A neuron cellular automata modeling method and system for continuous evolution of coastal ground objects

Abstract

The application discloses a kind of neuron cellular automaton modeling methods and systems for coastal ground object continuous evolution, the method includes: constructing cell complex state vector, neighborhood perception is carried out to cell complex state vector and the feature extraction of update, obtain perception vector, and perception vector is input into the preset multilayer perception machine to extract update feature;Based on neighborhood gradient gate mechanism, the adaptive update is carried out to update feature, the candidate update increment and the gate coefficient are determined respectively by parallel update proposal branch and gate branch, the final update amount is determined according to the product of candidate update increment and gate coefficient, and the current cell state is updated using final update amount;The ground object proportion vector in the cell state after updating is normalized constraint, and the neighborhood perception and update feature extraction step are repeated iteratively to the normalization constraint step, complete ground object evolution simulation;The application can improve the training stability and long-term evolution accuracy of model.

Description

Technical Field

[0001] This invention relates to the field of neuronal cellular automata modeling technology, specifically to a neuronal cellular automata modeling method and system for the continuous evolution of coastal land features. Background Technology

[0002] Coastal wetlands are among the most dynamic ecological transition zones between land and sea, and their landform evolution is driven by a combination of factors, including tidal processes, topographic conditions, vegetation competition, and human activities. Due to the continuous, gradual, and nonlinear nature of wetland evolution, traditional evolutionary simulation methods often suffer from insufficient detail reproduction of land features and significant accumulation of long-term iteration errors in complex dynamic scenarios. With the development of remote sensing technology and ecological modeling theory, the requirements for spatiotemporal resolution and process continuity in coastal wetland evolution research are constantly increasing, leading to a corresponding increase in the complexity of evolutionary simulations.

[0003] Evolutionary simulation methods for coastal wetlands can generally be divided into two categories: discrete simulation methods based on hard classification and gradual simulation methods based on continuous proportions. Discrete simulation methods can maintain the clarity of feature boundaries well, but they are difficult to express the gradual transition phenomena that are common in the intertidal zone. In contrast, gradual simulation methods can better describe the continuous changing relationships between wetland features by expressing the proportion of different features within a pixel, and therefore have greater applicability in long-term continuous evolution simulations.

[0004] Existing gradual change models mainly include multi-agent system models and neuron cellular automata (NCA) models. Neuron cellular automata are a type of spatial evolution simulation method that combines deep learning with cellular automata in recent years. Traditional NCA models represent the attribute information of each spatial unit with a continuous cellular state vector. They learn state update rules from neighborhood perception information through neural networks, replacing the manually preset discrete transformation rules in classic cellular automata. In each iteration step, the model first extracts the spatial gradient and its own state within the neighborhood of each cell using a fixed perception kernel (such as the Sobel gradient operator or the Laplacian operator), forming a perception vector. This perception vector is then input into a lightweight neural network (usually a multilayer perceptron), which outputs the update increments for each state channel. Finally, these increments are superimposed onto the current state with a fixed step size, completing one round of state update. Through multiple iterations, the NCA model can gradually evolve from an initial state to a target state, achieving dynamic simulation of spatial patterns.

[0005] In the traditional NCA framework, the network's update output directly affects the cell state, with all cells receiving state updates in each iteration with a uniform step size and random update probability. This approach assumes that each cell has an equal need for updates in each iteration, and the update increment of the network output is the final change applied to the state. During training, the model optimizes network parameters by minimizing the difference between the predicted and true states, enabling the network to learn to infer reasonable directions of state change from neighborhood information. However, due to the lack of an explicit mechanism for determining whether each cell needs an update and the magnitude of the update, traditional NCA models may experience over-updating and error accumulation in long-term iterations, especially in regions with strong spatial heterogeneity, where a uniform update strategy struggles to accommodate the differentiated needs for update accuracy at different locations.

[0006] Therefore, due to the complex hydrological processes, dynamic vegetation succession, and significant human disturbance within coastal wetlands, their land cover patterns exhibit significant spatiotemporal heterogeneity and dynamic non-stationarity. Existing gradual change models based on continuous proportions still suffer from problems such as local detail degradation, insufficient characterization of gradual change regions, and difficulty in suppressing error accumulation during long-term iterations. In particular, traditional NCA models struggle to fully utilize local neighborhood information and are prone to spatial oversmoothing during multiple evolutionary rounds, thus affecting the preservation of stable regions and the detailed representation of dynamic regions. Summary of the Invention

[0007] To address the aforementioned issues, this application provides a neuronal cellular automata modeling method and system for the continuous evolution of coastal landforms, thereby reducing evolutionary distortion caused by error accumulation during multiple iterations and improving the stability and accuracy of long-term evolution simulation of coastal wetlands.

[0008] According to one aspect of the present invention, a method for modeling neuronal cellular automata for the continuous evolution of coastal features is provided, the method comprising: Construct a cellular composite state vector, which includes a land cover proportion vector, static auxiliary features, and hidden state channels; The cellular composite state vector is subjected to neighborhood perception and update feature extraction to obtain a perception vector, and the perception vector is input into a preset multilayer perceptron to extract update features. The update features are adaptively updated based on the neighborhood gradient gating mechanism. Candidate update increments and gating coefficients are determined by parallel update proposal branches and gating branches, respectively. The final update amount is determined by the product of the candidate update increments and the gating coefficients, and the current cell state is updated using the final update amount. The land cover proportion vector in the updated cell state is normalized and constrained, and the neighborhood perception and updated feature extraction steps are repeatedly executed until the normalization constraint step to complete the land cover evolution simulation.

[0009] According to another aspect of the present invention, a neuronal cellular automata modeling system for the continuous evolution of coastal land features is provided, comprising: The state construction module is used to construct a cellular composite state vector, which includes a land cover proportion vector, static auxiliary features, and hidden state channels. The feature extraction module is used to perform neighborhood perception and update feature extraction on the cellular composite state vector to obtain a perception vector, and input the perception vector into a preset multilayer perceptron to extract update features. The gated update module is used to adaptively update the update features based on the neighborhood gradient gating mechanism. It determines the candidate update increment and the gating coefficient through parallel update proposal branches and gating branches, respectively. It determines the final update amount based on the product of the candidate update increment and the gating coefficient, and uses the final update amount to update the current cell state. The iterative constraint module is used to normalize the feature proportion vector in the updated cell state and trigger the feature extraction module to execute the gated update module in a loop until the preset number of iterative evolution simulations are completed.

[0010] Compared with the prior art, the present invention has the following significant advantages: by introducing a neighborhood gradient gating mechanism to achieve adaptive update of cell state, the NCA model can autonomously determine whether a cell needs to be updated and the update magnitude based on the spatial gradient characteristics of each cell's neighborhood, suppressing over-correction of cells that are close to the target state, and adaptively adjusting the update intensity of different regions according to the degree of spatial heterogeneity, thereby improving the training stability and long-term evolution accuracy of the NCA model. Attached Figure Description

[0011] Figure 1 This invention provides a schematic flowchart of a neuronal cellular automata modeling method for the continuous evolution of coastal features.

[0012] Figure 2 This is a comparison chart of prediction results between gated NCA and traditional NCA provided by the present invention. Detailed Implementation

[0013] Existing methods for simulating the evolution of coastal wetland features often face challenges in handling dynamic scenarios, including insufficient detail reproduction of features and the accumulation of errors over long-term iterations. The Neuron Cellular Automaton (NCA) model, in particular, suffers from this problem. Because all cells are updated according to uniform rules and step sizes, the incremental updates from the network output are directly applied to the cell states without any filtering or regulation. This makes the NCA model highly sensitive to initial conditions during training, resulting in significant differences in model performance under different random initializations. Furthermore, this method cannot determine whether the current state of each cell has approached its optimum. Cells that are close to the target state are continuously updated in subsequent iterations, easily leading to over-correction and the gradual accumulation of errors over multiple iterations. In addition, the uniform update strategy does not consider the differentiated requirements for update intensity at different spatial locations, making it difficult to maintain consistent prediction accuracy in areas with strong spatial heterogeneity, thus limiting the applicability of the NCA model in complex spatial patterns.

[0014] To address this issue, this application proposes a neural cellular automata modeling method and system for the continuous evolution of coastal land features. This method constructs a composite cellular state vector and extracts neighborhood perception and update features to obtain a perception vector. Further, it adaptively updates the update features based on a neighborhood gradient gating mechanism. Candidate update increments and gating coefficients are determined through parallel update proposal branches and gating branches, respectively. The final update amount is determined by the product of the candidate update increment and the gating coefficient, and this final update amount is used to update the current cellular state. Subsequently, the land feature proportion vector in the updated cellular state is normalized, and the above steps are iteratively repeated to complete the land feature evolution simulation.

[0015] For ease of understanding, the following explains some key terms in this embodiment: Static auxiliary features refer to the feature channels in the cellular composite state vector that remain unchanged throughout the entire evolution simulation. These features typically provide background information such as the cell's geographical location, topography, and hydrology, providing stable spatial context constraints for the model.

[0016] Neighborhood awareness refers to the process of processing the state information of a target cell and its surrounding neighboring cells to obtain local spatial context features. This is typically achieved through convolutional operations, aiming to capture the interactions and spatial relationships between a cell and its neighborhood.

[0017] Feature extraction updates refer to processing the raw perceptual vectors obtained from neighborhood sensing through one or more nonlinear transformation layers (such as neural networks) to extract more abstract and discriminative feature representations. These features are used to guide subsequent cell state updates.

[0018] Neighborhood gradient gating is a mechanism that adaptively adjusts the cell state update amplitude based on the spatial gradient information of the cell's neighborhood. By introducing gating units, this mechanism enables the model to determine the update needs of different regions, thereby suppressing over-correction and improving evolutionary accuracy.

[0019] This embodiment provides a neuronal cellular automata modeling method for the continuous evolution of coastal features. (See also...) Figure 1 It is achieved through the following steps: S1. Construct a cellular composite state vector, which includes a land cover proportion vector, static auxiliary features, and hidden state channels.

[0020] Specifically, the coastal wetland study area is discretized into a regular grid, with each grid cell representing a unit. The composite state vector of each cell is constructed by concatenating three parts along the channel dimension: a land feature proportion vector, static auxiliary features, and hidden state channels. The land feature proportion vector represents the area percentage of each type of land feature within the current cell. For example, land features within a cell can be categorized into water bodies, mudflats, Suaeda salsa, Spartina alterniflora, reeds, and aquaculture ponds, with each category's percentage recorded. Static auxiliary features can include two channels: distance from the shoreline and the Digital Elevation Model (DEM). The hidden state channels can be a set of channels initialized with all zeros. The land feature proportion vector and hidden state channels are dynamically updated based on the model output in subsequent iterations, while the static auxiliary features remain unchanged throughout the evolution process, providing the network with continuous spatial location and terrain context information.

[0021] S2. Perform neighborhood perception and update feature extraction on the cellular composite state vector to obtain a perception vector, and input the perception vector into a preset multilayer perceptron to extract update features.

[0022] Further, neighborhood sensing of the cellular composite state vector includes: performing a convolution operation on the cellular composite state vector using a set of fixed sensing kernels, the sensing kernels including an identity kernel, a horizontal Sobel gradient kernel, and a vertical Sobel gradient kernel, respectively extracting the self-value, horizontal spatial gradient, and vertical spatial gradient of each state channel; and concatenating the extracted self-value, horizontal spatial gradient, and vertical spatial gradient along the channel dimension to form the sensing vector.

[0023] Specifically, the identity kernel is a convolution kernel with a central element of 1 and all other elements of 0. Its function is to directly extract the original information of the cell's current state, ensuring that basic attributes are not lost during perception. The horizontal and vertical Sobel gradient kernels are discrete differential operators used for edge detection; they calculate the approximate gradients of the cell's composite state vector in the horizontal and vertical directions, respectively. The horizontal Sobel gradient kernel captures the trend of change in the cell's composite state vector in the horizontal space, while the vertical Sobel gradient kernel captures the trend of change in the vertical space. All local features extracted from the identity kernel, horizontal Sobel gradient kernel, and vertical Sobel gradient kernel are concatenated along the channel dimension. The concatenated features form a perception vector three times the total number of channels, which is then input into a multilayer perceptron for feature extraction updates.

[0024] Furthermore, the multilayer perceptron includes two 1×1 convolutional layers, a batch normalization layer, and a ReLU activation function layer; the 1×1 convolutional layers are used to realize cross-channel information interaction, the batch normalization layer is used to stabilize the training process, and the ReLU activation function introduces nonlinearity to enhance feature representation capability.

[0025] Specifically, this multilayer perceptron consists of two cascaded 1×1 convolutional layers, batch normalization, and ReLU activation functions. By introducing two 1×1 convolutional layers, the proposed multilayer perceptron effectively fuses and interacts information along the channel dimension. This allows cells to not only acquire spatial gradients when perceiving neighborhood information but also capture the complex correlation between the proportion of different land features and the hidden state through cross-channel weight learning, thereby enhancing the richness of feature representation. Simultaneously, the introduction of batch normalization layers effectively alleviates the gradient vanishing problem that may occur in deep networks during iterative evolution by normalizing the output of each layer, ensuring the stability of the training process and enabling the model to maintain stable parameter updates during long-term evolutionary deduction. Combined with the ReLU activation function layer, this structure introduces necessary nonlinear transformations into the model while ensuring computational efficiency. This enables the perception network to fit more complex evolutionary patterns, thereby enhancing the model's overall ability to characterize the dynamic evolution of coastal wetlands. It effectively addresses the shortcomings of simple perception structures in handling high-dimensional spatial feature interactions and maintaining model training stability, thus improving the accuracy of land cover evolution simulation.

[0026] S3. Adaptively update the updated features based on the neighborhood gradient gating mechanism. Determine the candidate update increment and gating coefficient through parallel update proposal branches and gating branches, respectively. Determine the final update amount based on the product of the candidate update increment and the gating coefficient, and use the final update amount to update the current cell state.

[0027] Furthermore, a method for adaptively updating update features based on a neighborhood gradient gating mechanism includes: inputting the update features into the update proposal branch and outputting candidate update increments for each channel through a 1×1 convolution; inputting the update features into the gating branch and outputting gating coefficients with values ​​in the range (0,1) through a 1×1 convolution and a sigmoid activation function; multiplying the candidate update increments element-wise with the gating coefficients, and calculating the final update amount applied to the cell state by combining a preset random update mask and a fixed stride. After calculating the update amount, the update amount corresponding to the static auxiliary features is forcibly set to zero to ensure that the spatial location and terrain context information remain constant during the evolution process.

[0028] Specifically, the proposal branch receives update features extracted by the multilayer perceptron and converts them into candidate update increments Δx for each channel through a 1×1 convolution operation. The gate branch also receives update features as input and converts them into a gate signal through another parallel 1×1 convolutional layer. This gate signal is then processed by a sigmoid activation function to output a gate coefficient g with values ​​ranging from (0,1), representing the update activation level of each channel in the current iteration step.

[0029] The candidate update increment Δx is determined by element-wise multiplication with the gating coefficient g. Specifically, only candidate increments Δx corresponding to g close to 1 are fully applied, while updates corresponding to g close to 0 are effectively suppressed. Furthermore, to enhance model robustness, this method incorporates a pre-defined random update mask. This mask randomly selects some cells to participate in the update with a certain probability in each iteration. Finally, the update amount is scaled with a fixed step size and superimposed onto the current cell state to complete the state update for this round. The update amount corresponding to the static auxiliary channel is forcibly set to zero to ensure its invariance. The value of the gating coefficient is determined by the gradient characteristics of the cell's neighborhood: in areas with high spatial heterogeneity and drastic changes in ground features, the gating coefficient approaches 1 to allow sufficient updates; in areas where the state has stabilized, the gating coefficient approaches 0 to reduce unnecessary perturbations, thereby suppressing over-correction and the gradual accumulation of errors.

[0030] This application achieves refined and adaptive control of the cell state update process by introducing parallel update proposal branches and gating branches. The update proposal branch generates preliminary candidate update increments based on update characteristics, providing directional guidance for the evolution of the cell state. The gating branch outputs gating coefficients with values ​​between (0,1) through the sigmoid activation function. These coefficients dynamically evaluate and adjust the update activation level of each channel based on the local features and evolutionary needs of the cell. By multiplying the candidate update increments element-wise with the gating coefficients, the model effectively filters out unnecessary update signals, ensuring that only increments that meet the current evolutionary needs are applied, thereby avoiding over-correction in the stable state region.

[0031] S4. Normalize the land cover proportion vector in the updated cell state and repeat the neighborhood perception and updated feature extraction steps up to the normalization constraint step to complete the land cover evolution simulation.

[0032] Furthermore, the normalization constraint includes: clamping the proportion values ​​of various land features in the land feature proportion vector within the interval [0,1]; determining whether the sum of the proportions of various land features is greater than 1; if it is greater than 1, scaling each proportion value proportionally to make the sum equal to 1; if the sum is less than or equal to 1, keeping the current proportion value unchanged.

[0033] Specifically, after each state update, a normalization constraint is applied to the land feature proportion vector in the cell state: the proportions of each type of land feature are clamped within the interval [0,1]. If the sum of the proportions of each type is greater than 1, it is scaled proportionally to a sum equal to 1. At the same time, a sum less than 1 is allowed to accommodate water bodies, unclassified areas, etc. By repeating the iterations specified in steps S2 to S4, the land feature evolution simulation from the initial year to the target year is completed. Finally, the land feature proportion vector is extracted from the cell composite state as the prediction result.

[0034] This embodiment introduces a neighborhood gradient gating mechanism, enabling the model to adaptively adjust the cell update amplitude based on local spatial characteristics, effectively suppressing error accumulation and over-correction during the long-term evolution of coastal wetland features. This method improves the model's training stability in dynamic scenarios and enhances its ability to depict the details of feature evolution in spatially heterogeneous regions, thereby achieving a refined simulation of the long-term continuous evolution of coastal wetland feature patterns.

[0035] This application further proposes that the static auxiliary features include digital elevation model (DEM) data and distance data from the shoreline; the hidden state channel is initialized to all zeros at the initial moment; during the iterative evolution process, the static auxiliary features remain unchanged, while the land feature proportion vector and the hidden state channel are dynamically updated with iteration.

[0036] Static auxiliary features refer to those features that remain unchanged throughout the entire land feature evolution simulation process, providing the model with geographical environmental background information. Digital elevation model (DEM) data can provide topographic information such as surface relief, slope, and aspect, which is crucial for understanding natural processes such as water flow direction, vegetation distribution, and soil erosion. Distance data from the shoreline reflects the spatial relationship between cells and the coastline, which is instructive for simulating coastal-specific land feature evolution mechanisms such as tidal influences, salinity gradients, and coastal erosion and siltation. In addition to DEM data and shoreline distance data, static auxiliary features can also include soil type data, geological structure data, historical land use type data, and distance data from rivers or roads, all of which can provide stable physical or human background constraints for land feature evolution.

[0037] Hidden state channels are part of the cellular composite state vector. Their role is to provide the model with internal memory and learning capabilities, enabling it to capture and transmit complex temporal dependencies and evolutionary patterns during iterative evolution. Initializing the hidden state channels with all zeros at the initial time step means that these channels do not carry any pre-defined information at the start of evolution. This allows the model to learn and construct its internal representation autonomously from scratch, avoiding biases that might be introduced by pre-defined values.

[0038] This application provides continuous and stable geographic environmental constraints for land cover evolution simulation. This allows the model to fully perceive and follow physical constraints such as topographic relief and land-water boundaries when updating land cover proportions, effectively avoiding the phenomenon of evolution results deviating from actual geographic laws. Simultaneously, by initializing the hidden state channels to all zeros at the initial moment and allowing them to be dynamically updated along with the land cover proportion vector during iteration, the model gains the ability to autonomously learn and record long-term temporal evolution patterns, enhancing its ability to capture complex evolutionary patterns. This combination of static geographic constraints and dynamic internal memory significantly improves the physical interpretability, long-term stability, and accuracy of land cover evolution simulation, enabling the model to more realistically reflect the continuous evolution process of coastal land cover.

[0039] This application further proposes a neuronal cellular automata modeling system for the continuous evolution of coastal features, which includes a state construction module, a feature extraction module, a gating update module, and an iterative constraint module.

[0040] The state construction module is used to construct the cellular composite state vector, which includes the land feature proportion vector, static auxiliary features, and hidden state channels. The land feature proportion vector represents the area proportion distribution of various coastal land features within the cell, the static auxiliary features provide fixed geographic information such as digital elevation model and distance from the shoreline, and the hidden state channels are used to store temporal memory information during the evolution process.

[0041] The feature extraction module is used to perform neighborhood perception and update feature extraction on the composite state vector of cells. It obtains the state of the cell itself and its horizontal and vertical spatial gradients through a fixed perceptron, forms a perceptron vector, and inputs it into a preset multilayer perceptron. High-dimensional update features are extracted through nonlinear transformation.

[0042] The gated update module is used to adaptively update the update features based on a neighborhood gradient gating mechanism. It determines candidate update increments and gating coefficients through parallel update proposal and gating branches, respectively. The update proposal branch outputs candidate update increments for each channel, while the gating branch generates gating coefficients with values ​​ranging from (0,1) using a sigmoid activation function. The two are then multiplied element-wise to determine the final update amount, which is used to update the current cell state. This mechanism enables the model to autonomously determine update requirements based on the spatial gradient characteristics of the cell's neighborhood. In areas with high spatial heterogeneity and drastic changes in land cover, the gating coefficient approaches 1 to allow for sufficient updates, while in areas where the state has stabilized, the gating coefficient approaches 0 to suppress over-correction, thus effectively preventing the gradual accumulation of errors over multiple iterations.

[0043] The iterative constraint module is used to normalize the land feature proportion vector in the updated cell state, clamp the proportion of various land features within the [0,1] interval and ensure that the sum conforms to physical laws. At the same time, it triggers the feature extraction module to the gated update module to execute in a loop until the preset number of iterative evolution simulations are completed.

[0044] Furthermore, the feature extraction module uses a perceptual kernel, including an identity kernel, a horizontal Sobel gradient kernel, and a vertical Sobel gradient kernel, to extract the self-value, horizontal spatial gradient, and vertical spatial gradient of each state channel.

[0045] Furthermore, the gated update module outputs a gating coefficient through the Sigmoid activation function and performs an element-wise product of the candidate update increment with the gating coefficient to increase the update intensity in regions with high spatial heterogeneity and suppress over-correction in stable regions.

[0046] This application introduces a gating unit into the update pathway of a proportionate neuron cellular automata, enabling the model to autonomously determine update needs and adjust update magnitude based on the gradient characteristics of each cell's neighborhood. Under the same conditions, after multiple independent training runs, the standard deviation of the optimal test loss of the model employing the gating mechanism decreased from 0.008 in the ungated scheme to 0.001, effectively overcoming the significant performance fluctuations caused by random initialization in traditional schemes. The gating mechanism prevents cells that are close to the target state from being continuously over-corrected, avoiding the problem of traditional schemes getting stuck in local optima and continuously degrading in the early stages of training, allowing the model to continuously improve over longer training periods. The optimal test loss of the model employing the gating mechanism reaches 0.266, which is better than the optimal result of the ungated scheme under the same conditions. The peak value of the cosine loss during testing decreased from 0.69 in the ungated scheme to 0.46, indicating that the gating mechanism effectively suppresses the problem of excessive prediction direction deviation in spatially heterogeneous transitional areas. The aforementioned technical effects are directly derived from the autonomous update judgment capability provided by the gating unit, which verifies the role of the neighborhood gradient gating mechanism in improving the training stability and evolution accuracy of neuronal cellular automata.

[0047] The following example will provide a more detailed explanation of the above technical solution: Suppose researchers need to simulate the continuous evolution of landforms in a coastal wetland. The area is divided into a series of regular cellular grids.

[0048] S1. For each cell, construct its composite state vector; by representing the distribution of land features and geographical constraints in the input space with pixel-level state vectors, a detailed simulation of the evolution of large-scale coastal wetlands can be achieved. This vector consists of three parts: land feature proportion vector, static auxiliary features, and hidden state channels.

[0049] This embodiment uses percentage-based annual distribution data of coastal wetland features obtained from multi-source remote sensing images through multi-endmember spectral mixing analysis and unmixing as observation data for the evolution history of land features. The spatial range of the observation data is 2126×1998 pixels, with a spatial resolution of 10 meters, and a time span from 2017 to 2025. At each cell, the land feature status is composed of the area percentage of six main coastal land feature types, including water bodies, mudflats, Suaeda salsa, Spartina alterniflora, reeds, and aquaculture ponds.

[0050] In year t, the cell feature percentage vector at a pixel is represented as: The feature proportion vector satisfies the normalization constraint, meaning each component is between 0 and 1, and the sum of the proportions of all feature components does not exceed 1.0. To provide long-term spatial evolution context constraints, two static auxiliary feature channels are introduced into the cell state vector: digital elevation model data and distance data from the shoreline, both with dimensions of 2×2126×1998. During the iterative updates of the model evolution, the data in these two static auxiliary feature channels remain constant, providing a stable physical background for the network. Furthermore, 16 hidden state channels are designed for each cell, initialized as all-zero vectors in the initial year. These hidden state channels allow cells to autonomously record and transmit long-term temporal change information and wetland succession patterns during multi-step iterative evolution. The total number of channels in the complete composite state vector of each cell in year t is 6 (feature proportion) + 2 (geographic static channels) + 16 (hidden memory channels) = 24 channels.

[0051] S2. Perform neighborhood sensing and feature extraction on the constructed cellular composite state vector. Neuron cellular automata rely on interactions between local cells to simulate complex global evolution. This embodiment extracts local spatial gradient features by designing gradient sensing operators and multilayer perceptrons in the cell neighborhood.

[0052] For each cell, spatial gradients are first calculated in the horizontal and vertical directions on its composite state vector using a 3×3 gradient convolution kernel, resulting in a gradient vector with the same number of channels as the cell's state vector, both being 24-dimensional. The spatial gradients are calculated individually for each channel through channel-wise grouped convolutions to preserve independent physical features. Next, the cell's current state is concatenated with its horizontal and vertical gradients along the channel dimension, forming a 72-dimensional neighborhood-aware feature vector. This neighborhood-aware feature vector is then input into a deep perception network consisting of two 1×1 convolutional layers, batch normalization, and activation functions. The specific calculation process is as follows: The first perception layer extracts features through a 1×1 convolutional layer with 72 input channels and 128 output channels, then inputs them to a batch normalization layer for stable distribution, and outputs 128-dimensional features through a ReLU activation function; the second perception layer further learns deep feature combinations through a 1×1 convolutional layer with 128 input channels and 128 output channels, ultimately obtaining 128-dimensional cell update features.

[0053] By introducing a two-layer perceptron structure and a batch normalization layer, the perceptron network can not only learn more complex spatial topological neighborhood features, but also maintain the stability of gradient flow in multi-step iterative computation.

[0054] S3. Traditional neuronal cellular automata directly superimpose the candidate increments output by the update proposal branch onto the cell state, which can easily lead to over-updating of cells already in a stable state and error accumulation at the transition edges of ground features. This embodiment introduces a gradient gating mechanism into the update path to achieve adaptive evaluation and control of the update magnitude.

[0055] The cell update features output by the perceptual network are fed into two parallel 1×1 convolutional branches: the update proposal branch maps the 128-dimensional features to candidate update increments Δx through a 1×1 convolutional layer, with the number of channels matching the number of composite states (24 dimensions), and no bias is set (bias=False); the gating branch extracts update activation requirement features through another 1×1 convolutional layer, adds a trainable bias (bias=True), and uses a sigmoid activation function to restrict the output values ​​to the (0,1) interval, obtaining adaptive gating coefficients g, representing the update probability and intensity of each cell on each channel. To stabilize cell updates in the early stages of training, the bias of this gating branch is initialized to -6.0, making the gated channels approach 0 in the initial state (i.e., in a suppressed state by default). As training progresses, the model automatically learns the update threshold.

[0056] Building upon this foundation, to enhance the model's generalization ability and prevent overfitting, this embodiment introduces a stochastic mask. In each iteration microstep, the cell randomly selects whether to perform an update at a preset update rate (fire_rate=0.5). The final update amount is determined by the product of the candidate update amount Δx, the gating coefficient g, the stochastic mask, and the step size parameter (step_size=0.5). After the state overlay update, to ensure the physical regularity of the geographic static features, the model forcibly sets the update amounts corresponding to the elevation model (DEM) and the distance to the shoreline channel to zero. The cell-gated state update formula is as follows:

[0057] S' = S + Δx⊙ g ⊙ mask × 0.5; where ⊙ represents the element-wise product of the channel dimension, and the gate coefficient g is adaptively adjusted by the difference in neighborhood gradients: in areas with drastic changes in spatial gradients, such as wetland transition zones, the gate coefficient g approaches 1 to allow the state to evolve fully; in stable, homogeneous areas, the gate coefficient g tends to 0 to reduce update disturbances and suppress over-correction.

[0058] S4. After each cell state update, the model performs physical constraint normalization on the first 6 land feature proportion channels. First, the land feature proportion is forcibly clipped to the [0,1] interval. Then, the sum of the 6 types of proportions is calculated. If the sum is greater than 1.0, it is scaled and normalized to 1.0 by dividing by the sum; if the sum is less than 1.0, the current state is allowed to be maintained to meet the physical constraints of coastal wetland geographic features.

[0059] To prevent memory overflow due to excessive spatial range during full-map training, this embodiment uses non-overlapping grid tiles (256 pixels stride, 256×256 tile size) to crop the 2126×1998 spatial map during training and evaluation, filtering out regions that completely belong to invalid masks, resulting in 50 256×256 data tiles for actual computation. The model uses a time-stepping method for interannual extrapolation, dividing each year into 10 evolutionary microsteps (steps_per_year=10). During training and inference, the model starts from the actual land cover distribution in 2017, iteratively predicts the output for each year using autoregression, and then concatenates the predicted land cover proportions with the retained hidden memory states as the input for the next year's iteration, realizing a long-sequence autoregressive extrapolation process.

[0060] S5. To verify the effectiveness of this invention, model training and comparative experiments were conducted in this embodiment under the same hardware and software configuration and dataset. The experiments used historical images from 2017-2022 (a total of 6 years of data sequence, lc) as the training set and images from 2023-2025 (a total of 3 years of data sequence, lc) as the test set. The comparative model was a conventional NCA model without a gating mechanism. All models used the Adam optimizer with an initial learning rate of 1×10⁻⁶. -4 The evaluation metric is a hybrid loss function (weighted by 0.8×RMSE and 0.2×cosine similarity loss). Horizontal flipping and temporal perturbation enhancement are not performed during training (temporal=False, hflip=False).

[0061] The comparative experiment tested stability using two independent random initializations. (See attached document.) Figure 2 The results showed that: The gated NCA model of this invention exhibits extremely high convergence stability in two independent training sessions, with the optimal test loss stabilizing at 0.2661 (corresponding to...). Figure 2 The left figure shows the optimal epochs (16 and 17) and the range is 0.2675 (17), with a range of only 0.0014 and a standard deviation of 0.0010. This indicates that the gating mechanism can autonomously determine the update requirement based on the gradient characteristics, suppress error accumulation, and enable the model to converge stably.

[0062] Traditional NCA models without gating mechanisms exhibit significant fluctuations and uncertainty in two independent training sessions. The best test loss was 0.2680; the worst test loss degraded to 0.2788 (corresponding to...). Figure 2(See the right figure in the image). This training reached its optimum in the second epoch, but the test loss subsequently exhibited frequent and drastic rebounds and degradations, resulting in significant overfitting and error accumulation in long-term extrapolation. The optimal loss range between the two training iterations was 0.0108, with a standard deviation of 0.0077.

[0063] In summary, during two independent training sessions, the optimal test loss standard deviation of the gated NCA model was 0.001, while that of the ungated model was 0.0077. The gating mechanism reduced the fluctuation of the training results by approximately 87%. These results demonstrate that the gated NCA model proposed in this invention, by adaptively adjusting the local update amplitude, not only improves the prediction accuracy of the evolution of coastal wetland land cover proportions but also significantly enhances the model's repeatability and reliability in practical applications.

[0064] Table 1. Core Calculation Formulas for Domain Gradient Gating Mechanism Candidate update calculation <![CDATA[Δx = W proposal ·F]]> Candidate cell state update vectors are generated based on feature representation F. Gating coefficient calculation <![CDATA[g = σ(W gate ·F + b gate )]]> Adaptively evaluate neighborhood gradient features and output the updated activation strength with values ​​in the (0, 1) interval. Gated adaptive update S' = S + Δx ⊙ g ⊙ mask × 0.5 By combining the gating coefficient with a randomly updated mask, the cellular feature proportion is updated with a fixed step size (0.5), effectively suppressing error accumulation.

[0065] Table 2 Model performance evaluation results Gated NCA model 0.262110 0.282250 0.266138 Traditional NCA model 0.268126 0.321689 0.278839

[0066] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

Claims

1. A method for modeling neuronal cellular automata for the continuous evolution of coastal land features, characterized in that, The method includes: Construct a cellular composite state vector, which includes a land cover proportion vector, static auxiliary features, and hidden state channels; The cellular composite state vector is subjected to neighborhood perception and update feature extraction to obtain a perception vector, and the perception vector is input into a preset multilayer perceptron to extract update features. The update features are adaptively updated based on the neighborhood gradient gating mechanism. Candidate update increments and gating coefficients are determined by parallel update proposal branches and gating branches, respectively. The final update amount is determined by the product of the candidate update increments and the gating coefficients, and the current cell state is updated using the final update amount. The land cover proportion vector in the updated cell state is normalized and constrained, and the neighborhood perception and updated feature extraction steps are repeatedly executed until the normalization constraint step to complete the land cover evolution simulation.

2. The method according to claim 1, characterized in that, The static auxiliary features include digital elevation model (DEM) data and distance data from the shoreline; the hidden state channel is initialized to all zeros at the initial moment; during the iterative evolution process, the static auxiliary features remain unchanged, while the land feature proportion vector and the hidden state channel are dynamically updated with each iteration.

3. The method according to claim 1, characterized in that, The process of performing neighborhood sensing on the composite state vector of the cells includes: The cell composite state vector is convolved using a fixed set of perceptual kernels, including an identity kernel, a horizontal Sobel gradient kernel, and a vertical Sobel gradient kernel, which respectively extract the self-value, horizontal spatial gradient, and vertical spatial gradient of each state channel. The extracted self-value, the horizontal spatial gradient, and the vertical spatial gradient are concatenated along the channel dimension to form the perception vector.

4. The method according to claim 1, characterized in that, The multilayer perceptron includes two 1×1 convolutional layers, a batch normalization layer, and a ReLU activation function layer; the 1×1 convolutional layers are used to realize cross-channel information interaction, and the batch normalization layer is used to stabilize the training process.

5. The method according to claim 1, characterized in that, The adaptive update of the updated features based on the neighborhood gradient gating mechanism includes: The update features are input into the update proposal branch, and the candidate update increments for each channel are output through a 1×1 convolution. The updated features are input into the gated branch, and the gated coefficients with values ​​in the range of (0,1) are output through 1×1 convolution and Sigmoid activation function. The candidate update increment is multiplied element-wise by the gating coefficient, and combined with a preset random update mask and a fixed step size, the final update amount applied to the cell state is calculated.

6. The method according to claim 5, characterized in that, After calculating the update amount, the update amount corresponding to the static auxiliary feature is forcibly set to zero to ensure that the spatial location and terrain context information remain constant during the evolution process.

7. The method according to claim 1, characterized in that, The normalization constraints include: The proportion values ​​of various land features in the land feature proportion vector are clamped within the interval [0,1]. Determine if the sum of the proportions of all types of land features is greater than 1. If it is greater than 1, scale each proportion value proportionally to make the sum equal to 1. If the sum is less than or equal to 1, keep the current proportion value unchanged.

8. A neuronal cellular automata modeling system for the continuous evolution of coastal land features, characterized in that, include: The state construction module is used to construct a cellular composite state vector, which includes a land cover proportion vector, static auxiliary features, and hidden state channels. The feature extraction module is used to perform neighborhood perception and update feature extraction on the cellular composite state vector to obtain a perception vector, and input the perception vector into a preset multilayer perceptron to extract update features. The gated update module is used to adaptively update the update features based on the neighborhood gradient gating mechanism. It determines the candidate update increment and the gating coefficient through parallel update proposal branches and gating branches, respectively. It determines the final update amount based on the product of the candidate update increment and the gating coefficient, and uses the final update amount to update the current cell state. The iterative constraint module is used to normalize the feature proportion vector in the updated cell state and trigger the feature extraction module to execute the gated update module in a loop until the preset number of iterative evolution simulations are completed.

9. The system according to claim 8, characterized in that, The feature extraction module uses a perceptual kernel, including an identity kernel, a horizontal Sobel gradient kernel, and a vertical Sobel gradient kernel, to extract the self-value, horizontal spatial gradient, and vertical spatial gradient of each state channel.

10. The system according to claim 8, characterized in that, The gated update module outputs a gating coefficient through the Sigmoid activation function and performs an element-wise product of the candidate update increment with the gating coefficient to increase the update intensity in regions with high spatial heterogeneity and suppress over-correction in stable regions.

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