log probabilities:

[0104]

[0105] in, Represents the mathematical expectation. and This represents the generator function and the discriminator function. This represents the network parameters of the generator function. This represents random noise, while Indicate its probability distribution;

[0106] The discriminator function receives a real topological code and a pseudo-topological distribution generated by a generator function, and outputs a probability to determine the authenticity of the input topology. The discriminator function is trained by maximizing the following log probabilities:

[0107]

[0108] in, This represents the network parameters of the discriminator function. Representing the real topology The probability distribution;

[0109] In the above optimization process of generative adversarial networks, the generator function and the discriminator function compete with each other, forming a zero-sum game. The learning estimation model of graph generative adversarial networks can be expressed as a minimax game in the following form:

[0110]

[0111] However, this topology estimation model struggles to generate topologies that correspond to specific scenarios. In reality, current measurement data also changes over time as load demands and topology conditions vary. To generate topologies suitable for specific conditions, the following additional information is introduced:

[0112]

[0113] in, The current characteristics extracted in step S2, This represents the total active power of the system. The total reactive power of the system can be represented by the minimax game as follows:

[0114] .

[0115] The training method for the generative adversarial topology estimation model is as follows:

[0116] On the one hand, when the discriminator is trained to a certain extent, GAN can be viewed as using JS divergence to measure the distance between the real data distribution and the data distribution generated by the generator. The JS divergence between any two non-overlapping distributions is always log2. It should be noted that it is very likely that the real topological distribution and the generator's estimated topological distribution will not overlap. In this case, the generator's loss function will remain constant, causing gradient vanishing and making it impossible to continue training, thus causing the model to lose its discriminative ability. On the other hand, it is difficult for the discriminator and generator to converge simultaneously during GAN training, which can easily lead to mode collapse. This results in the generator being able to generate only a few topologies, making it impossible to achieve a correct correspondence between current measurement information and topology.

[0117] Unlike JS divergence, Wasserstein distance accurately reflects the proximity of two non-overlapping distributions, thus providing a precise training direction for the generator to fit the topological data distribution. Therefore, using Wasserstein distance to define the generator's loss function can effectively solve the above problem. The Wasserstein distance is defined as follows:

[0118]

[0119] The discriminator function needs to satisfy the 1-Lipschitz condition, but this may sacrifice convergence speed to some extent. Therefore, a loss term is set in the topology estimation model, as shown below:

[0120]

[0121]

[0122] in, Indicates the penalty parameter. It is a random number that follows a uniform distribution in the interval [0,1]. This represents the pseudo-topology generated by the generator function. For the true topology, To be The L2 norm of the gradient after input to the discriminator. for pass The expected value obtained from sampling.

[0123] Step S4: Construct an observability layout optimization design model;

[0124] Adding variational Dropout regularization to the input layer of GCN-GAN allows the observability layout optimization design model to reduce the dropout rate of topologically important features correctly predicted by the GCN-GAN model, while increasing the dropout rate of other unimportant features. This effectively filters out important current features, providing theoretical support for the selection of current sensor placement.

[0125] To identify which current features are sensitive to topology recognition accuracy, a Dropout feature ranking strategy is introduced to filter key current features and guide the deployment of current transformers. This Dropout feature ranking is essentially a regularization method that improves learning efficiency and reduces overfitting risk by randomly discarding a portion of neurons with a certain probability. The proportion of randomly discarded neurons in the Dropout strategy is obtained by minimizing the following logarithmic probability:

[0126]

[0127] in, Let represent a mask that follows a Bernoulli distribution and is obtained by sampling according to the above formula. Indicates the discard rate. Represents the Sigmoid function;

[0128] In this configuration, the loss functions for the generator function and the discriminator function are respectively expressed as:

[0129]

[0130]

[0131] The weight parameters of the generator function and the discriminator function are updated using stochastic gradient descent in the following ways:

[0132]

[0133]

[0134] in, This indicates noise or a small batch of topological samples.

[0135] The importance ranking of current features using Dropout is integrated into the proposed topology estimation model, thereby improving the quality and recognition accuracy of the generated topology. During training, the discriminator function gradually reduces the Wasserstein distance between the real and generated topologies and adjusts the Dropout ratio of current features through Dropout ranking. Simultaneously, the generator function adaptively generates topologies based on feedback from the discriminator function to better match the real topology distribution and conditional information.

[0136] Clearly, GCN-GAN with Dropout FR integrates the importance of features into the model's learning process, allowing feature selection and model optimization to occur simultaneously with consistent optimization goals. This helps to better select features that contribute to the performance of the GCN-GAN model, improving the model's generation quality and discrimination accuracy. During training, the discriminator continuously narrows the Wasserstein distance between the real topology and the generator's estimated topology. Simultaneously, influenced by the regularization term of Dropout FR, it continuously controls the feature retention probability to optimize its feature selection ability. Meanwhile, the generator adjusts its generated topology based on feedback from the discriminator to better match the distribution and measurement features of the real topology.

[0137] It's important to note that Dropout FR can essentially be viewed as a feature selection method based on policy gradients, that is, optimizing the output of the best feature combination in the feature space corresponding to the training set topology. In other words, the proposed model's placement optimization strategy selects the placement scheme with the best identification effect from among many placement methods based on the topology in the training set. However, in practice, since the distribution network topology needs to maintain a radial pattern, its commonly used forms are limited. Therefore, it is entirely possible to collect historical operating topologies to construct a library of commonly used feasible topologies, using the power flow calculation results as the basic data for the training set, thereby achieving precise control over the placement scheme for identifying commonly used feasible topologies.

[0138] The above description is merely a preferred embodiment of the present invention and does not constitute any limitation on the present invention. Any person skilled in the art can make many possible variations and modifications to the technical solution of the present invention, or modify it into equivalent embodiments, without departing from the scope of the present invention. Therefore, any modifications, equivalent changes, and alterations made to the above embodiments based on the technology of the present invention without departing from the scope of the present invention are within the protection scope of the present invention.

Claims

1. A graph generative adversarial learning estimation method for active distribution network topology under incomplete measurement, characterized by: Includes the following steps: Step S1: Distribution network topology transformation; The original power distribution network topology is transformed to obtain a linear topology diagram; Step S2: Graph convolution feature extraction; Based on line topology graphs, graph convolutional neural networks propagate the dependencies between node features through graph structures, extract spatial features of graph data, obtain hidden information, and thus update their own line status. In step S2, the line topology graph is represented as an undirected connected graph. ,in, Represents a node. Edge representation, adjacency matrix The topology is represented as a binary matrix, where each element indicates whether nodes are connected; the node feature matrix. Includes available measurements for each node; matrix Defined as: ； in, Indicates the amplitude of the current. The phase angle of the current; Step S3: Construct a generative adversarial topology estimation model; A generative adversarial network (GAN) is constructed, and the extracted spatial features are input into the GAN for training. The generator function is trained by minimizing the log probability, and the discriminator function is trained by maximizing the log probability. In step S3, to generate a topology suitable for a specific state, the following additional information is introduced: ； in, The current characteristics extracted in step S2, This represents the total active power of the system. The total reactive power of the system can be represented by the minimax game as follows: ； Step S4: Construct an observability layout optimization design model; Variational Dropout regularization is added to the input layer of GCN-GAN. By optimizing the design model through observability layout, the dropout rate of topologically important features correctly predicted by the GCN-GAN model is reduced, while the dropout rate of other unimportant features is increased, thus filtering out important current features. In step S4, variational Dropout regularization randomly discards a portion of neurons with a certain probability, thereby improving learning efficiency and reducing the risk of overfitting. The proportion of randomly discarded neurons in the Dropout is obtained by minimizing the following logarithmic probability: ； ； in, Let represent a mask that follows a Bernoulli distribution and is obtained by sampling according to the above formula. Indicates the discard rate. Represents the Sigmoid function; In this configuration, the loss functions for the generator function and the discriminator function are respectively expressed as: ； ； The weight parameters of the generator function and the discriminator function are updated using stochastic gradient descent in the following ways: ； ； in, This indicates noise or a small batch of topological samples.

2. The graph generative adversarial learning estimation method for active distribution network topology under incomplete measurement as described in claim 1, characterized in that: In step S1, based on the Whitney isomorphism principle, for each branch in the original distribution network topology, a node is created in the line graph topology; for every two branches in the original distribution network topology that share a node, a branch is created between their corresponding line graph topology nodes to obtain the line topology graph.

3. The graph generative adversarial learning estimation method for active distribution network topology under incomplete measurement as described in claim 1, characterized in that: The graph convolutional neural network uses an adjacency matrix. and node feature matrix binary pairs As input, its expression is: ； in, Indicates the first The hidden output feature matrix of the layer; In the In the layer, the forward propagation rule of GCN is defined as: ； in, Indicates the first The learning weight matrix of the layer, express Activation function.

4. The graph generative adversarial learning estimation method for active distribution network topology under incomplete measurement as described in claim 3, characterized in that: In step S2, an identity matrix is ​​introduced: ； in, It is an adjacency matrix with a self-connected graph topology. It is the identity matrix; For adjacency matrix Perform the following normalization: ； in, Let represent the degree absolute matrix of the self-loop adjacency matrix; No. The layer-by-layer propagation rule is restated as follows: ； when At that time, there were: 。 5. The graph generative adversarial learning estimation method for active distribution network topology under incomplete measurement as described in claim 1, characterized in that: In step S3, the generative adversarial network is trained simultaneously with the generator function and the discriminator function. The training objective of the generator function is to minimize the following log probabilities: ； in, Represents the mathematical expectation. and This represents the generator function and the discriminator function. This represents the network parameters of the generator function. This represents random noise, while Indicate its probability distribution; The discriminator function is trained by maximizing the following log probabilities: ； in, This represents the network parameters of the discriminator function. Representing the real topology The probability distribution.

6. The graph generative adversarial learning estimation method for active distribution network topology under incomplete measurement as described in claim 5, characterized in that: In the optimization process of the generative adversarial network, the generator function and the discriminator function compete with each other, forming a zero-sum game. The learning estimation model of the graph generative adversarial network is expressed as a minimax game in the following form: 。 7. The graph generative adversarial learning estimation method for active distribution network topology under incomplete measurement as described in claim 1, characterized in that: Step S3 uses Wasserstein distance to define the loss function of the generator. The Wasserstein distance is defined as follows: ； The discriminator function needs to satisfy the 1-Lipschitz condition. A loss term is set in the topology estimation model, as shown below: ； ； in, Indicates the penalty parameter. It is a random number that follows a uniform distribution in the interval [0,1]. This represents the pseudo-topology generated by the generator function. For the true topology, To be The L2 norm of the gradient after input to the discriminator. for pass The expected value obtained from sampling.

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