A continuous-time dynamic prediction method, system, terminal, and medium for fusion diffusion model and Tushen ordinary differential equation.

Abstract

This invention discloses a continuous-time dynamics prediction method, system, terminal, and medium that integrates diffusion models and graph god regular differential equations, belonging to the field of dynamics prediction technology. The method includes: acquiring multi-node time series; performing network structure inference on the multi-node time series using a diffusion model to obtain the potential graph structure between nodes; performing continuous-time dynamics modeling using graph god regular differential equations to predict the node state at any time point; constructing diffusion reconstruction loss, dynamics prediction error, and structural sparsity constraints to establish a total loss; and based on the total loss, coupling the network structure inference based on the diffusion model with the dynamics modeling based on graph god regular differential equations to achieve collaborative training optimization. This invention can not only stably recover the potential graph structure of a system under complex noise environments but also perform high-precision, continuous prediction of its dynamic evolution, overcoming the limitations of existing technologies that cannot simultaneously handle structure inference and continuous-time modeling.

Description

Technical Field

[0001] This invention relates to the field of dynamics prediction technology, and in particular to a continuous-time dynamics prediction method, system, terminal, and medium based on a fusion diffusion model and Tussine constant differential equations. Background Technology

[0002] Complex dynamical systems are widely found in physics, biology, engineering control, and human behavior modeling. Their core characteristic lies in the implicit interactions between multiple entities within the system, relationships that are often difficult to observe directly, while the system state evolves continuously over time. To understand the internal mechanisms of such systems and the trends in their future states, researchers typically need to obtain two key pieces of information from limited, noisy, or even irregularly sampled historical observations: first, the system's underlying interaction structure, i.e., the relationship graph between entities; and second, the continuous-time dynamics determined by this interaction structure. However, real-world observations are often limited by noise interference, partial omissions, and sparse sampling, making structural inference and dynamic prediction both challenging. Furthermore, continuous-time modeling requires the ability to predict the system state at any point in time, not just discrete predictions with fixed time steps; therefore, the modeling capabilities of existing methods are significantly limited under complex conditions.

[0003] Existing technologies still have significant limitations in structural inference and continuous-time modeling of complex dynamical systems. For example, traditional statistical methods, including Granger causality analysis, mutual information estimation, and transfer entropy methods, often fail to stably recover potential interaction relationships under conditions of high noise, irregular sampling, or missing observations. While deep learning-based structural inference models improve the ability to model nonlinear interaction patterns through neural networks, their structural inference and dynamic prediction processes are usually independent of each other, making it difficult to achieve synergistic optimization. They are also highly sensitive to noise and sparse observations; when observation trajectories are missing or sampling intervals are uneven, their predictive performance and structural stability both significantly decrease. Furthermore, existing dynamical modeling methods, such as LSTM (Long Short-Term Memory) networks, only support discrete-time series prediction. Although continuous-time models based on Neural ODEs (Neural ODEs) can be used for irregular time modeling, they typically assume that the graph structure is known or fixed. This prevents the models from automatically identifying potential structural relationships that dynamically evolve with state changes from real observations. Meanwhile, although generative methods, represented by diffusion models, exhibit good robustness under noisy conditions, existing work mainly focuses on static graph generation and has not solved the problem of unifying relation inference under time-driven conditions with continuous dynamic modeling.

[0004] In summary, existing methods either lack stable structural inference capabilities, cannot handle continuous-time systems, or lack a joint modeling mechanism for structure and dynamics, making it difficult to meet the modeling needs of complex systems in real-world scenarios.

[0005] Therefore, existing technologies still have shortcomings. Summary of the Invention

[0006] The technical problem to be solved by this invention is to provide a continuous-time dynamics prediction system, method, terminal, and medium that integrates diffusion models and TuShen frequent differential equations, addressing the aforementioned deficiencies of existing technologies. The technical solution adopted by this invention is as follows:

[0007] In a first aspect, the present invention provides a continuous-time dynamics prediction method for fusion diffusion models and TuShen frequent differential equations, the method comprising:

[0008] A multi-node time series is acquired, and under a noisy perturbation environment, the network structure of the multi-node time series is inferred through a diffusion model to obtain the potential graph structure between nodes.

[0009] Under the constraints of the potential graph structure, continuous-time dynamics modeling is performed using graph god ordinary differential equations to predict the node state at any time point;

[0010] A diffusion reconstruction loss, dynamic prediction error, and structural sparsity constraint are constructed. A total loss is established based on the diffusion reconstruction loss, dynamic prediction error, and structural sparsity constraint. Based on the total loss, the network structure inference based on the diffusion model is coupled with the dynamic modeling based on graph god ordinary differential equations to achieve collaborative training optimization.

[0011] In one implementation, a multi-node time series is acquired. Under a noisy perturbation environment, a diffusion model is used to infer the network structure of the multi-node time series, yielding the potential graph structure between nodes, including:

[0012] Select the target node time series from the multi-node time series, and perform forward diffusion on the target node time series based on the diffusion model to gradually add noise;

[0013] In each diffusion step, a condition matrix is ​​constructed, and the target node to be noisy and the other unnoisy nodes are input into the multi-scale temporal feature extraction network. The short-term local dynamics are extracted through the convolution branch and the long-term global dependencies are extracted through the self-attention branch.

[0014] The potential graph structure is obtained based on the short-term local dynamics and the long-term global dependencies.

[0015] In one implementation, the potential graph structure is obtained based on the short-term local dynamics and the long-term global dependencies, including:

[0016] The short-term local dynamics and the long-term global dependencies are aligned and fused through a cross-scale interactive fusion module to obtain a fused representation;

[0017] A differentiable structure sampling mechanism generates differentiable edge types for each pair of nodes.

[0018] During the de-diffusion stage, the target node is progressively denoised and reconstructed under the current structure estimation conditions, and the potential structure is updated at each step.

[0019] After multiple rounds of node iteration and multi-step diffusion, the potential graph structure is obtained.

[0020] In one implementation, under the constraints of the latent graph structure, continuous-time dynamics modeling is performed using graph god frequent differential equations to predict the node states at any time point, including:

[0021] The time evolution of the system is described as a graphical ordinary differential equation;

[0022] By using graph god frequent differential equations to realize message passing between nodes and state derivative calculation, the node state at any time point can be obtained.

[0023] In one implementation, graph god frequent differential equations are used to realize message passing and state derivative calculation between nodes, obtaining the node state at any time point, including:

[0024] The information propagation path and intensity are determined based on the potential graph structure;

[0025] By integrating the graphical ordinary differential equation using a numerical ordinary differential equation solver, the nodal states at any time point can be obtained starting from a given initial state.

[0026] In one implementation, a diffusion reconstruction loss, a dynamic prediction error, and a structural sparsity constraint are constructed, including:

[0027] In the process of inferring the network structure of multi-node time series using a diffusion model, the inverse diffusion network predicts the noise added to the target node in the forward diffusion step, and uses the mean square error to constrain the deviation between the predicted noise and the real noise, thus obtaining the diffusion reconstruction loss.

[0028] In the process of continuous-time dynamic modeling using the TuShen ordinary differential equation, the TuShen ordinary differential equation is used to predict the trajectory at multiple future time points given the initial state and inference structure. The deviation between the predicted trajectory and the actual trajectory is constrained in the form of mean square error, and the dynamic prediction loss is obtained.

[0029] By imposing constraints on the average edge density of the potential graph structure, structural sparsity constraints are obtained.

[0030] In one implementation, a total loss is established based on diffusion reconstruction loss, dynamic prediction error, and structural sparsity constraints. Based on this total loss, network structure inference based on the diffusion model is coupled with dynamic modeling based on graph god frequent differential equations to achieve collaborative training optimization, including:

[0031] The diffusion reconstruction loss, dynamic prediction error, and structural sparsity constraint are integrated to obtain the total loss;

[0032] Based on the total loss, the parameters of the diffusion model and the graph god regular differential equation are jointly backpropagated and updated, so that the network structure inference based on the diffusion model and the dynamic modeling based on the graph god regular differential equation are trained and optimized together under the same objective.

[0033] Secondly, embodiments of the present invention also provide a continuous-time dynamics prediction system for a fusion-diffusion model and a TuShin regular differential equation, wherein the system is used to implement the steps of the continuous-time dynamics prediction method for the fusion-diffusion model and the TuShin regular differential equation described in the above scheme, and the system includes:

[0034] The diffusion network structure inference module is used to acquire multi-node time series. Under noisy perturbation environment, the network structure of the multi-node time series is inferred through the diffusion model to obtain the potential graph structure between nodes.

[0035] The dynamics learning module is used to perform continuous-time dynamics modeling using graph-based ordinary differential equations under the constraints of the potential graph structure, and to predict the node state at any time point.

[0036] The joint training and optimization module is used to construct diffusion reconstruction loss, dynamic prediction error and structural sparsity constraint. Based on diffusion reconstruction loss, dynamic prediction error and structural sparsity constraint, a total loss is established. Based on the total loss, the network structure inference based on diffusion model and the dynamic modeling based on graph god ordinary differential equation are coupled to achieve collaborative training optimization.

[0037] Thirdly, embodiments of the present invention also provide a terminal, wherein the terminal includes a memory, a processor, and a continuous-time dynamics prediction program for the fusion diffusion model and the Tussin regular differential equation stored in the memory and executable on the processor. When the processor executes the continuous-time dynamics prediction program for the fusion diffusion model and the Tussin regular differential equation, it implements the steps of the continuous-time dynamics prediction method for the fusion diffusion model and the Tussin regular differential equation in any of the above schemes.

[0038] Fourthly, embodiments of the present invention also provide a computer-readable storage medium, wherein the computer-readable storage medium stores a continuous-time dynamics prediction program for the fusion-diffusion model and the Tussin regular differential equation, the continuous-time dynamics prediction program for the fusion-diffusion model and the Tussin regular differential equation implementing the steps of the continuous-time dynamics prediction method for the fusion-diffusion model and the Tussin regular differential equation as described in any of the above schemes on the computer-readable storage medium.

[0039] Beneficial Effects: Compared with existing technologies, this invention provides a continuous-time dynamics prediction method that integrates a diffusion model and graph-based regular differential equations. First, this invention acquires multi-node time series. Under a noisy perturbation environment, it uses a diffusion model to infer the network structure of the multi-node time series, obtaining the potential graph structure between nodes. Then, under the constraints of the potential graph structure, it uses graph-based regular differential equations for continuous-time dynamics modeling to predict the node state at any time point. Finally, it constructs a diffusion reconstruction loss, a dynamics prediction error, and a structural sparsity constraint. Based on these constraints, a total loss is established. Based on this total loss, the network structure inference based on the diffusion model and the dynamics modeling based on graph-based regular differential equations are coupled to achieve collaborative training optimization.

[0040] This invention forms a complete unified scheme for structure recognition, continuous dynamics modeling, and training optimization. It can not only stably recover the potential relationship structure of a system under complex noise environment, but also make high-precision and continuous predictions of its dynamic evolution. It significantly overcomes the limitations of existing technologies that cannot take into account both structure inference and continuous time modeling. It is applicable to various complex system modeling scenarios such as physical systems, biological systems, engineering control, and multi-body behavior analysis. Attached Figure Description

[0041] Figure 1 This is a flowchart illustrating a preferred embodiment of the continuous-time dynamics prediction method for the fusion diffusion model and the Tushen ordinary differential equation provided in this invention.

[0042] Figure 2 The diagram illustrates the execution principle of the continuous-time dynamics prediction method for the fusion diffusion model and the Tushen ordinary differential equation provided in this embodiment of the invention.

[0043] Figure 3 This is an architecture diagram of the continuous-time dynamics prediction system for the fusion diffusion model and the Tushen frequent differential equation provided in an embodiment of the present invention.

[0044] Figure 4 A schematic diagram of a terminal provided in an embodiment of the present invention. Detailed Implementation

[0045] To make the objectives, technical solutions, and effects of this invention clearer and more explicit, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0046] The flowchart shown in the attached diagram is for illustrative purposes only and does not necessarily include all content, operations, or steps, nor does it require execution in the described order. For example, some operations or steps can be broken down, combined, or partially merged, so the actual execution order may change depending on the actual situation.

[0047] It should be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0048] It should be understood that, in order to clearly describe the technical solutions of the embodiments of the present invention, the terms "first" and "second" are used in the embodiments of the present invention to distinguish identical or similar items with essentially the same function and effect. For example, "first control information" and "second control information" are only used to distinguish different control information and do not limit their order.

[0049] Those skilled in the art will understand that the words "first" and "second" do not limit the quantity or the order of execution, and that the words "first" and "second" do not necessarily imply that they are different.

[0050] It should also be understood that the term “and / or” as used in this specification and the appended claims refers to any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0051] The modeling of complex systems urgently needs a unified modeling scheme that can simultaneously infer the underlying structure and learn continuous-time dynamics under irregular and noisy observation conditions, in order to overcome the limitations of existing technologies in terms of robustness, interpretability and generalization ability.

[0052] In existing structural inference techniques, traditional statistical methods such as Granger causality analysis, mutual information estimation, and transfer entropy calculation can measure the statistical dependencies between variables. However, their core assumptions are usually linear or weakly nonlinear and rely on relatively ideal sampling conditions, making it difficult to maintain stability in real-world complex systems with high-noise, missing, or non-stationary data scenarios. Furthermore, these methods typically cannot automatically capture the implicit relationship structure in high-dimensional time-series data, making it difficult to meet the needs of modern complex system modeling.

[0053] The development of deep learning has driven the development of relation inference methods for time-series systems. For example, Interaction Networks use graph structures to model the interaction relationships between objects in a physical system; Neural Relational Inference (NRI) models employ a variational inference framework to learn the potential discrete structure from time-series trajectories, and subsequent extensions, such as multi-relation modeling or message passing mechanisms, have further improved the performance of relation inference. However, NRI and its variants generally use discrete-time encoders and decoders, separating structural inference from dynamic prediction, which fails to form an effective synergy. Furthermore, the stability of structural inference decreases significantly when observations are noisy, missing, or irregularly sampled. In addition, these methods typically assume that the graph structure is static and fixed, making it difficult to describe the interaction strength that changes with state in real systems.

[0054] In dynamic modeling, traditional recurrent neural networks (RNNs), long short-term memory networks (LSTMs), and gated recurrent units (GRUs) rely on discrete prediction methods with fixed step sizes, making them ill-suited for modeling continuous-time systems. Neural ODEs, by representing state evolution as differentiable equations, can model system dynamics in the continuous-time domain and support predictions at arbitrary time points. However, existing Graph Neural ODE methods only perform continuous-time predictions under given or defined graph structures, lacking the ability to automatically infer graph structures from observational data, thus limiting their application in real-world complex systems.

[0055] Furthermore, generative models, represented by diffusion models, exhibit good robustness in handling noise, missing values, and high-dimensional distribution modeling. However, existing diffusion graph models are mainly used for static graph generation, which differs significantly from time series-driven dynamic structure inference scenarios, and cannot achieve joint optimization of structure inference and dynamic prediction.

[0056] In summary, existing technologies either lack the ability to stably infer potential structures under noisy and missing conditions, or are unable to perform dynamic predictions in the continuous time dimension, or the two are independent and lack a unified framework. These limitations prevent existing methods from meeting the comprehensive requirements of robustness, interpretability, and continuous prediction capability in complex system modeling. To address this, this embodiment provides a continuous-time dynamic prediction method that integrates diffusion models and graph-Shen regular differential equations. By simultaneously achieving structure identification and dynamic learning, the system can achieve stable, interpretable, and arbitrary time-point prediction integrated modeling capability under noisy, missing, and irregular sampling conditions, thereby effectively overcoming the limitations of existing technologies.

[0057] The fusion-diffusion model and continuous-time dynamics prediction method for the TuShin ordinary differential equation provided in this embodiment can be applied to terminals, such as computers and other intelligent product terminals. Figure 1 As shown in the figure, the continuous-time dynamics prediction method of the fusion diffusion model and the TuShen ordinary differential equation in this embodiment includes the following steps:

[0058] Step S100: Obtain multi-node time series. Under noisy perturbation, infer the network structure of the multi-node time series using a diffusion model to obtain the potential graph structure between nodes.

[0059] This embodiment obtains multi-node time series. Using multi-node time series as a unified input, where For the number of nodes, For time steps, This represents the set of real numbers. When a multi-node time series is input into the diffusion network structure inference module, the target node time series is first selected from the multi-node time series. Then, based on the diffusion model, forward diffusion is performed on the target node time series, gradually adding noise. Specifically, in this embodiment, Indicates the first row node Time series, column vector Indicates time The state of all nodes. Potential relationships between nodes are represented by the adjacency matrix. Indicates that the element or edge type variable Represents a node and The strength or type of interaction between them. System dynamics in continuous time can be expressed as:

[0060] ,in, The subsequent solution is provided by an ordinary differential equation model based on a graph neural network.

[0061] This embodiment uses a given multi-node time series. Under these conditions, on the one hand, the potential graph structure is inferred through a diffusion framework. On the other hand, continuous-time dynamics are fitted onto this structure to predict the node state at any future time.

[0062] Specifically, in combination Figure 2 As shown in the figure, this embodiment adopts a conditional diffusion strategy: selecting a target node each time. The time series of the target node is gradually increased with noise, while the time series of other nodes remain unchanged as conditional information. Let the original time series of the target node be... ,pass Step diffusion obtained .like Figure 2 As shown, single-step diffusion satisfies Gaussian noise perturbation:

[0063] ,in, For the target node to pass through the first The time series obtained by step diffusion, For the target node to pass through the first The time series obtained by step diffusion, For the first The noise intensity of the step, Indicates a Gaussian distribution. The identity matrix. To improve efficiency, this embodiment employs closed-form reparameterization:

[0064] , Among them, random noise variables In this way, forward diffusion does not require training; it simply uses pre-defined noise scheduling to gradually "submerge" the target node's trajectory in noise. The time series of other nodes... It remains unchanged throughout the process, serving as conditional information for reverse recovery and structural inference, prompting the model to learn the relational structure from the overall dynamics of the system.

[0065] Furthermore, in this embodiment, a conditional matrix is ​​constructed at each diffusion step. The target node to be noisy and the remaining unnoisy nodes are input into a multi-scale temporal feature extraction network. Short-term local dynamics are extracted through convolutional branches, and long-term global dependencies are extracted through self-attention branches. Specifically, to identify potential dependencies between nodes, this embodiment performs conditional matrix construction at each diffusion time step. Construct the condition matrix:

[0066] ,in, Indicates the position located in the matrix at the th The time series of the target node after adding noise The remaining rows correspond to the original time series of other nodes. Next, a multi-scale temporal feature extraction module is used to... The module is encoded as consisting of short-term convolutional branches and long-term self-attention branches, used to simultaneously handle short-term local dynamics and long-term global dependencies.

[0067] Specifically, on the one hand, the short-term convolutional branches extract short-term local dynamics using one-dimensional convolution and residual structures, which can be represented as:

[0068] ,in, It is an activation function. Batch Normalization is a technique used to accelerate the training of deep neural networks. This represents a convolutional layer. This refers to residual connections. This branch mainly focuses on changes between adjacent or short-distance points on the time axis, such as sudden responses and small-scale oscillations. It plays an important role in determining whether two nodes produce synchronous reactions or influence each other in a short period of time. At the same time, the convolution and residual structure also make it highly robust to noise.

[0069] On the other hand, the long-term self-attention branch uses a self-attention mechanism to model long-term global dependencies over the entire time span. Figure 2 In this context, "Trans" represents the Transformer model, and long-term global dependencies are represented as follows:

[0070] ,in, The term "Locally Connected" indicates a partial connection. This represents a self-attention mechanism. This branch can capture macroscopic dynamic features such as co-variation across time, phase locking, and slow evolutionary trends, which helps to identify node pairs that are not immediately strongly correlated but maintain high coupling over long time scales.

[0071] In obtaining short-term local dynamics Long-term global dependencies Subsequently, in this embodiment, the two types of information are aligned and fused through a cross-scale interactive fusion module to obtain the aligned and fused representation, which is expressed as:

[0072] ,in, This represents a Cross-Attention structure, which allows short-term local dynamics to be reweighted in the long-term context, and long-term global dependencies to be more stable under the constraints of local details. Ultimately, for any node pair... All of these can be derived from fusion representation. Extract the fusion representation of the corresponding node pairs from the middle This provides a well-informed and physically / dynamically meaningful basic representation for subsequent edge type sampling. In other words, the role of the multi-scale temporal feature extraction module is to translate "how things move in time" into an intermediate representation of "what relationships might exist between nodes," considering both local transients and overall trends.

[0073] Furthermore, this embodiment generates differentiable edge types for each pair of nodes based on a differentiable structure sampling mechanism; then, in the inverse diffusion stage, the target nodes are progressively denoised and reconstructed under the current structure estimation conditions, and the potential structure is updated at each step. After multiple rounds of node and multi-step diffusion iterations, the potential graph structure is obtained. Specifically, in obtaining the fusion representation of node pairs... Subsequently, the present invention through Layered graph neural networks embed fused representations to obtain Furthermore, a differentiable structure sampling mechanism is used to generate edge types for each pair of nodes. Edge Type Specifically, it can be expressed as:

[0074] ,in, , It indicates that it is differentiable. The temperature parameter controls the "hard / soft" level of the sampling. express This mechanism is numerically close to discrete edge types, but still maintains differentiability, allowing the structure inference module to perform gradient optimization along with the entire model. All edge types. The potential structure matrix at the current diffusion step .

[0075] In the back-diffusion stage, this embodiment needs to gradually recover the true time series of the target node from highly perturbed noisy data, while continuously correcting the inferred potential structure. To this end, this invention uses a parameter... The neural network representing the diffusion step The noise level corresponding to the data is estimated. The network uses the condition matrix of the current diffusion state. ,step and the structure matrix obtained in the preceding iterations. As input, used to predict noise terms Based on this, the conditional distribution of reverse diffusion can be expressed as:

[0076] .

[0077] in, For variance, denoised mean The key to original signal recovery is as follows:

[0078] ,in, ,and .

[0079] Throughout the inverse diffusion process, this embodiment uses a time series of a target node initialized with completely Gaussian noise. Starting from this point, through gradual iteration, we obtain... Each iteration not only performs denoising on the target node, but also re-estimates and refines the latent structure matrix between nodes. Such a two-way feedback mechanism can gradually weaken or eliminate structures that do not conform to the laws of real dynamics, thereby obtaining a stable and interpretable latent graph structure after convergence of multiple diffusion steps. The resulting potential graph structure This will serve as an important foundation for subsequent continuous-time dynamics modeling.

[0080] Therefore, this embodiment first applies progressive noise perturbation to the time series of the target node while keeping the other node sequences unchanged as conditional context. Then, during the progressive denoising and reconstruction process, the relationship structure between nodes is updated synchronously and repeatedly, allowing the structure to converge from coarse to fine during denoising. This ensures stable recovery of the true potential interaction relationships even under noise interference, missing observations, or irregular sampling. Furthermore, this embodiment introduces a multi-scale temporal feature extraction and fusion mechanism during network structure inference. Short-term convolutional branches capture short-term local dynamics, while long-term self-attention branches capture long-term global dependencies. A cross-scale interaction fusion module aligns and fuses these two types of information into a relational representation of node pairs. By employing a differentiable structure sampling mechanism, the structure can learn end-to-end and continuously optimize during the inference process.

[0081] Step S200: Under the constraints of the potential graph structure, continuous-time dynamics modeling is performed using graph-based constant differential equations to predict the node state at any time point.

[0082] After obtaining the latent graph structure, the data flow enters the dynamics learning module. In this embodiment, the system's temporal evolution is described as a graph-based regular differential equation. Then, the graph-based regular differential equation is used to realize message passing between nodes and calculate state derivatives, obtaining the node states at any time point. Specifically, after inferring the latent graph structure... Subsequently, this embodiment uses the TuShen ordinary differential equation to perform continuous-time modeling of the system dynamics, enabling the model to predict the nodal states at any time point under given structural constraints.

[0083] This invention describes the time evolution of the system as an ordinary differential equation of the following form:

[0084] ,in, , Indicates the first row of nodes exist Time series of moments Indicates the first row node exist Time series of moments This represents a nonlinear function implemented using a graph neural network. Latent graph structure. It plays a role in constraining the path and intensity of information propagation: the larger the edge weight, the stronger the influence between nodes.

[0085] In its implementation, the graph god frequently uses differential equations to calculate the state change rate of each node through a message-passing mechanism, and determines the information propagation path and intensity based on the underlying graph structure. For nodes... First, information is aggregated from its neighboring nodes. For nodes The message can be written as:

[0086] ,in, This refers to a multilayer perceptron. This represents the activation function in a multilayer perceptron. Indicates the first row node exist Time series of moments Indicates the first row node exist Time series of moments Represents a node and nodes The potential graph structure between them.

[0087] The aggregate obtained by summing all neighboring nodes is then represented as:

[0088] It is then concatenated with the node's own state and input into another multilayer perceptron, represented as:

[0089] ,in, This is represented as the activation function in another multilayer perceptron. Serving as residual terms helps improve the stability and expressive power of solving ordinary differential equations. Through the above form, the instantaneous rate of change of a node depends not only on its own state but also explicitly on the underlying graph structure. The state of the middle neighbors influences the system. This structured dynamics is well-suited for describing real-world scenarios such as physical networks, coupled oscillator systems, and social interaction networks.

[0090] Finally, the graphical ordinary differential equation is integrated using a numerical ordinary differential equation solver to obtain the nodal states at any given time point, starting from the initial state. Specifically, combined with... Figure 2 As shown, when the derivative function is obtained Then, this invention utilizes a numerical ordinary differential equation solver to integrate the ordinary differential equation from the initial time. Node status Departure, any time obtained Node status:

[0091] , express The node state at any given time is expressed as a continuous representation in time. This embodiment can naturally handle irregular sampled data and support long-term extrapolation, while avoiding the error accumulation problem caused by multi-step iteration in traditional discrete-time models.

[0092] Step S300: Construct diffusion reconstruction loss, dynamic prediction error and structural sparsity constraint. Based on diffusion reconstruction loss, dynamic prediction error and structural sparsity constraint, establish total loss. Based on the total loss, couple network structure inference based on diffusion model with dynamic modeling based on graph god frequent differential equation to achieve collaborative training optimization.

[0093] Furthermore, following the diffusion network structure inference module and the dynamics learning module, this embodiment tightly couples structure inference and dynamics modeling through a joint training and optimization module. This module constructs a unified total loss function to comprehensively balance the prediction error of diffusion noise, the prediction error of continuous-time trajectory, and the sparsity constraint of graph structure.

[0094] Specifically, in this embodiment, during the network structure inference of multi-node time series using a diffusion model, the inverse diffusion network predicts the noise added to the target node in the forward diffusion step, and uses the mean square error to constrain the deviation between the predicted noise and the actual noise, thus obtaining the diffusion reconstruction loss, expressed as:

[0095] ,in, Represents the mathematical expectation. Represents real noise. This represents the square of the L2 norm. This diffusion reconstruction loss ensures that the inverse diffusion process can accurately reconstruct the noise-inundated node sequence, thereby improving the latent structure matrix. An indirect requirement is proposed: only a reasonable structure can help the model recover the original trajectory from the conditional context.

[0096] In this embodiment, during continuous-time dynamics modeling using the TuShen ordinary differential equation, the TuShen ordinary differential equation is used to predict the trajectory at multiple future time points given an initial state and inference structure. The deviation between the predicted trajectory and the actual trajectory is constrained using the mean squared error, resulting in the dynamics prediction loss, expressed as:

[0097] ,in, and Representing nodes respectively The predicted trajectory and the actual trajectory. Because the dynamic prediction process is highly dependent on the underlying graph structure... The adjacency information provided by this loss imposes a constraint on the structure graph from the perspective of "dynamic interpretability." Incorrect or redundant edges will cause the prediction error to increase, thus being penalized during training.

[0098] To avoid overly dense inferred graph structures, this embodiment imposes constraints on the average edge density of the potential graph structure, resulting in structural sparsity constraints, expressed as follows:

[0099] ,in, Represents a node With nodes edge strength, This represents the prior density. The sparsity constraint of the structure encourages the model to learn a "few but fine" structure, which helps to improve the interpretability and generalization of the structure and avoids the degenerate solution of "fully connected graph" due to over-connection.

[0100] Furthermore, this embodiment integrates the diffusion reconstruction loss, dynamic prediction error, and structural sparsity constraint to obtain the total loss, specifically expressed as:

[0101] .

[0102] in, To mitigate the damage caused by the reconstruction efforts, For dynamic prediction error, As a constraint on structural sparsity, This is a hyperparameter.

[0103] Finally, based on the total loss, the parameters of the diffusion model and the graph god regular differential equation are jointly backpropagated and updated, so that the network structure inference based on the diffusion model and the dynamic modeling based on the graph god regular differential equation are trained and optimized together under the same objective.

[0104] In each training iteration, the diffuse network structure inference module continuously adjusts the latent graph structure based on the diffuse reconstruction loss, enabling the structure to better serve time series reconstruction under noisy conditions. Simultaneously, the dynamics learning module evaluates whether the current structure can support high-precision continuous-time prediction through dynamics prediction loss. Structural sparsity constraints prevent the latent graph structure from becoming too dense, maintaining good interpretability. Through end-to-end backpropagation, the diffuse network structure inference module and the dynamics learning module are no longer two independent processes, but rather collaborate to optimize under the same goal: the latent graph structure provides reasonable topological priors for the dynamics, and the dynamics fitting effect, in turn, filters out latent graph structures that better conform to the system's laws. Figure 2 The document also illustrates the connections between modules and the flow of data in the process of "time series input → diffusion-based structure inference → latent graph structure generation → continuous-time prediction of graph neural network regular differential equations → joint loss optimization". Thus, this embodiment uses the inferred latent graph structure for continuous-time graph neural network dynamics modeling to achieve prediction at any time point; simultaneously, it uses a unified training objective to jointly optimize structure inference and dynamics prediction, and incorporates prior structural constraints to ensure reasonable structure and accurate prediction.

[0105] Based on the above embodiments, the present invention also provides a continuous-time dynamics prediction system that integrates diffusion models and graph-based frequent differential equations. This system is used to implement the steps in the above method embodiments, such as... Figure 3 As shown, the system includes: a diffusion-based network structure inference module 10, a dynamics learning module 20, and a joint training and optimization module 30. Specifically, the diffusion-based network structure inference module 10 is used to acquire multi-node time series, and under a noisy perturbation environment, to infer the network structure of the multi-node time series using a diffusion model to obtain the potential graph structure between nodes. The dynamics learning module 20 is used to perform continuous-time dynamics modeling using graph god regular differential equations under the constraints of the potential graph structure to predict the node state at any time point. The joint training and optimization module 30 is used to construct diffusion reconstruction loss, dynamics prediction error, and structural sparsity constraints, establish a total loss based on the diffusion reconstruction loss, dynamics prediction error, and structural sparsity constraints, and couple the network structure inference based on the diffusion model with the dynamics modeling based on graph god regular differential equations based on the total loss to achieve collaborative training and optimization.

[0106] The principles of each module in the fusion diffusion model and the continuous-time dynamics prediction system of the TuShen ordinary differential equation in this embodiment are the same as the execution principles of the steps in the above method embodiment, and will not be elaborated further here.

[0107] Based on the above embodiments, the present invention also provides a terminal, the principle block diagram of which can be as follows: Figure 4As shown. The terminal may include one or more processors 100 ( Figure 4 (Only one is shown in the image), memory 101, and computer program 102 stored in memory 101 and executable on one or more processors 100. For example, a continuous-time dynamics prediction program for fusion-diffusion models and Tushin frequent differential equations. When one or more processors 100 execute computer program 102, they can implement the various steps in the embodiment of the method for continuous-time dynamics prediction of fusion-diffusion models and Tushin frequent differential equations. Alternatively, when one or more processors 100 execute computer program 102, they can implement the functions of various modules / units in the embodiment of the system for continuous-time dynamics prediction of fusion-diffusion models and Tushin frequent differential equations, without limitation herein.

[0108] In one embodiment, the processor 100 may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor.

[0109] In one embodiment, memory 101 may be an internal storage unit of an electronic device, such as a hard drive or RAM. Memory 101 may also be an external storage device of the electronic device, such as a plug-in hard drive, Smart Media Card (SMC), Secure Digital Card (SD), or Flash Card. Furthermore, memory 101 may include both internal and external storage units. Memory 101 is used to store computer programs and other programs and data required by the terminal. Memory 101 can also be used to temporarily store data that has been output or will be output.

[0110] Those skilled in the art will understand that Figure 4 The block diagram shown is merely a partial structural diagram related to the present invention and does not constitute a limitation on the terminal to which the present invention is applied. A specific terminal may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0111] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided by this invention can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), direct memory bus RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0112] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A continuous-time dynamics prediction method that integrates a diffusion model and a graph-based frequent differential equation, characterized in that, The method includes: A multi-node time series is acquired, and under a noisy perturbation environment, the network structure of the multi-node time series is inferred through a diffusion model to obtain the potential graph structure between nodes. Under the constraints of the potential graph structure, continuous-time dynamics modeling is performed using graph god ordinary differential equations to predict the node state at any time point; Construct diffusion reconstruction loss, dynamic prediction error, and structural sparsity constraint; establish total loss based on diffusion reconstruction loss, dynamic prediction error, and structural sparsity constraint; and couple network structure inference based on diffusion model with dynamic modeling based on graph god ordinary differential equation based on total loss to achieve collaborative training optimization. A multi-node time series is acquired. Under a noisy perturbation environment, a diffusion model is used to infer the network structure of the multi-node time series, yielding the potential graph structure between nodes, including: Select the target node time series from the multi-node time series, and perform forward diffusion on the target node time series based on the diffusion model to gradually add noise; In each diffusion step, a condition matrix is ​​constructed, and the target node to be noisy and the other unnoisy nodes are input into the multi-scale temporal feature extraction network. The short-term local dynamics are extracted through the convolution branch and the long-term global dependencies are extracted through the self-attention branch. Based on the short-term local dynamics and the long-term global dependencies, the potential graph structure is obtained; Under the constraints of the underlying graph structure, continuous-time dynamics modeling is performed using graph god frequent differential equations to predict the node states at any time point, including: The time evolution of the system is described as a graphical ordinary differential equation; Using graph-based frequent differential equations, message passing and state derivative calculation between nodes are realized, and the node state at any time point is obtained. The diffusion reconstruction loss, dynamic prediction error, and structural sparsity constraints are constructed, including: In the process of inferring the network structure of multi-node time series using a diffusion model, the inverse diffusion network predicts the noise added to the target node in the forward diffusion step, and uses the mean square error to constrain the deviation between the predicted noise and the real noise, thus obtaining the diffusion reconstruction loss. In the process of continuous-time dynamic modeling using the TuShen ordinary differential equation, the TuShen ordinary differential equation is used to predict the trajectory at multiple future time points given the initial state and inference structure. The deviation between the predicted trajectory and the actual trajectory is constrained in the form of mean square error, and the dynamic prediction loss is obtained. By imposing constraints on the average edge density of the potential graph structure, structural sparsity constraints are obtained.

2. The continuous-time dynamics prediction method for the fusion diffusion model and the TuShen ordinary differential equation according to claim 1, characterized in that, Based on the short-term local dynamics and the long-term global dependencies, the potential graph structure is obtained, including: The short-term local dynamics and the long-term global dependencies are aligned and fused through a cross-scale interactive fusion module to obtain a fused representation; A differentiable structure sampling mechanism generates differentiable edge types for each pair of nodes. During the de-diffusion stage, the target node is progressively denoised and reconstructed under the current structure estimation conditions, and the potential structure is updated at each step. After multiple rounds of node iteration and multi-step diffusion, the potential graph structure is obtained.

3. The continuous-time dynamics prediction method for the fusion diffusion model and the TuShen ordinary differential equation according to claim 1, characterized in that, Using graph god frequent differential equations to realize message passing and state derivative calculation between nodes, the node state at any time point is obtained, including: The information propagation path and intensity are determined based on the potential graph structure; By integrating the graphical ordinary differential equation using a numerical ordinary differential equation solver, the nodal states at any time point can be obtained starting from a given initial state.

4. The continuous-time dynamics prediction method for the fusion diffusion model and the TuShen ordinary differential equation according to claim 1, characterized in that, A total loss is established based on diffusion reconstruction loss, dynamic prediction error, and structural sparsity constraints. Based on this total loss, network structure inference based on the diffusion model is coupled with dynamic modeling based on graph god ordinary differential equations to achieve collaborative training optimization, including: The diffusion reconstruction loss, dynamic prediction error, and structural sparsity constraint are integrated to obtain the total loss; Based on the total loss, the parameters of the diffusion model and the graph god regular differential equation are jointly backpropagated and updated, so that the network structure inference based on the diffusion model and the dynamic modeling based on the graph god regular differential equation are trained and optimized together under the same objective.

5. A continuous-time dynamics prediction system that integrates a diffusion model and a graph-based frequent differential equation, characterized in that, The system is used to implement the continuous-time dynamics prediction method of the fusion diffusion model and the TuShen ordinary differential equation as described in any one of claims 1-4, and the system comprises: The diffusion network structure inference module is used to acquire multi-node time series. Under noisy perturbation environment, the network structure of the multi-node time series is inferred through the diffusion model to obtain the potential graph structure between nodes. The dynamics learning module is used to perform continuous-time dynamics modeling using graph-based ordinary differential equations under the constraints of the potential graph structure, and to predict the node state at any time point. The joint training and optimization module is used to construct diffusion reconstruction loss, dynamic prediction error and structural sparsity constraint. Based on diffusion reconstruction loss, dynamic prediction error and structural sparsity constraint, a total loss is established. Based on the total loss, the network structure inference based on diffusion model and the dynamic modeling based on graph god ordinary differential equation are coupled to achieve collaborative training optimization.

6. A terminal, characterized in that, The terminal includes a memory, a processor, and a continuous-time dynamics prediction program for the fusion-diffusion model and the Tushen regular differential equation, stored in the memory and executable on the processor. When the processor executes the continuous-time dynamics prediction program for the fusion-diffusion model and the Tushen regular differential equation, it implements the steps of the continuous-time dynamics prediction method for the fusion-diffusion model and the Tushen regular differential equation as described in any one of claims 1-4.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a continuous-time dynamics prediction program for the fusion-diffusion model and the Tussin regular differential equation, wherein the continuous-time dynamics prediction program for the fusion-diffusion model and the Tussin regular differential equation implements the steps of the continuous-time dynamics prediction method for the fusion-diffusion model and the Tussin regular differential equation as described in any one of claims 1-4 on the computer-readable storage medium.

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