Geographic multi-factor classification and fusion modeling method based on state space model

Abstract

The invention discloses a geographic multi-factor classification and fusion modeling method based on a state space model, and relates to the fields of geographic information and environmental monitoring, and the method comprises the steps: carrying out the geographic data sampling and geographic element factor division; time feature representation is optimized through multi-scale time information coding, and space coordinates are mapped to a continuous vector space; through selective encoder design and feature extraction, selective sequence scanning and long-range dependence capture are realized by using a state space model; a residual gating fusion module and multi-source factor selection fusion are adopted, gradual fusion of different types of geographic factors and spatio-temporal information is realized through a cascade structure, and a decoder is constructed to generate a result suitable for specific earth science application. According to the method, through a multi-factor division strategy, a selection mechanism based on a state space model and a residual gating fusion mechanism, differential processing and fusion of different types of geographic factors are realized, and the modeling precision is improved under the condition that linear calculation complexity is kept.

Description

Technical Field

[0001] The present invention relates to the fields of geographic information, remote sensing, environmental monitoring, and climate analysis, and particularly relates to a geographical multi-factor classification and fusion modeling method based on a state space model. Background Art

[0002] With the development of Earth observation technology, sensor networks, and the Internet of Things, multi-source, multi-scale, and multi-resolution geographical spatio-temporal data continue to emerge, including satellite remote sensing images, ground monitoring station data, data collected by unmanned aerial vehicles, and mobile device positioning data, etc., providing a rich information source for fields such as environmental monitoring, climate change research, urban planning, and disaster warning. However, such data presents multi-source heterogeneity, complex spatio-temporal dependence, and high-dimensional non-linear relationships, bringing significant challenges to data processing and modeling.

[0003] Existing geographical data modeling methods have the following limitations: Statistical methods such as interpolation and weighted regression can consider spatial autocorrelation, but it is difficult to handle high-dimensional non-linear relationships; Machine learning methods such as random forests and support vector machines can handle complex non-linear relationships, but it is difficult to capture the spatio-temporal dependence characteristics between data and achieve multi-source data fusion; In deep learning methods, convolutional neural networks are difficult to effectively handle long-range dependencies, recurrent neural networks have the problem of gradient disappearance, and Transformer-based models can capture long-range dependencies, but the computational complexity increases quadratically with the sequence length, facing serious computational resource consumption and low efficiency problems in large-scale geographical data processing.

[0004] In addition, there are dynamic change factors such as meteorological elements, relatively stable static factors such as terrain, and discrete category factors such as land cover types in the geographical system. These factors with different characteristics need to adopt differential processing strategies, but existing methods lack an effective multi-factor integration mechanism and are difficult to simultaneously take into account time periodicity and spatial position specificity, resulting in difficulty in achieving high-precision modeling while maintaining high computational efficiency. Summary of the Invention

[0005] The problem to be solved by the present invention is: to provide a geographical multi-factor classification and fusion modeling method based on a state space model, which effectively solves the problems of multi-source heterogeneity, spatio-temporal dependence, multi-scale characteristics, and high-dimensional complexity in geographical spatio-temporal data modeling through a multi-factor division strategy, an adaptive spatio-temporal encoder, and a selective fusion mechanism, and significantly improves the accuracy of geographical data modeling while maintaining high computational efficiency.

[0006] The present invention adopts the following technical solution: A geographical multi-factor classification and fusion modeling method based on a state space model, comprising the following steps: Step 1. Geographic data sampling and factor division: Collect multi-source geographic spatio-temporal data and perform preprocessing. Identify and divide geographic data into multiple factors according to the time-varying characteristics, construct a spatio-temporal reference grid, and perform grid processing on each factor. Step 2. Multi-scale time information encoding: Adopt an optimized sine and cosine periodic encoding method to preserve the continuity of the time information of geographic data and perform periodic topological mapping. Then, fuse multi-scale periodic features through a hierarchical processing strategy. Step 3. Adaptive spatial information encoding: Map the spatial coordinates of geographic data to a continuous vector space. Step 4. Selective encoder construction and feature extraction: Perform non-linear transformation and spatial expansion on the input factors through a projection layer, and perform selective sequence scanning and long-range dependence capture through a state space model. Step 5. Residual gating and multi-source factor fusion: Use a residual gating fusion module and multi-source factor selection fusion, and gradually fuse different types of geographic factors and spatio-temporal information through a cascade structure to generate a unified geographic spatio-temporal fusion representation. Step 6. Decoder module construction and spatio-temporal prediction output: Construct a decoding module, take the unified geographic spatio-temporal fusion representation as the input, perform dimensionality reduction through a combination structure of the KAN layer and the selective encoder module, use a stacked structure of Mamba components to model the sequence tensor, capture the dependencies between data points, and map the features to the target output space for result parsing and post-processing to generate the final predicted values, class results, spatial distribution maps, or simulation data.

[0007] Preferably, the geographic data sampling and factor division in Step 1 are implemented through the following sub-steps: Step 1.1. Collection and preprocessing of original geographic spatio-temporal data: Collect original geographic data containing time, spatial location, and multi-dimensional attribute information, and perform data cleaning, normalization, and missing value filling. Step 1.2. Multi-factor identification and division. In this sub-step, the data is divided into three types of factors according to the spatio-temporal variation characteristics of geographic elements: dynamic geographic factors , static geographic factors , and categorical geographic factors . Step 1.3. Spatio-temporal grid construction and sampling: Construct a unified spatio-temporal reference coordinate system, determine appropriate spatial resolution and time granularity according to the research area and application requirements, generate a regular grid based on the determined spatio-temporal resolution, and perform grid processing and resampling on the three types of factor data to ensure data alignment under the same spatio-temporal reference framework.

[0008] Specifically, dynamic factors refer to elements that exhibit obvious changes in the time series, such as meteorological elements like air temperature, precipitation, air humidity, etc.; static factors refer to elements that remain relatively stable within the research time scale, such as topographic features like terrain elevation, surface slope, aspect, etc.; categorical factors refer to categorical data with discrete characteristics, such as data with clear categorical attributes like land use type, vegetation cover type, etc.

[0009] Preferably, the multi-scale time information encoding described in step 2 is achieved through the following sub-steps: Step 2.1: The multi-scale time encoding adopts a sine and cosine periodic encoding method, which is optimized for continuous preservation, periodic topological mapping, and multi-dimensional periodic feature fusion. For a single input time tensor , assuming the time period length is , then the obtained two-dimensional encoding vector ; Step 2.2: For multi-scale periodic feature fusion, a hierarchical processing strategy is adopted to fuse multi-scale periodic features, and root mean square normalization and KAN mapping are applied to convert the time variable into a continuous vector representation .

[0010] Preferably, for the adaptive spatial information encoding described in step 3, the adaptive spatial information encoder will connect the original coordinate vector , and then apply a sequential KAN layer to embed the spatial information into the continuous vector .

[0011] Preferably, the construction and feature extraction of the selective encoder described in step 4 are achieved through the following sub-steps: Step 4.1: Input feature projection and spatial expansion, aiming to increase the diversity of features and prepare for subsequent selective scanning: The input geographical factor or fused feature tensor is non-linearly transformed through a KAN projection layer, and the feature space dimension is expanded to , obtaining the tensor ; Step 4.2: Feature dimension reshaping and projection: Reshape the tensor , and pass it through the KAN projection layer again to map it to the hidden dimension , obtaining the tensor suitable for sequence scanning; Step 4.3: Selective sequence scanning based on the selection state space model Mamba: Input the tensor into the stacked structure composed of Mamba. Each Mamba component uses the state space model selection mechanism to perform efficient one-way scanning processing along the embedded space dimension to capture long-range dependencies.

[0012] Specifically, residual connections are applied between Mamba component stacks to enhance the stability of gradient propagation and model training, and this process is expressed as: ; Wherein, represents the residual connection, represents root mean square normalization, represents the feed-forward network, represents the number of layers of represents the stacking times of is a sequence processing component based on the selective state space model (SSM), and is a feature extraction unit that efficiently captures long-range dependence features through a structured state space representation and a selective scanning mechanism.

[0013] Step 4.4: Based on the "scan-select-activate" mechanism, enhance feature generation, and pass the tensor processed by the Mamba component through the normalization layer and the KAN projection layer for dimension compression and non-linear activation to obtain the final enhanced feature representation .

[0014] Preferably, the residual gating and multi-source factor fusion in step 5 are implemented through the following sub-steps: Step 5.1: The residual gating fusion is based on a gating-like mechanism, and uses a feed-forward network FFN to precisely control the feature information flow. Given the input features and , the output feature is generated through the residual gating fusion module; Step 5.2: The dynamic factor and the category factor are selectively fused. The feature representation of the dynamic geographical factor obtained in step 1 and the feature representation of the category geographical factor are used as inputs and input into the cascaded structure of the first-level residual gating fusion and the selective encoder module to realize the interactive fusion, selective feature selection and enhancement of the two factor features, and generate the fusion representation of the dynamic and category geographical factors; Step 5.3: The fusion representation of the geographical factors is fused with the time encoding. The fusion representation of the dynamic and category geographical factors generated in step 5.2 and the continuous vector representation generated by the time scale encoder obtained in step 2 are used as inputs and input into the cascaded structure of the second-level residual gating fusion and the selective encoder module for residual gating fusion and selective processing to generate a representation that fuses time, dynamic and category geographical factors ; Step 5.4, Fusion of the fused representation and static factors: Use the fused representation generated in Step 5.3 and the feature representation of the static geographical factors obtained in Step 1 as inputs, and input them into the cascaded structure of the third-level residual gated fusion and selective encoder module for fusion processing to generate a representation that fuses temporal and dynamic, classification, and static geographical factors ; Step 5.5, Generation of the final geographical spatio-temporal fusion representation: Use the fused representation generated in Step 5.4 and the position encoding vector generated by the adaptive spatial information encoding in Step 3 as inputs, and input them into the cascaded structure at the fourth level for final residual fusion and selective processing to generate a unified geographical spatio-temporal fusion representation that contains all geographical factors and spatio-temporal information , which is used as the input to the decoder described in Step 6

[0015] Preferably, the decoder module described in Step 6 constructs and outputs for spatio-temporal prediction, receives the unified geographical spatio-temporal fusion representation generated after the processing in Step 5.5 as the input, and generates the final output result applicable to a specific downstream geoscience application based on this input, which specifically includes the following sub-steps: Step 6.1, Dimensionality reduction of the encoder output: Use the unified geographical spatio-temporal fusion representation obtained in Step 5.5 as the input, and perform non-linear transformation and feature selective processing through the combined structure of multiple Kolmogorov-Arnold network layers and selective encoder modules to reduce the feature dimension and generate a sequence tensor applicable to downstream tasks ; Step 6.2, Sequence modeling based on the state-space Mamba: Input the sequence tensor generated in Step 6.1 into the stacked structure composed of multiple Mamba components. Each Mamba component uses the state-space model and content-related selection mechanism to model the proximity relationship and dependence between input data points along the sequence dimension, and further extract and refine features ; Step 6.3, Final output projection: Project the sequence tensor processed in Step 6.2 through one or more KAN layers for final non-linear projection and dimensionality transformation to obtain , and map the feature space to the dimension of the target output space; Step 6.4, Generation of the output result: According to the requirements of a specific downstream geoscience task, process the result projected in Step 6.3 Perform parsing and post-processing, rely on various loss functions and end-to-end backpropagation training, and finally generate output results in the form of final predicted values, classification results, spatial distribution maps, or simulation data, etc.

[0016] Preferably, the end-to-end backpropagation training and parameter optimization include the following sub-steps: Step 7.1, construct an end-to-end differentiable computational graph from data input to final output; Step 7.2, select a loss function suitable for the task type and apply an optimizer to update the model parameters; Step 7.3, calculate the gradient of the loss function with respect to the model parameters through automatic differentiation; Step 7.4, iteratively execute the training process on the computing platform until the model converges or reaches the preset accuracy requirement.

[0017] Compared with the prior art, the present invention adopts the above technical solutions and has the following technical effects: 1. Efficiently process heterogeneous geographical data: The method of the present invention can adaptively process geographical data of different types and sources through the division strategies of dynamic, static, and classified geographical factors, improving the model's adaptability to heterogeneous data.

[0018] 2. Accurately capture spatio-temporal dependencies: The present invention can simultaneously capture the temporal dynamics and spatial correlations of geographical data by virtue of the efficient sequence processing ability of the state space model and the accurate numerical fitting ability of KAN.

[0019] 3. Significantly improve computational efficiency: The method of the present invention adopts the Mamba selection mechanism with linear complexity, which can process long-sequence geographical spatio-temporal data more efficiently compared with the quadratic complexity of the traditional Transformer model.

[0020] 4. Greatly improve the model accuracy: The present invention effectively integrates multi-source geographical factor information through an adaptive spatio-temporal encoder and a selective fusion mechanism, improving the prediction accuracy and generalization ability of the geographical spatio-temporal model.

[0021] 5. Strong adaptability: The method of the present invention can flexibly adapt to different geographical spatio-temporal modeling tasks through the cascaded structure of residual gating fusion and selective encoder modules, and the modular design of the decoder enables it to be applicable to various application scenarios, including but not limited to air quality prediction, climate change analysis, land use change monitoring, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a flow block diagram of the geographical multi-factor classification and fusion modeling method based on the state space model of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0023] To make the objectives, technical solutions, and advantages of the present invention clearer, the following further elaborates on the technical solutions of the application in conjunction with the accompanying drawings. The described embodiments are only a part of the embodiments related to the present invention. All non-innovative embodiments of other researchers in the field based on this embodiment fall within the protection scope of the present invention. At the same time, for the step numbers in the embodiments of the present invention, they are only set for the convenience of elaboration and explanation, and no limitation is imposed on the order between the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0024] In one embodiment of the present invention, a geographic multi-factor classification and fusion modeling method based on a state space model is as Figure 1 shown and includes the following steps: (1) Geographic data sampling and factor division.

[0025] (1.1) Acquisition and preprocessing of original geographic spatio-temporal data: In this embodiment, original geographic data is collected from various sources including satellite remote sensing images, ground monitoring stations, unmanned aerial vehicles, mobile devices, etc. These data contain time information, spatial location information, and multi-dimensional attribute information. To ensure data quality and consistency, necessary preprocessing is performed on the collected data, including but not limited to: data cleaning to remove or correct redundant and format-error records; data normalization; and filling of missing values.

[0026] (1.2) Multi-factor identification and division: After the data preprocessing is completed, according to the change characteristics of geographic elements in the time series or their inherent attributes, the multi-dimensional attribute factors in the data are divided into three categories: Dynamic factors: Refer to those geographic elements whose attribute values change significantly over time, such as air temperature, precipitation, air humidity, surface temperature, wind speed, etc. These factors usually have obvious time-series dependence and volatility.

[0027] Static factors: Refer to those geographic elements whose attribute values are relatively stable, change slowly, or do not change within the research time scale, such as terrain elevation, surface slope, aspect, soil type, average annual precipitation, etc. These factors mainly reflect the characteristics in space.

[0028] Category factors: Refer to those geographic elements whose attribute values are discrete categories, such as land use types (such as forests, cultivated lands, urban areas), vegetation cover types, administrative divisions, etc. These factors describe the category attributes of geographic entities.

[0029] (1.3) Spatio-temporal grid construction and sampling, constructing a regular spatio-temporal reference grid covering the research area: First, according to the specific application requirements and the scope of the research area, determine the appropriate spatial resolution and time granularity (e.g., daily, monthly). Based on the determined spatio-temporal resolution, generate a two-dimensional or three-dimensional spatio-temporal grid, which contains spatial position indices and time step indices.

[0030] Then, perform grid processing on the three types of factor data, namely dynamic, static, and categorical, divided in (1.2). For the data located within the same grid cell, perform aggregation or resampling to ensure that all factor data are aligned under the same spatio-temporal reference framework, forming a structured input tensor.

[0031] (2) Multi-scale time information encoding.

[0032] (2.1) The multi-scale time encoding adopts the sine and cosine periodic encoding method, which is optimized for continuous preservation, periodic topological mapping, and multi-dimensional periodic feature fusion.

[0033] Specifically, for a single input time tensor , assuming the time period length is , then the obtained two-dimensional encoding vector is: ; where , are the cosine periodic encoding and sine periodic encoding of the time tensor , respectively.

[0034] (2.2) For multi-scale periodic feature fusion, adopt a hierarchical processing strategy: ; where is the maximum index value of the year embedding, is the actual year value, is the element-wise multiplication operator, is the embedding layer in the neural network that maps discrete indices to dense vectors; represents the cosine-sine encoding applied to the contained multi-scale time variables, are the time granularity units such as month, day, hour, minute, etc.; refers to the tensor concatenation operation, are the embedding representations of the year and the periodic encodings of other time units, respectively; is the dimension of the final dimension of the concatenated tensor, represents the root mean square normalization layer, represents mapping the tensor to dimension using the Kolmogorov Arnold Network (KAN).Function of the continuous vector space

[0035] (3) Adaptive spatial information encoding, which transforms the two-dimensional spatial location information of geographical data into a continuous vector representation that can be processed by the model and enables it to generate codes adaptively according to the specific spatial location.

[0036] Specifically, the adaptive position encoder will connect the original coordinate vector , and then apply the sequential KAN layer to embed the spatial information into the continuous vector : ; Among them, is a multi-layer non-linear mapping function based on the Kolmogorov-Arnold network, which is used to encode the spatial information and map it to the continuous vector space of dimension .

[0037] (4) Selective coding module design and feature extraction, which is used to perform efficient and selective feature extraction on geographical factor features, especially to capture long-range dependencies.

[0038] (4.1) Input feature projection and spatial expansion: Aimed at increasing the diversity of features and preparing for subsequent selective scanning, the input geographical factor or fused feature tensor is non-linearly transformed through the KAN projection layer, and the feature space dimension is expanded to to obtain the tensor , where are the batch size, the spatial sequence length, and the input feature dimension respectively.

[0039] (4.2) Feature dimension reshaping and projection: Reshape the tensor , and pass it through the KAN projection layer again to map it to the hidden dimension to obtain the tensor suitable for sequence scanning.

[0040] (4.3) Selective sequence scanning based on the selection state space model Mamba: Input the tensor into the stacked structure composed of Mamba components. The Mamba components perform efficient one-way scanning processing along the embedded space dimension to capture long-range dependencies.

[0041] In this embodiment, residual connections are applied between Mamba components to enhance the stability of gradient propagation and model training. This process is expressed as: ; Among them, represents a residual connection, represents root mean square normalization, represents a feedforward network, represents the number of layers of represents the stacking times of is a sequence processing component based on the selective state space model (SSM), a feature extraction unit that efficiently captures long-range dependencies through a structured state space representation and a selective scanning mechanism.

[0042] (4.4) Based on the "scan-select-activate" mechanism, enhance feature generation: The tensor after being processed by the Mamb component is dimensionally compressed and non-linearly activated through a normalization layer and a KAN projection layer to obtain the final enhanced feature representation .

[0043] (5) Residual gating fusion mechanism and multi-source factor fusion to achieve selective fusion of different types of geographical factors and spatio-temporal encoding.

[0044] (5.1) Residual gating fusion is based on a gating-like mechanism: Use a feedforward network to precisely control the feature information flow. Given the input features and , the output feature generated by the residual gating fusion module is: ; Among them, is the learnable weight parameter matrix of the i-th KAN linear layer, is the Gaussian error linear unit activation function, providing a smooth non-linear transformation.

[0045] (5.2) Dynamic factor and classification factor selective fusion: Take the feature representations of the dynamic geographical factors obtained in step (1) and the feature representations of the categorical geographical factors as inputs and input them into the cascaded structure of the first-level residual gating fusion and selective encoder module to achieve the interaction and residual fusion of the two factor features and selective feature selection and enhancement based on the state space model, generating the fusion representation of the dynamic and categorical geographical factors.

[0046] (5.3) Fusion Representation of Geographical Factors and Fusion with Time Encoding: Use the fusion representation of dynamic and categorical geographical factors generated in step (5.2) and the time encoding tensor generated by the time scale encoder obtained in step (2) as inputs, and input them into the cascaded structure of the second-level residual gated fusion and selective encoder module for residual gated fusion and selective processing to generate a representation that fuses time, dynamic, and categorical geographical factors .

[0047] (5.4) Fusion of Fusion Representation and Static Factors: Use the fusion representation generated in step (5.3) and the feature representation of the static geographical factors obtained in step (1) as inputs, and input them into the cascaded structure of the third-level residual gated fusion and selective encoder module for fusion processing to generate a representation that fuses time, dynamic, categorical, and static geographical factors .

[0048] (5.5) Generation of Final Geo-Spatial-Temporal Fusion Representation: Use the fusion representation generated in step (5.4) and the position encoding vector generated by the adaptive spatial information encoding in step (3) as inputs, and input them into the cascaded structure of the fourth level for final residual fusion and selective processing to generate a unified geo-spatial-temporal fusion representation that contains all geographical factors and spatio-temporal information .

[0049] (6) Decoder Module Design and Spatio-Temporal Prediction Output.

[0050] Specifically, receive the unified geo-spatial-temporal fusion representation generated after being processed in step (5.5) as an input, and generate a final output result applicable to specific downstream geoscience applications based on this input.

[0051] (6.1) Dimensionality Reduction of Encoder Output: Use the unified geo-spatial-temporal fusion representation obtained in step (5.5) as an input, and perform non-linear transformation and feature selective processing through the combined structure of multiple Kolmogorov - Arnold network layers and selective encoder modules to reduce the feature dimension and generate a sequence tensor applicable to downstream tasks .

[0052] (6.2) Sequence Modeling Based on State Space Mamba: Use the sequence tensor generated in step (6.1) Input into a stacked structure composed of multiple Mamba components, each with a state space model and content-related selection mechanism, along the sequence dimension Model the proximity relationships and dependencies between input data points, and further extract and refine features .

[0053] (6.3) Final output projection: The sequence tensor processed in step (6.2) Undergoes final non-linear projection and dimensional transformation through one or more KAN layers to map the feature space to the dimensions of the target output space.

[0054] (6.4) Output result generation: According to the requirements of a specific downstream geoscience task, the result projected in step (6.3) is parsed and post-processed, relying on various loss functions and end-to-end backpropagation training in step (7), and finally generates output results in the form of final predicted values, class results, spatial distribution maps, or simulated data, etc.

[0055] Specifically, the geospatial multi-factor classification and fusion modeling method based on the state space model in this embodiment further includes: step (7) end-to-end training and parameter optimization.

[0056] Specifically, from the input data in step (1) to the final output in step (6), it is constructed as an end-to-end differentiable computational graph, and the parameters of the model (including but not limited to KAN layer parameters, Embedding layer parameters, Mamba component parameters, and RMSNorm parameters, etc.) are optimized through a standard deep learning training process.

[0057] First, select an appropriate loss function, which measures the difference between the model output result and the true target value; for example, mean squared error (MSE) can be selected for regression tasks, and cross-entropy loss can be selected for classification tasks.

[0058] Then, use an optimizer (such as Adam, AdamW, etc.) to update the model parameters.

[0059] During the training process, batches of labeled geo-spatiotemporal data are input into the model, the loss between the model output and the true target is calculated, and the gradients of the loss function with respect to all model parameters are calculated through automatic differentiation techniques. Finally, the optimizer updates the model parameters according to the gradients to minimize the loss function. This process is iteratively executed on a high-performance computing platform (e.g., leveraging the parallel computing capabilities of GPUs or TPUs) until the model converges on the validation set or achieves high-precision modeling.

[0060] In summary, the present invention provides a method for spatio-temporal modeling of geo-big data based on state space model, which effectively partitions and fuses dynamic, static, and categorical geo-factor data, while taking into account the feature extraction in both time and space dimensions, realizes the differential processing and effective fusion of different types of geo-factors, and effectively solves the problems of multi-source heterogeneity, spatio-temporal dependence, multi-scale characteristics, and high-dimensional complexity in geo-spatiotemporal data modeling. At the same time, it can effectively capture the spatio-temporal characteristics of various geo-elements, significantly improve the accuracy of geo-data modeling while maintaining high computational efficiency, and has universality and self-adaptability for the multi-factor comprehensive modeling of geo-data.

[0061] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A geographical multi-factor classification and fusion modeling method based on a state space model, characterized in that, It includes the following steps: Step 1, Geographic data sampling and factor division: Collect multi-source geographic spatio-temporal data and perform preprocessing. Identify and divide multi-factors of geographic data according to time variation characteristics, construct a spatio-temporal reference grid, and perform grid processing on each factor; Step 2, Multi-scale time information encoding: Adopt an optimized sine and cosine periodic encoding method to preserve the continuity of geographic data time information and perform periodic topological mapping, and fuse multi-scale periodic features through a hierarchical processing strategy; Step 3, Adaptive space information encoding: Map the spatial coordinates of geographic data to a continuous vector space; Step 4, Selective encoder construction and feature extraction: Perform non-linear transformation and spatial expansion on the input factors through a projection layer, and perform selective sequence scanning and long-range dependence capture through a state space model; Step 5, Residual gating and multi-source factor fusion: Adopt a residual gating fusion module and multi-source factor selection fusion, and gradually fuse different types of geographic factors and spatio-temporal information through a cascade structure to generate a unified geographic spatio-temporal fusion representation; Step 6, Decoder module construction and spatio-temporal prediction output; Construct a decoding module, take the unified geographic spatio-temporal fusion representation as the input, perform dimensionality reduction processing through the combined structure of the KAN layer and the selective encoder module, use the stacked structure of the Mamba component to model the sequence tensor, capture the dependencies between data points, and map the features to the target output space, perform result parsing and post-processing to generate the final predicted value, category result, spatial distribution map or simulation data.

2. The geographical multi-factor classification and fusion modeling method based on the state space model according to claim 1, wherein The geographic data sampling and factor division described in Step 1 includes the following sub-steps: Step 1.1, Original geographic spatio-temporal data collection and preprocessing: Collect multi-source original geographic data containing time, spatial location and multi-dimensional attribute information, and perform data cleaning, normalization and missing value filling processing; Step 1.2, Multi-factor Recognition and Division: Divide the multi-dimensional attribute factors in the original geographic data into three categories according to the spatio-temporal change characteristics of geographic elements: dynamic geographic factors , static geographic factors , and categorical geographic factors ; Step 1.3, Spatio-temporal grid construction and sampling: Construct a unified spatio-temporal reference coordinate system, determine the spatio-temporal resolution according to the research area and application requirements, including: spatial resolution and time granularity, and generate a regular grid, perform grid processing and resampling on the three types of factor data to align the data in the same spatio-temporal reference framework to form a structured input tensor.

3. The geographical multi-factor classification and fusion modeling method based on the state space model according to claim 2, characterized in that, In Step 1.2, the dynamic geographic factors refer to meteorological elements that show obvious changes in the time series, including: air temperature, precipitation, air humidity; The static geographic factors refer to topographic elements that remain relatively stable within the research time scale, including: terrain elevation, surface slope, slope aspect; The categorical geographic factors refer to categorical data with discrete characteristics, including: land use type, vegetation cover type.

4. The geographical multi-factor classification and fusion modeling method based on the state space model according to claim 2, characterized in that The multi-scale time information encoding described in Step 2 includes the following sub-steps: Step 2.1: Adopt the sine and cosine periodic encoding method to optimize continuous preservation, periodic topological mapping, and multi-dimensional periodic feature fusion for a single input time tensor , with a time period length of , to obtain a two-dimensional encoded vector as follows: ； Among them, and are the cosine periodic encoding and sine periodic encoding of the time tensor respectively; Step 2.2: Integrate multi-scale periodic features through a hierarchical processing strategy, and apply root mean square normalization and KAN mapping to convert the time variable into a continuous vector representation : ； Among them, is the maximum index value of the year embedding, is the actual year value, is the element-wise multiplication operator, is the embedding layer in the neural network that maps discrete indices to dense vectors; represents the cosine-sine encoding applied to the contained multi-scale time variables, are the time granularity units of month, day, hour, and minute respectively; refers to the tensor concatenation operation, are the embedding representation of the year and the periodic encoding of other time units respectively; is the dimension of the last dimension of the concatenated tensor, represents the root mean square normalization layer, represents the tensor using KAN to map to the dimension of the continuous vector space function.

5. The geographical multi-factor classification and fusion modeling method based on the state space model according to claim 4, wherein The adaptive spatial information encoding described in step 3 connects the coordinate vectors of the original geographic data through an adaptive spatial information encoder , and applies a sequence of KAN layers to embed the spatial information into a continuous vector as follows: ； Among them, is a multi-layer non-linear mapping function based on the Kolmogorov-Arnold network, which is used to encode spatial information and map it to a continuous vector space of dimension .

6. The geographical multi-factor classification and fusion modeling method based on the state space model according to claim 5, characterized in that The selective encoder construction and feature extraction described in Step 4 includes the following sub-steps: Step 4.

1. Input Feature Projection and Spatial Expansion: Project the input geographical factors or fused feature tensors through the KAN projection layer for non-linear transformation, expand the feature space dimension to , and obtain the tensor to increase feature diversity; where are the batch size, the spatial sequence length, and the input feature dimension respectively; Step 4.2, Feature Dimension Reshaping and Projection: Reshape the tensor , and then pass through the KAN projection layer again to map to the hidden dimension , obtaining a tensor suitable for sequence scanning ; Step 4.3, Selective Sequence Scanning Based on the Selected State Space Model Mamba: Input the tensor into the stacked structure composed of Mamba. Each Mamba component uses the state space model selection mechanism to perform unidirectional scanning processing along the embedding space dimension to capture long-range dependencies; Step 4.

4. Enhancement feature generation based on the scan-select-activate mechanism: The tensor processed by the Mamba component is passed through the normalization layer and the KAN projection layer for dimensionality compression and non-linear activation to obtain the final enhanced feature representation .

7. The method for geographical multi-factor classification and fusion modeling based on the state space model according to claim 6, characterized in that, In Step 4.3, in the stacked structure composed of Mamba, residual connections are applied between Mamba components to enhance gradient propagation and model training stability, expressed as: ； Among them, represents a residual connection, represents root mean square normalization, represents a feedforward network, represents the number of layers of, is a sequence processing component based on a selective state space model, represents the number of stacking times of.

8. The method for geographical multi-factor classification and fusion modeling based on the state space model according to claim 7, characterized in that The residual gating and multi-source factor fusion described in Step 5 includes the following sub-steps: Step 5.

1. Perform residual gating fusion based on a class gating mechanism: Use a feed-forward network to control the information flow of features. Given the input features and , generate the output feature through the residual gating fusion module as follows: ； Among them, is the learnable weight parameter matrix of the i-th KAN linear layer, is the Gaussian error linear unit activation function, providing a smooth non-linear transformation; Step 5.2, Fusion of Dynamic Factor and Category Factor: The feature representation of the dynamic geographical factor obtained in Step 1 and the feature representation of the category geographical factor are input into the cascaded structure of the first-level residual gated fusion and selective encoder module to perform interactive fusion, selective feature selection, and enhancement of the two-factor features, generating the fusion representation of the dynamic and category geographical factors; Step 5.3, Fusion Representation of Geographic Factors and Temporal Encoding Fusion: The fused representation and the continuous vector representation obtained in Step 2 are input into the cascaded structure of the second-level residual gated fusion and selective encoder module for residual gated fusion and selective processing to generate a representation that fuses temporal, dynamic, and categorical geographic factors ; Step 5.4: Fusion of the fusion representation and the static factor: The fusion representation and the feature representation of the static geographical factor obtained in Step 1 are input into the cascaded structure of the third-level residual gated fusion and selective encoder module for fusion processing to generate a representation that fuses time and dynamics, classification, and static geographical factors ; Step 5.5, Generation of the final geo-spatio-temporal fusion representation: The fusion representation and the position encoding vector generated by the adaptive spatial information encoding in Step 3 are input into the fourth-level R cascade structure for final residual fusion and selective processing to generate a unified geo-spatio-temporal fusion representation containing all geographical factors and spatio-temporal information , which serves as the input to the decoder module described in Step 6.

9. The method for geographical multi-factor classification and fusion modeling based on a state space model according to claim 8, wherein, The decoder module construction and spatio-temporal prediction output described in Step 6 includes the following sub-steps: Step 6.

1. Encoder output dimensionality reduction: Using the unified geographical spatio-temporal fusion representation obtained in the above Step 5.5 as input, perform non-linear transformation and feature selective processing through a combined structure of multiple Kolmogorov-Arnold network layers and a selective encoder module to reduce the feature dimensionality and generate a sequence tensor suitable for downstream tasks ; Step 6.

2. Sequence Modeling Based on State-Space Mamba: Input the sequence tensor into a stacked structure composed of multiple Mamba components. Each Mamba component uses a state-space model and a content-related selection mechanism to model the proximity relationships and dependencies between input data points along the sequence dimension to extract and refine features, resulting in the sequence tensor ; Step 6.3, Output Projection: Project the sequence tensor through one or more KAN layers for non-linear projection and dimensional transformation to obtain the projected result , mapping the feature space to the dimension of the target output space; Step 6.4, Output result generation: According to the requirements of specific downstream geoscience tasks, the projected results are parsed and post-processed, and the final predicted values, classification results, spatial distribution maps, or output results of simulated data are generated by relying on the loss function and end-to-end backpropagation training and parameter optimization.

10. The geographic multi-factor classification and fusion modeling method based on the state space model according to claim 8, characterized in that, The end-to-end backpropagation training and parameter optimization include the following sub-steps: Step 7.1: Construct an end-to-end differentiable computational graph from data input to the final output; Step 7.2: Select a loss function suitable for the task type and apply an optimizer to update the model parameters; Step 7.3: Calculate the gradient of the loss function with respect to the model parameters through automatic differentiation; Step 7.4: Iteratively execute the training process on the computing platform until the model converges or meets the preset accuracy requirements.

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