A spatiotemporal organization dynamic modeling method based on a graph neural network and an unbalanced optimal transmission

Abstract

This invention discloses a spatiotemporal tissue dynamics modeling method based on graph neural networks and imbalanced optimal transport. Belonging to the field of bioinformatics, this invention acquires spatial transcriptome data from multiple time points, constructs a low-dimensional latent space for gene expression, and aligns the spatial coordinates. It models the continuous evolution of gene expression states using graph neural differential equations; calculates cell growth rate using imbalanced optimal transport to obtain information on cell number changes; and constructs a spatiotemporal vector field integrating gene expression, cell number, and spatial coordinates to predict tissue state at target time points. This invention achieves collaborative and continuous modeling of cell state, spatial location, and population size during tissue development and regeneration, enabling generative prediction of tissue conformations at future unobserved time points. Furthermore, it is robust to spatial transcriptome data at different resolutions, providing an efficient and reliable computational analysis tool for developmental biology and regenerative medicine research.

Description

Technical Field

[0001] This invention belongs to the field of bioinformatics processing, and in particular relates to a spatiotemporal organization dynamic modeling method based on graph neural networks and imbalanced optimal transport. Background Technology

[0002] The development of spatial transcriptomics technology has made it possible to simultaneously acquire gene expression data and spatial coordinates in the context of native tissues. High-throughput sequencing has constructed large-scale spatiotemporal maps covering development, regeneration, and disease processes at multiple time points. However, existing computational tools struggle to effectively analyze the coordinated dynamic changes in cell state, spatial location, and population size from these multi-time-point data.

[0003] Inferring biological dynamics from static sequencing snapshots initially relied on pseudo-temporal analysis methods, such as Monocle, which sorts cells along a pseudo-timeline based on transcriptome similarity. However, pseudo-temporal analysis only represents the sequence of processes and lacks a dynamic model for predicting future cell states. RNA rate analysis introduces a dynamic component by estimating instantaneous state changes using RNA splicing kinetics, but these methods rely on simplified kinetic assumptions and act on isolated cells, neglecting the constraints of the spatial microenvironment on cell fate.

[0004] Optimal transport frameworks provide mathematical tools for connecting cell distributions at different time points. Waddington OT uses optimal transport to infer developmental trajectories, while TIGON employs dynamic non-equilibrium optimal transport to simultaneously reconstruct cell dynamics and population growth. Because traditional single-cell RNA sequencing data lacks spatial coordinates, these methods cannot simulate cell migration in physical space. In recent years, spatial transcriptome analysis methods based on optimal transport have made progress: Spateo obtains cell migration velocities by aligning spatial coordinates through optimal mapping, SpaTrack considers both spatial location and gene expression, and STORIES utilizes the fusion of Gromov-Wasserstein distance to learn spatially informative potential.

[0005] However, existing methods still suffer from the following technical limitations: First, they lack generative prediction capabilities and cannot infer tissue configurations at unobserved future time points; second, traditional optimal transport enforces mass conservation, making it difficult to handle population size changes caused by cell division and death; third, they are primarily designed for single-cell resolution data and are not widely applicable to multi-cell resolution platforms. Therefore, there is an urgent need for a spatiotemporal tissue dynamics modeling method that is robust to morphological changes, capable of cross-temporal prediction, and scalable across data resolutions. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a spatiotemporal organization dynamic modeling method based on graph neural networks and imbalanced optimal transport, comprising: Acquire spatial transcriptome data at multiple time points, construct a low-dimensional potential space and initial causal graph of gene expression based on the spatial transcriptome data, and align the spatial coordinates of each time point. Based on the aligned spatial coordinates, the low-dimensional latent space, and the initial causal graph, a graph neural differential equation is constructed to model the continuous evolution of gene expression states. Based on the cell metric in the low-dimensional potential space, the cell growth rate is calculated through non-equilibrium optimal transport to obtain information on changes in cell number; Based on the continuous evolution of gene expression status, changes in cell number, and aligned spatial coordinates, a spatiotemporal vector field is constructed to predict the tissue state at the target time point.

[0007] Optionally, the construction of the low-dimensional potential space for gene expression includes: A graph autoencoder is used to reduce the dimensionality of the original gene expression space. Spatial neighborhood relationships are incorporated into the encoder through a graph convolutional network, and the graph autoencoder is trained using a mean squared error loss function.

[0008] Optionally, aligning the spatial coordinates at each time point includes: By employing rotation and translation transformations, the spatial coordinates of all time points are aligned to the same common coordinate system.

[0009] Optionally, the calculation of cell growth rate via non-equilibrium optimal transport includes: Based on cell measurements at adjacent time points, a transmission coupling matrix is ​​calculated by minimizing the transmission cost through entropy regularization and marginal relaxation penalty, and the cell growth rate is determined based on the transmission coupling matrix.

[0010] Optionally, modeling the continuous evolution of gene expression states includes: Based on historical gene expression data and an initial causal graph, gene expression at the current time point is predicted using a graph neural network, and the network parameters are updated by minimizing the loss function between the predicted and observed values.

[0011] Optionally, the update of the initial causal graph includes: The initial causal graph is updated by the causal influence coefficients between time series, and the graph parameters are optimized based on the prediction loss and sparse regularization term to determine the causal driving relationship between genes.

[0012] Optionally, the construction of the spatiotemporal vector field includes: By parameterizing the spatial coordinates through the constant differential equations, the spatial coordinates at the starting time point are integrated to obtain the predicted spatial coordinates at the target time point.

[0013] Optionally, the method further includes: Using the predicted gene expression, spatial coordinates, and tissue state as inputs, the tissue evolution state at multiple future time points is predicted through iterative reasoning.

[0014] On the other hand, the present invention also provides an electronic device including a memory, a processor, and a computing program stored in the memory and executable on the processor, wherein the processor implements the method when executing the computing program.

[0015] On the other hand, the present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method.

[0016] Compared with the prior art, the present invention has the following advantages and technical effects: First, this invention models the continuous evolution of gene expression states using graph neural differential equations. Combined with spatial coordinate prediction based on optimal transport, it constructs a unified spatiotemporal vector field, achieving collaborative and continuous modeling of cell states and spatial locations during tissue development and regeneration. This enables generative prediction of tissue configurations at unobserved future time points, overcoming the limitation of existing methods that can only align discrete time points and lack predictive capabilities. Second, this invention introduces non-equilibrium optimal transport as the core training objective. By allowing probability quality increases or decreases through marginal relaxation penalties, it can automatically infer population changes caused by cell division and death without pre-setting growth characteristic genes, breaking through the limitation of traditional optimal transport's forced quality conservation and achieving accurate simulation of cell turnover processes. Third, this invention integrates spatial neighborhood information through graph autoencoder dimensionality reduction and graph convolutional networks, enabling it to adapt to spatial transcriptome data of different resolutions from single-cell to multi-cell. Even under low-resolution conditions, it can robustly infer cell growth, death, and recombination processes, demonstrating good generalization ability across data resolutions. Fourth, by constructing causal graphs and spatial regularization constraints, this invention can identify critical fate transitions and spatial migration trajectories of key cell types, linking predictive dynamics with mechanistic driving factors, and providing an efficient, reliable and interpretable computational analysis tool for developmental biology, regenerative medicine and aging research. Attached Figure Description

[0017] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1This is a schematic diagram of STG-OT (Spatiotemporal Graph neural networks Ordinary Differential Equations with unbalanced optimal transport) according to an embodiment of the present invention; Figure 2 This is a comparison chart of the prediction results of STG-OT on the salamander brain regeneration dataset and the experimental results according to an embodiment of the present invention; Figure 3 This is a diagram showing the evolution of tissue morphology after spatial coordinate alignment at different time points according to an embodiment of the present invention; Figure 4 This is a graph showing the distribution and trend of cell growth rate at different time points in an embodiment of the present invention. Figure 5 This is a comparison chart of the cell type composition at each time point in the predicted and experimental data of this invention embodiment; Figure 6 This is a diagram illustrating the developmental lineage reconstruction and transformation relationships of key cell types in embodiments of the present invention; Figure 7 This diagram illustrates the spatiotemporal migration trajectory and nonlinear acceleration process of key cell types in embodiments of the present invention. Detailed Implementation

[0018] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0019] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0020] Example 1 like Figure 1As shown, this embodiment develops the model STG-OT (Spatiotemporal Graph neuralnetworks Ordinary Differential Equations with unbalanced optimal transport), a unified model for inferring continuous hierarchical dynamic systems of tissues from multi-timepoint spatial omics data. By directly predicting future spatial patterns, lineage trajectories, and cell population dynamics based on static snapshot data, STG-OT provides a powerful tool for studying tissue morphogenesis, regeneration, and other synergistic biological processes. It learns spatiotemporal dynamics from multi-timepoint spatial omics data. (A) Data preprocessing: For each timepoint, gene expression profiles are embedded into a low-dimensional latent space, and a graph structure is constructed, while the spatial coordinates of consecutive slices are aligned to the same reference coordinate system. (B) Model architecture. STG-OT employs customized modules to process data from different modalities: (i) the graph neural ODE models the continuous evolution of gene expression states by learning vector fields on the cell graph; (ii) for spatial coordinates, optimal transport (OT) is first used to infer the probabilistic coupling of cells between time points, and then the neural ODE learns continuous coordinate vector fields to predict future positions; (iii) to cope with changes in cell number, unbalanced optimal transport (UOT) is used as the training target, enabling it to naturally adapt to cell division, death, and migration processes without pre-setting growth characteristics. This integrated system ultimately forms a unified, continuous dynamic model of tissue-level changes. (C) Downstream analysis. The learned model can support the prediction of tissue states at unobserved time points, inference of local cell growth rates, and reconstruction of developmental or regeneration trajectories, providing interpretable insights into tissue morphogenesis and cell turnover.

[0021] Corresponding to the above model architecture, this embodiment provides a spatiotemporal organization dynamic modeling method based on graph neural networks and imbalanced optimal transport, including: Acquire spatial transcriptome data at multiple time points, construct a low-dimensional potential space and initial causal graph of gene expression based on the spatial transcriptome data, and align the spatial coordinates of each time point. Based on the aligned spatial coordinates, the low-dimensional latent space, and the initial causal graph, a graph neural differential equation is constructed to model the continuous evolution of gene expression states. Based on the cell metric in the low-dimensional potential space, the cell growth rate is calculated through non-equilibrium optimal transport to obtain information on changes in cell number; Based on the continuous evolution of gene expression status, changes in cell number, and aligned spatial coordinates, a spatiotemporal vector field is constructed to predict the tissue state at the target time point.

[0022] Furthermore, the construction of the low-dimensional potential space for gene expression includes: A graph autoencoder is used to reduce the dimensionality of the original gene expression space. Spatial neighborhood relationships are incorporated into the encoder through a graph convolutional network, and the graph autoencoder is trained using a mean squared error loss function.

[0023] Furthermore, aligning the spatial coordinates of each time point includes: using rotation and translation transformations to align the spatial coordinates of all time points to the same common coordinate system.

[0024] Specifically, to address the inherent high-dimensional sparsity of spatial transcriptome data, a graph autoencoder (GAE) is employed to transform the original high-dimensional gene expression space into a compact, dense, and information-rich low-dimensional latent space, thereby alleviating the curse of dimensionality and improving data organization efficiency. To integrate neighborhood context information of cells or spatial points, a graph structure is constructed and modeled using a graph convolutional network (GCN). The GCN is integrated only into the encoder, used to incorporate spatial neighborhood relationships during embedding; the decoder is responsible for reconstructing the interpolated embeddings back to the original space and does not involve the graph structure. The training of the graph autoencoder (GAE) uses mean squared error (MSE) as the loss function. ; Construction and Projection of Gene Co-expression Network: Based on the gene expression matrix, pairwise correlations between genes are calculated. A scale-free gene co-expression network is constructed using soft thresholding. The topological overlap matrix (TOM) is used to measure gene functional similarity and identify highly co-expressed gene modules. Subsequently, this WGCNA gene network is projected onto the latent space learned by GAE to obtain a gene-level graph structure for subsequent prediction tasks.

[0025] Spatial coordinate alignment: Rotation and translation transformations are used to align the spatial coordinates of all time-point slices to the same common coordinate system, ensuring coordinate consistency in spatiotemporal modeling. The transformation form is denoted as... ,in It is a two-dimensional rotation matrix. It is a translation vector.

[0026] Furthermore, calculating cell growth rate through non-equilibrium optimal transport includes: Based on cell measurements at adjacent time points, a transmission coupling matrix is ​​calculated by minimizing the transmission cost through entropy regularization and marginal relaxation penalty, and the cell growth rate is determined based on the transmission coupling matrix.

[0027] Specifically, unlike classical optimal transport which enforces strict mass conservation, UOT uses Csiszár divergence to relax marginal constraints. This formula is crucial for dynamics because it explicitly explains the probabilistic mass nonconservation caused by cell proliferation (source generation) and apoptosis (sink disappearance). Therefore, it can be used to consider cell growth. Let... and Let represent the cellular empirical measures embedded in the latent gene expression space at times 1 and 2, respectively. We seek a transport coupling matrix. This minimizes the total transmission cost under entropy regularization and marginal relaxation penalty: ; Optimal Coupling As a probabilistic transfer kernel, the forward transfer matrix T is defined by normalizing the transfer scheme relative to the source quality to explicitly calculate cell growth and apoptosis.

[0028] Furthermore, modeling the continuous evolution of gene expression states includes: Based on historical gene expression data and an initial causal graph, gene expression at the current time point is predicted using a graph neural network, and the network parameters are updated by minimizing the loss function between the predicted and observed values.

[0029] Specifically, the gene expression prediction phase aims to use time series... The data is fitted with a generating function, which is then used by a neural network. The neural network is defined by taking into account its parent nodes in the causal graph. It is then used to predict future points in time.

[0030] The graph neural network input includes all historical data points (with the largest time delay). ) And the initial causal graph that has been discovered. During training, the causal graph is sampled using a Bernoulli distribution to predict... It is a neural network Output ; in , , This represents the Hadamard product. Each training sample in a mini-batch is sampled. Fitting is performed under the supervision of observed data points. Specifically, the network parameters are updated by minimizing the following loss function. : ; in This represents the MSE loss function.

[0031] Simultaneously, a spatial information regularization term is added to the loss function. The corrected objective function can be expressed as follows: ; in, Representing a spatial point and The Euclidean distance between them Points representing the embedded space and The distance between them. It is the normalization term, where This refers to the number of cells or spots in the ST data. Spatial regularization penalizes the generation of tight embeddings of cells or spots that are spatially far apart. In other words, if expression similarities are spatially far apart, the tight embeddings caused by expression similarities will be even further apart. Strong spatial regularization may overemphasize the generation of spatially smooth embeddings, which do not necessarily coincide with the more textured biological heterogeneity. To mitigate this problem, a regularization strength parameter is added. Controls the spatial regularization strength relative to reconstruction loss. Default regularization strength. Set to 0.1 as a loose prior (values ​​range from 0 to 1).

[0032] Furthermore, constructing the spatiotemporal vector field includes: By parameterizing the spatial coordinates through the constant differential equations, the spatial coordinates at the starting time point are integrated to obtain the predicted spatial coordinates at the target time point.

[0033] Specifically, this embodiment uses neural ordinary differential equations to parameterize the continuous migration process of cells in physical space. The instantaneous velocity of a cell at position Z(t) is determined by a learnable vector field. : Define, and thus predict the spatial coordinates of the target time point: ; In this phase, the parameter θ is optimized by minimizing the following objective function: ; Furthermore, the construction of the initial causal graph includes: An initial causal graph is constructed using the causal influence coefficients between time series, and the graph parameters are optimized based on prediction loss and sparse regularization terms to determine the causal driving relationships between genes.

[0034] Specifically, a cause-effect graph is used as the initial cause-effect graph. )in Indicates from arrive The efficiency of causal effects. Since there is no transient effect, time series... Granger caused A causal discovery graph is defined if and only if a causal relationship exists at at least one time lag. The maximum value of all time lags ; . In particular, if If the value is 0 (or below a certain threshold), infer the time series. No impact on time series forecasting ,Right now Non-causal .

[0035] Therefore, after forecasting the time series, a causal graph fitting stage is performed to determine the causal probability. ,use To model this possibility, where This represents the sigmoid function. This is the set of parameters to be learned. Since it is assumed that there are no transient effects, it is not necessary to learn the edge directions in the initial causal graph.

[0036] At this stage, the graph parameters were optimized by minimizing the following objective function. : ; in , yes The regularizer forces sparse connections on the initial causal graph of the learned dataset. If for , Punished as Then, the time series can be derived. no The reason.

[0037] The method further includes: Using the predicted gene expression, spatial coordinates, and tissue state as inputs, the tissue evolution state at multiple future time points is predicted through iterative reasoning.

[0038] Specifically, during training, an optimizer is used, with parameters set to atol=1×10. -5 rtol=1×10 -5 , sinkhorn_scaling=0.7 and weight_decay=1×10 -5 To ensure convergence, the learning rate is set to 1×10. -3In the growth rate model, an optimizer is used, with the parameter set to epsilon = 1 × 10⁻⁶. -8 The parameters are set as follows: entropy_reg = 0.1, reg_2 = 10000, and reg_1 equals alpha. The value of the alpha parameter ranges from 0 to 2, and its final value is determined by the mean and standard deviation of the calculated growth coefficients. Using the trained model and inputting training data, the target predicted value is directly output.

[0039] The following experiments were also conducted in this embodiment: We used a publicly available salamander telencephalon regeneration dataset, selecting spatial transcriptome data at five time points (DPI): 2, 5, 10, 15, and 20 days post-injury. Data preprocessing included logarithmic normalization of gene expression data at each time point. A gene co-expression network was constructed using WGCNA, and gene expression data were reduced to a 128-dimensional latent space using GAE. The spatial coordinates of each time point were aligned to a unified coordinate system, such as... Figure 3 As shown in Figure 4, the cell growth rate was significantly higher at the initial injury stage (2 DPI) than at other time points. At 10 DPI, as the wound partially healed, the high growth rate region was specifically confined to the wound area, contrasting sharply with the surrounding area, indicating that cell activity was primarily focused on promoting wound closure. By 15 DPI, the wound had closed, and the growth rate of all cells returned to steady-state levels. To evaluate the model performance, this embodiment compared the predicted states at 10, 15, and 20 DPI with the corresponding experimental results. Figure 2 Quantitative assessment results showed that the RMSE values ​​were 49.51, 53.24, and 65.71, respectively, and the SSIM scores were 0.9910, 0.9954, and 0.9942, respectively. Furthermore, the predicted cell type composition at each time point was highly consistent with the experimental data. Figure 5 Furthermore, STG-OT demonstrated the ability to reconstruct the organizational state at unobserved time points.

[0040] STG-OT reconstructed the developmental lineage of key cell types ( Figure 6The results showed that reaEGCs decreased sharply after 15 DPI; MCG cells decreased in number after brain injury and transformed into VLMC cells. Lineage tracing of sfrpEGC and reaEGC revealed dynamic plasticity among the three EGC subtypes (wntEGC, sfrpEGC, reaEGC), and this bidirectional transformation may be driven by the wound healing process. tlNBL cells showed the ability to differentiate into sfrpEGC, ribEGC, and MSN. Using STG-OT aligned spatial embedding, this embodiment mapped the spatiotemporal trajectories of key cell types ( Figure 7 The migration of reaEGC is confined to the lesion periphery, playing a structural support role; while tlNBL and wntEGC exhibit a "centripetal" migration towards the wound center, promoting tissue filling. Predictions at intermediate time points (12.5 and 17.5 DPI) reveal a nonlinear acceleration process in migration.

[0041] On the other hand, this embodiment also provides an electronic device, including a memory, a processor, and a computing program stored in the memory and executable on the processor, wherein the processor implements the method when executing the computing program.

[0042] On the other hand, this embodiment also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the method.

[0043] This invention proposes a novel spatiotemporal omics dynamic modeling framework, STG-OT, which deeply integrates graph neural networks, neural ordinary differential equations, and optimal transport theory to achieve continuous modeling of cell state, spatial coordinates, and population size for multi-time-point spatial transcriptome data. STG-OT organically combines graph neural ODE, optimal transport (OT), and unbalanced optimal transport (UOT) to construct a collaborative learning framework for gene expression and spatial coordinates oriented towards tissue dynamics. On one hand, it uses graph neural ODE to learn the continuous evolutionary distribution characteristics of gene expression and constructs a model to predict gene expression; on the other hand, based on OT matching and neural ODE, it reconstructs cell migration trajectories from discrete spatial snapshots to form a spatial coordinate prediction model. Furthermore, it learns changes in cell quality through unbalanced optimal transport and simultaneously outputs changes in population size caused by cell division and apoptosis.

[0044] Based on this collaborative architecture, STG-OT takes multi-timepoint spatial transcriptome data as input and, through alternating optimization of graph neural ODE and OT, maps high-dimensional gene expression and spatial coordinates to a unified dynamic system. With end-to-end joint training, it outputs tissue states at any future time—including gene expression profiles, spatial distribution, and cell type composition. This enhances the model's interpretability in cell fate analysis and overcomes the key problems of insufficient interpretability and difficulty in predicting future spatial locations in traditional models using spatiotemporal biological data.

[0045] STG-OT possesses the core capability to output continuous spatiotemporal tissue dynamics, supporting the prediction of tissue evolution. With its unified framework and interpretable design, this framework achieves outstanding predictive performance on multiple real-world biological datasets, including those related to development, regeneration, and aging. It provides an efficient, reliable, and interpretable deep learning solution for developmental biology, regenerative medicine, and aging research, demonstrating strong performance.

[0046] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A spatiotemporal organization dynamic modeling method based on graph neural networks and unbalanced optimal transport, characterized in that, include: Acquire spatial transcriptome data at multiple time points, construct a low-dimensional potential space and initial causal graph of gene expression based on the spatial transcriptome data, and align the spatial coordinates of each time point. Based on the aligned spatial coordinates, the low-dimensional latent space, and the initial causal graph, a graph neural differential equation is constructed to model the continuous evolution of gene expression states. Based on the cell metric in the low-dimensional potential space, the cell growth rate is calculated through non-equilibrium optimal transport to obtain information on changes in cell number; Based on the continuous evolution of gene expression status, changes in cell number, and aligned spatial coordinates, a spatiotemporal vector field is constructed to predict the tissue state at the target time point.

2. The method according to claim 1, characterized in that, The construction of the low-dimensional latent space for gene expression includes: A graph autoencoder is used to reduce the dimensionality of the original gene expression space. Spatial neighborhood relationships are incorporated into the encoder through a graph convolutional network, and the graph autoencoder is trained using a mean squared error loss function.

3. The method according to claim 1, characterized in that, The alignment of spatial coordinates at each time point includes: By employing rotation and translation transformations, the spatial coordinates of all time points are aligned to the same common coordinate system.

4. The method according to claim 1, characterized in that, The calculation of cell growth rate via non-equilibrium optimal transport includes: Based on cell measurements at adjacent time points, a transmission coupling matrix is ​​calculated by minimizing the transmission cost through entropy regularization and marginal relaxation penalty, and the cell growth rate is determined based on the transmission coupling matrix.

5. The method according to claim 1, characterized in that, The modeling of the continuous evolution of gene expression states includes: Based on historical gene expression data and an initial causal graph, gene expression at the current time point is predicted using a graph neural network, and the network parameters are updated by minimizing the loss function between the predicted and observed values.

6. The method according to claim 5, characterized in that, The update of the initial causal graph includes: The initial causal graph is updated by the causal influence coefficients between time series, and the graph parameters are optimized based on the prediction loss and sparse regularization term to determine the causal driving relationship between genes.

7. The method according to claim 1, characterized in that, The construction of the spatiotemporal vector field includes: By parameterizing the spatial coordinates through the constant differential equations, the spatial coordinates at the starting time point are integrated to obtain the predicted spatial coordinates at the target time point.

8. The method according to claim 1, characterized in that, Also includes: Using the predicted gene expression, spatial coordinates, and tissue state as inputs, the tissue evolution state at multiple future time points is predicted through iterative reasoning.

9. An electronic device comprising a memory, a processor, and a computing program stored in the memory and executable on the processor, characterized in that, When the processor executes the computing program, it implements the method of any one of claims 1-8.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1-8.

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