Physiological irregular time series prediction method based on graph neural differential equation

Abstract

This invention discloses a method for predicting irregular physiological time series based on graph-based frequent differential equations, belonging to the field of irregular time series prediction. The method includes the following steps: S1, collecting raw, unstructured physiological IMTS time series containing missing values ​​and preprocessing them; S2, transforming the preprocessed unstructured physiological IMTS time series into a structured sparse bipartite graph; S3, performing continuous-time evolution on the node and edge features in the structured sparse bipartite graph and solving it using numerical integration methods to obtain node embeddings and edge embeddings; S4, mapping the edge embeddings to predicted time series values; S5, calculating the contribution of each node and edge to the prediction results and generating a visual report. This method for predicting irregular physiological time series based on graph-based frequent differential equations avoids the biases of traditional interpolation, while also ensuring accurate modeling of cross-variable associations and continuous time series, meeting the efficiency and reliability requirements of real-time clinical applications.

Description

Technical Field

[0001] This invention relates to the field of irregular time series prediction technology, and in particular to a method for predicting physiological irregular time series based on graph-God's constant differential equation. Background Technology

[0002] Artificial intelligence-driven clinical decision support systems have become a core support for improving the accuracy of diagnosis and treatment and optimizing the timing of interventions. Their performance highly depends on the in-depth analysis of physiological signals such as electroencephalograms (EEGs), electrocardiograms (ECGs), blood pressure, blood oxygen saturation, and inflammatory markers. However, these clinical signals are affected by factors such as sensor noise, patient motion artifacts, asynchronous acquisition from multiple devices, and interference from diagnostic and treatment operations, generally exhibiting irregular sampling times and random missing observations, forming irregular sampled multivariate time series (IMTS) with missing values. Robust modeling and accurate prediction of IMTS are key prerequisites for capturing dynamic physiological states, achieving early warning of severe disease risks (such as sepsis), and predicting acute exacerbations of chronic diseases (such as COPD), among other core clinical needs. However, existing technologies still face the following critical issues that urgently need to be addressed in terms of practicality, efficiency, and reliability in adapting to clinical scenarios: First, most traditional time series forecasting methods employ a separate framework of "data preprocessing + model prediction." This requires converting IMTS (Intense Time Series) sequences into regular sequences through interpolation (such as mean imputation or linear interpolation) or resampling before inputting them into traditional models like recurrent neural networks (RNN / LSTM) for prediction. This approach not only introduces false information that does not reflect the actual physiological state, disrupting the original distribution characteristics of the data, but also, in scenarios with high missing rates or non-stationary missing data (such as concentrated missing data due to sudden diagnostic or treatment procedures), the cumulative preprocessing bias leads to a sharp decline in model robustness, making it difficult to meet the stringent requirements of clinical decision-making regarding data accuracy.

[0003] Secondly, while continuous-time modeling methods based on Neural ODEs can naturally adapt to irregular sampling characteristics, support prediction at any time point, and avoid the bias introduced in the preprocessing stage, they face significant engineering bottlenecks in high-dimensional multivariate clinical scenarios. On the one hand, the numerical integration process in high-dimensional feature spaces has poor stability and is prone to gradient vanishing or exploding. On the other hand, the backpropagation process relies on the adjoint method for gradient calculation, and the computational cost increases exponentially with the variable dimension, resulting in excessively high inference latency, which cannot meet the low-latency requirements of clinical scenarios such as real-time monitoring in ICUs and real-time alerts from wearable devices.

[0004] Furthermore, existing graph neural network (GNN) methods can effectively capture the potential dependencies between multi-channel physiological indicators (such as the synergistic changes in heart rate and blood pressure) by constructing variable correlation graphs, but they lack an effective coupling mechanism with continuous-time dynamics: these models mostly focus on static graph structure modeling, making it difficult to characterize the smooth evolution of physiological signals over time. This makes it difficult to balance the dual modeling requirements of cross-variable dependencies and continuous-time evolution, and thus cannot accurately reproduce the dynamic interaction characteristics of clinical physiological states.

[0005] Finally, clinical decision-making places a rigid demand on the interpretability of AI models—doctors need to clearly understand the core supporting evidence for the predicted results (such as a high risk of sepsis stemming from a high lactate level at a certain moment) in order to trust and adopt the model's recommendations. However, existing GNN interpretation methods based on Shapley values ​​or subgraph search either require traversing all feature subsets, leading to an exponential increase in computational costs, or rely excessively on manually designed domain prior knowledge, making generalization difficult. Neither approach can control computational costs while ensuring interpretation accuracy, making them difficult to deploy in real-time clinical prediction scenarios. This results in the model falling into a black box dilemma, hindering its practical application in high-risk clinical decision-making.

[0006] In summary, existing technologies have not yet formed a solution that can simultaneously meet the four core requirements of unbiased processing, efficient continuous-time modeling, cross-variable dependency capture, and real-time interpretability in clinical IMTS modeling. Summary of the Invention

[0007] The purpose of this invention is to provide a method for predicting physiological irregular time series based on graph-based frequent differential equations, thereby solving the above-mentioned technical problems.

[0008] To achieve the above objectives, this invention provides a method for predicting physiological irregularities in time series based on graph-God's regular differential equations, comprising the following steps: S1. Collect raw, unstructured physiological IMTS time series containing missing values ​​and preprocess the raw, unstructured physiological IMTS time series. S2. The preprocessed unstructured physiological IMTS time series is transformed into a structured sparse bipartite graph. The sparse bipartite graph includes nodes and edges connecting the nodes, and the nodes include time nodes and channel nodes. S3. The node and edge features in the structured sparse bipartite graph are continuously evolved using the constant differential equation of the God and solved by numerical integration to obtain the node embedding and edge embedding. S4. Map the edge embeddings to time series predicted values; S5. Based on the sparse bipartite graph and time series predictions, calculate the contribution of each node and edge to the prediction results and generate a visualization report.

[0009] Therefore, the physiological irregularity time series prediction method based on the graph-God regular differential equation, as described above, has the following beneficial effects: 1. Improved data authenticity and robustness: By directly performing structured modeling of irregularly sampled multivariate time series with missing values ​​through sparse bipartite graphs, the traditional imputation / resampling operations are abandoned, avoiding the introduction of false information and distortion of data distribution. It can still maintain excellent robustness in clinical scenarios with high missing rates and non-stationary missing values, which is consistent with the real data characteristics of physiological signals. 2. Modeling efficiency and stability optimization: A neural ordinary differential equation evolution mechanism with node and edge collaboration is constructed on a sparse bipartite graph. Combined with a numerical integration method with adaptive time step, the computational complexity and integral instability in high-dimensional multivariable scenarios are effectively reduced, significantly improving the efficiency of model training and inference, and adapting to the low-latency clinical needs such as ICU real-time monitoring and wearable device early warning. 3. Enhanced adaptability to prediction scenarios: By adopting a graph-to-sequence decoding method, it supports the prediction of physiological signals at any continuous time point and the batch output of multiple time points, breaking through the dependence of discrete time series models on sampling time and meeting the core clinical needs for continuous tracking of dynamic physiological states and early risk warning. 4. Enhanced Credibility of Clinical Decisions: By introducing a graph-level interpretability module with controllable computational overhead, the contribution of time nodes, channel nodes, and edge pairs to the prediction results is quantified through SHAP values, and natural language interpretation reports related to clinical information are generated. This solves the "black box" problem of AI models and provides a traceable and reliable basis for clinical decision-making.

[0010] In summary, this invention effectively improves the accuracy, efficiency, and interpretability of predicting irregular clinical time series, enhances the model's adaptability in high missing rate and cross-clinical scenarios, and meets the comprehensive requirements of AI-driven clinical decision support systems for accuracy, real-time performance, and reliability.

[0011] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0012] Figure 1 The flowchart shows the physiological irregularity time series prediction method based on the graph-sense regular differential equation of the present invention. Figure 2 This is a visual comparison chart of the evaluation indicators described in Example 1; Figure 3 This is a visualization comparison of the efficiency results described in Example 2; Figure 4 The figure shows the interpretability experiment results described in Example 3; Figure 5 This is the application flowchart for Example 4; Figure 6 This is the application flowchart for Example 5. Detailed Implementation

[0013] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the embodiments of the present invention and are not intended to limit the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of this application. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout.

[0014] It should be noted that the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion, such as a process, method, system, product, or server that includes a series of steps or units, not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such process, method, product, or device.

[0015] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0016] like Figure 1 As shown, the method for predicting physiological irregularities based on graph-based frequent differential equations includes the following steps: S1. Collect raw, unstructured physiological IMTS time series (irregular multivariate time series) containing missing values, and preprocess the raw, unstructured physiological IMTS time series. The original unstructured physiological IMTS time series described in step S1 is in the form of ,in, Indicates the first The timestamp of the next sample; Indicates the first The channel observations of the second sampling, and , Indicates the total number of channels; if a certain channel is in If there is no observation at a given time, then The corresponding position is a missing value; Preprocessing includes missing value interpolation, normalization, and time interval segmentation.

[0017] S2. The preprocessed unstructured physiological IMTS time series is transformed into a structured sparse bipartite graph. The sparse bipartite graph includes nodes and edges connecting the nodes, and the nodes include time nodes and channel nodes. The structured sparse bipartite graph described in step S2 ,in, Represents a set of nodes, and , Indicates a time point. , This indicates the sampling time of the physiological IMTS time series, and time nodes with missing values ​​are marked as query nodes. ; Indicates a channel node. , Monitoring indicators representing physiological IMTS time series (e.g.) Represents heart rate, (represents blood oxygen saturation), and each channel node also carries metadata such as channel type and signal unit; Denotes an edge, and when time The channel has valid observations. At the same time, construct the observation edge At this point, the edge features are initialized to The normalized value (normalization range is [0,1], eliminating differences in the dimensions of different physiological signals); when time When the channel has a missing value, construct a query edge. At this point, the edge features are initialized to the mean of the historical observations of that channel, and the number of edges is only consistent with the total number of valid observations and missing values, avoiding computational redundancy caused by fully connected graphs (sparseness can usually reach more than 80%, depending on the missing rate of IMTS).

[0018] S3. The node and edge features in the structured sparse bipartite graph are continuously evolved using the constant differential equation of the God and solved by numerical integration to obtain the node embedding and edge embedding. Step S3 specifically includes the following steps: S31. Initial embedding encoding of nodes and edges: Embedding encoding is performed on the time nodes, channel nodes and edges of the sparse bipartite graph to transform discrete features into high-dimensional vectors to adapt to the calculation of the neural ordinary differential equation. S32. Define continuous-time evolution equations: Construct NODE evolution equations for nodes and edges respectively to capture the dynamic interaction and feature change patterns of nodes and edges over time. S33. Numerical integration to solve the evolution results: The Runge-Kutta method is used to numerically integrate the evolution equation to obtain the node embedding and edge embedding at any time.

[0019] In step S31, for time nodes : Uses sinusoidal encoding to convert timestamps Mapped to a high-dimensional vector , Indicates the embedding dimension. The encoding formula is as follows: ; ; In the formula, and Representing time nodes The first in the initial embedding vector peacekeeping Dimensional element value; Indicates time node The initial embedding vector; Indicates the dimension of the embedding vector; For channel nodes One-hot encoding is used, mapped as ,in, Indicates channel node The initial embedding vector; For the edge The initial edge features are concatenated with the embeddings of the corresponding time nodes and channel nodes to obtain the following initial edge embeddings: ; In the formula, Representing an edge The initial embedding vector; This represents a vector concatenation operation; Representing an edge The initial eigenvalues; In step S32, the time node evolution equation is as follows: ; In the formula, This represents a multilayer perceptron for a node; Represents a multilayer perceptron Network parameters; Indicates time node At any moment Real-time embedding features; The time node evolution equation represents the embedding of time nodes over time. t The rate of change is determined by the current node state, timestamp, and model parameters. The evolution equations for channel nodes are as follows: ; In the formula, Indicates channel node At any moment Real-time embedding features; The edge evolution equation is as follows: ; In the formula, This represents a multilayer perceptron for edges; Represents a multilayer perceptron Network parameters; Representing an edge At any moment Real-time embedding features; The edge evolution equation incorporates the real-time states of the corresponding time nodes and channel nodes on the basis of the edge's own state, ensuring that the edge features can reflect the dynamic correlation between time and channel (such as the effect of heart rate changes over time on blood pressure signals).

[0020] In step S33, time node At any moment t Embedding features The expression is: ; In the formula, Indicates time node At the initial moment The embedding vector; Indicates time node In the integral variable Real-time embedding vector at each moment; Channel Node At any moment t Embedding features The expression is: ; In the formula, Indicates channel node At the initial moment The embedding vector; Indicates channel node In the integral variable Real-time embedding vector at each moment; side At any moment The embedding feature expression is: .

[0021] During the integration process in this embodiment, the adaptive time step mechanism of NODE (Neuro-Normal Differential Equations) dynamically adjusts the step size. If the current integration error exceeds the threshold (default) If ), then decrease (Minimum) (seconds) to ensure accuracy; if the error is less than the threshold, then increase... (Up to 1 second) to improve efficiency, ultimately reducing the number of calculation steps by 30%-50% compared to the fixed step size method.

[0022] S4. Map the edge embeddings to time series predicted values; Step S4 specifically includes the following steps: S41. Target Time Localization and Edge Matching: Predict the target time based on user input. (This can be an unsampled time point that does not exist in the original IMTS), matching the time nodes of the original unstructured physiological IMTS time series. In, with The two nearest moments , The corresponding edge-evolved embeddings , ;in, ; S42. Temporal interpolation of edge embedding: The target time is calculated using a linear interpolation method. Corresponding edge embedding : ; This interpolation operation utilizes the continuous evolution characteristics of NODE to ensure that the edge embedding at unsampled times can still reflect the smooth changes in the signal, avoiding prediction discontinuities caused by discrete sampling.

[0023] S43, Lightweight Decoding Mapping: Embedding edges at the target time step using a single-layer MLP. Mapped to the final physiological signal prediction value : ; In the formula, Indicates decoder operation; Represents the Sigmoid function; and All represent decoder parameters; S44, Denormalization Reduction: This involves performing a denormalization operation to restore the original state. Restore to the true physiological signal unit (such as heart rate in "beats / minute").

[0024] In this embodiment, if it is necessary to predict multiple consecutive moments (such as one point every 5 minutes in the next hour), steps S41-S44 are repeated to generate time series prediction results in batches and arrange them into a continuous prediction sequence in chronological order, which is then directly output to the clinical monitoring system.

[0025] S5. Based on the sparse bipartite graph and time series predictions, calculate the contribution of each node and edge to the prediction results and generate a visualization report.

[0026] Step S5 specifically includes the following steps: S51. Definition of Feature Set: A sparse bipartite graph... All time nodes, channel nodes, and edges are used as explanatory features (each feature corresponds to an element whose contribution is to be calculated, such as a node). ,side ), to obtain the feature set ; S52, SHAP value calculation: Based on the Shapley value principle of game theory, traversing feature subsets. Calculate the effect of each feature on the prediction result Marginal contribution: ; ; ; In the formula, , and Representing time nodes Channel nodes and edge The SHAP value; Factorial operation representing the number of elements in a set; , and They respectively represent the feature subsets Add time nodes Channel nodes and edge The predicted value after; Positive SHAP values ​​indicate that the feature promotes an increase in the prediction result (e.g., a high heart rate edge feature at a certain moment increases the "sepsis risk prediction value"), while negative SHAP values ​​indicate that the feature inhibits an increase in the prediction result; the feature's specific information (e.g., nodes) is also labeled. Corresponding to "6 hours after admission", (Corresponds to "heart rate -120 beats / minute").

[0027] S53. Key Feature Filtering: Sort by absolute SHAP value, filter nodes and edges corresponding to each set SHAP value from front to back (in this embodiment, select the nodes and edges corresponding to the first 5 SHAP values), and output a SHAP value bar chart visualization result. At the same time, generate a natural language interpretation report by associating it with clinical information. For example: The current sepsis risk prediction value is 0.72 (high risk). The main contributing factors are: heart rate signal 6 hours after admission (SHAP=0.28) and blood oxygen saturation signal 8 hours after admission (SHAP=-0.15). Among them, high heart rate significantly increases the risk, and low blood oxygen saturation slightly reduces the risk, so as to directly provide clinicians with decision-making reference.

[0028] The following experiments, consisting of algorithm performance verification and clinical application, verify the prediction accuracy, computational efficiency, interpretability, and clinical suitability of GODEFITi.

[0029] Table 1 Experimental Configuration

[0030] Prepare the following experimental dataset: PhysioNet dataset: Data source: 48-hour multivariate clinical time series of ICU patients, containing 41 physiological signals (such as heart rate, blood pressure, and blood oxygen saturation); Preprocessing: missing value interpolation, segmented by 1-hour intervals; Prediction task: predict the next 3 time steps based on the data from the first 36 hours.

[0031] MIMIC-III dataset: Data source: 48-hour detailed clinical records of ICU patients, containing 96 clinical variables; Preprocessing: split into 30-minute intervals to preserve fine temporal dynamics; Prediction task: predict the next 3 time steps based on the data from the first 36 hours.

[0032] USHCN Dataset: Data Source: Daily-scale climate data (temperature, precipitation, snowfall) from 1000+ meteorological stations in a certain country, selecting 4 years of observation data from 1114 stations; Preprocessing: Subsampling induces sparsity, retaining approximately 60 records per station to simulate the "sparse sampling, missing data" scenario in remote health monitoring; Prediction Task: Predict the next 3 time steps based on the data from the previous 3 years; Prepare the following application dataset: Remote COPD monitoring dataset: Data source: 90-day remote monitoring data of 200 home-based COPD patients, collecting two core indicators: blood oxygen saturation (SpO2) and respiratory rate (RR); Preprocessing: outlier removal (SpO2 < 80%, RR > 30 breaths / minute), Min-Max normalization, and 7:2:1 splitting rule were applied according to the MIMIC-III dataset, resulting in a training set of 140 cases, a validation set of 40 cases, and a test set of 20 cases, with a data missing rate of 25% and a sampling interval of 10-30 minutes (irregular).

[0033] ICU sepsis prediction dataset: Data source: 48-hour clinical records of 180 ICU sepsis patients, collecting 12 indicators in Table 1; Preprocessing: same as the MIMIC-III dataset process, finally obtaining 126 cases for training set, 36 cases for validation set, and 18 cases for test set, with a data missing rate of 18% and a sampling interval of 5-60 minutes (irregular).

[0034] The model training configuration is as follows: Optimizer: Adam optimizer; Hyperparameter tuning: 5-fold cross-validation (20% data validation, 10% data testing); Loss function: Mean Squared Error (MSE), used to balance prediction accuracy and signal smoothness; Based on the above conditions, the following specific verification is performed: Example 1: Basic performance verification objective: To verify the prediction accuracy and robustness of GODEFITi for irregularly sampled multivariate time series (IMTS) with missing values.

[0035] Table 2 Model Parameter Configuration

[0036] Implementation process: Step 1: Data Input and Preprocessing: Input the original IMTS data for each dataset (PhysioNet / MIMIC-III for 48-hour clinical signals, USHCN for 4-year climate data); and perform missing value interpolation, normalization, and time interval segmentation on the original IMTS data. Step 2: Construct a sparse bipartite graph using TSSBG; Node construction: Time nodes (divided by sampling time, such as MIMIC-III 48 hours → 96 30-minute nodes), channel nodes (such as MIMIC-III 96 clinical variables). Edge construction: If an observation exists, an observation edge is constructed (feature is the normalized observation value); if the observation is missing, a query edge is constructed (feature is the historical mean or interpolation).

[0037] Step 3: SBGODE continuous evolution; 3.1 Initial Embedding: Sine coding of time nodes and one-hot coding of channel nodes generate the initial embedding of nodes. ; initial edge embedding =Time node embedding + Channel node embedding + Edge features; 3.2 NODE Integral: Solve the node evolution equation and edge evolution equation, starting from the initial time step. Integrate to the target time (e.g., the first 36 hours of MIMIC-III) to obtain the final embedding , .

[0038] Step 4: SBGTS Decoding Prediction: Based on Edge Embedding Mapped to predicted values ​​via MLP decoder The data is then reconstructed into a time-series format (such as the signal values ​​of the subsequent three 30-minute nodes of MIMIC-III).

[0039] Step 5: Performance Evaluation: Set the evaluation metrics as mean squared error (MSE) and standard deviation (STD), and set up comparative experiments to verify (comparison models are GRU-ODE-Bayes, Neural Flows, LinODENet, and GraFiTi), and the mean squared error (MSE, the smaller the value, the higher the accuracy) on the three core datasets. Table 3 Comparative Experiment Results (Data in Table 3 are presented in the form of "mean deviation (standard deviation)")

[0040] As shown in Table 3 and Figure 2 As shown, GODEFITi (the present invention) consistently outperforms other models across all datasets, demonstrating significant performance improvements. Specifically, on the PhysioNet dataset, GODEFITi's MSE value is 0.275, approximately 3.8% lower than GraFiTi; on the MIMIC-III dataset, its MSE value is 0.356, a 10.5% improvement over GraFiTi; and on the USHCN dataset, GODEFITi's MSE value is 0.253, a 7.6% improvement over the second-best performing model. This demonstrates the robustness and reliability of GODEFITi used in this invention across multiple independent experiments.

[0041] The above results have the following clinical implications: Taking the MIMIC-III dataset (containing 96 ICU clinical indicators) as an example, a 10.5% reduction in MSE means a significant reduction in the prediction error for critical physiological events such as sudden drop in blood pressure and abnormal increase in heart rate. Experiments show that the advance prediction time for sepsis risk warning in this invention is 1.2 hours longer than that of existing models, which provides a critical window for clinical intervention (existing models provide warnings on average 3.8 hours earlier, while this invention can provide warnings 5 ​​hours earlier), meeting the core needs of early detection and early intervention in intensive care.

[0042] Example 2: Inference Efficiency Verification Objective: To verify the computational efficiency (inference time) of GODEFITi.

[0043] Experimental preparation: Comparison models: GRU-ODE-Bayes, NeuralFlows, LinODENet, GraFiTi; Test dataset: Same as Example 1.

[0044] Implementation process: Test the single-sample inference time (total time from input to output prediction result) of each model on different datasets.

[0045] Verification results: such as Figure 3As shown, GODEFITi achieves the shortest inference time on all datasets, with the most significant advantage in the USHCN (long sequence high sparsity) scenario. The core reason is that the efficiency advantage of this invention stems from two major technical features: First, the Sparse Bipartite Graph Construction Module (TSSBG) transforms IMTS into a sparse graph structure, reducing the number of edges by more than 80% compared to a fully connected graph, thus reducing the computational basis; Second, SBGODE adopts NODE's adaptive time step mechanism, which dynamically adjusts the step size based on the numerical integration error, reducing redundant computation.

[0046] The above results have the following clinical implications: In real-time monitoring scenarios in intensive care units (ICUs), the prediction results of patients' physiological signals need to be updated every 5 minutes. This invention has a single-sample inference time of ≤186ms, supports parallel prediction of ≥50 patients (server-side), or achieves "second-level response" on wearable devices (such as dynamic electrocardiogram monitors) (lightweight alternative inference time ≤100ms), solving the prediction delay problem caused by the low efficiency of existing models and avoiding missing the best intervention opportunity.

[0047] Example 3: Interpretability verification objective: Verify GODEFITi's ability to quantify the feature contribution of prediction results.

[0048] Test data: IMTS (12 physiological indicators) of ICU sepsis patients; Implementation process: 1. Calculate the SHAP values ​​of time nodes, channel nodes, and edges; 2. Sort by the absolute value of SHAP values ​​and filter key features; 3. Generate feature contribution bar charts and natural language interpretation reports.

[0049] The verification results are as follows Figure 4 As shown, the key features of this invention can be accurately traced: the C-reactive protein observation edge and the 42-hour time node after admission are the core contributing features for sepsis risk prediction; doctors without technical background can quickly clarify the prediction logic through the SHAP value (e.g., SHAP=0.35 when C-reactive protein > 80 mg / L).

[0050] Example 4: Remote Clinical Monitoring Scenario (COPD Acute Exacerbation Prediction) Objective: To achieve early warning of acute exacerbations in patients with chronic obstructive pulmonary disease (COPD) at home.

[0051] Test data: Remote monitoring data of 200 COPD patients over 90 days (blood oxygen saturation, respiratory rate, missing rate 25%, sampling interval 10-30 minutes); like Figure 5As shown, the implementation process is as follows: 1. Data input: IMTS data collected by wearable devices (sampling interval 10-30 minutes, missing rate approximately 25%, such as blood oxygen saturation 90%-98%, respiratory rate 15-28 breaths / minute); 2. Model adaptation: using a simplified version of TSSBG (retaining only 2 core channel nodes) and SBGODE lightweight integration (reducing step complexity) to adapt to the computing power of terminal devices; 3. Early warning output: predicting the risk of acute exacerbation within the next 8 hours through SBGTS, triggering an early warning if the risk value ≥0.7; 4. Interpretation generation: SBGSHAP identifies the moment of sudden increase in respiratory rate and the edge of decrease in blood oxygen saturation as key features to generate a clinical interpretation report.

[0052] Application Results: (1) Excellent early warning timeliness: It can predict COPD acute exacerbation events 8 hours in advance. Compared with the traditional remote monitoring mode of "only collecting data and no active early warning", it greatly extends the intervention window period, enabling patients to adjust their medication or seek medical treatment in a timely manner and avoid further deterioration of the condition; (2) Strong adaptability to terminal devices: Through lightweight configuration (simplifying the graph structure complexity of the time series to sparse bipartite graph module (TSSBG) and optimizing the numerical integration steps of the sparse bipartite graph divine constant differential equation module (SBGODE)), it can be directly deployed on terminal devices such as smart bracelets and dynamic monitoring instruments. The power consumption is controlled within 5mW, which meets the low power consumption requirements of portable devices. At the same time, because the device is easy to operate and does not require frequent manual intervention, the patient compliance score is 4.1 points (out of 5), which is significantly higher than the 2.8 points of the traditional monitoring program. (3) Significant clinical and economic value: Clinical application data shows that COPD patients who use the present invention for remote monitoring have 40.3% fewer emergency hospitalizations due to acute exacerbations than the traditional monitoring group. This reduces the patient's pain and medical burden, and also reduces the medical insurance fund's expenditure on hospitalization, achieving a double improvement in clinical and economic benefits.

[0053] Example 5: Intensive Care Scenario (Sepsis Risk Prediction) Objective: To achieve early risk warning and intervention guidance for sepsis in the ICU.

[0054] Test data: 48-hour IMTS (12 physiological indicators, missing rate 18%) of 180 ICU sepsis patients. like Figure 6As shown, the implementation process is as follows: 1. Data input: IMTS data collected by ICU bedside monitoring equipment (sampling interval 5-60 minutes, missing rate approximately 18%, such as C-reactive protein 0-100 mg / L, lactate 0.5-5 mmol / L); 2. Model operation: TSSBG constructs a sparse bipartite graph with 12 channel nodes, SBGODE captures the continuous upward trend of inflammatory markers (C-reactive protein, lactate), and SBGTS predicts the risk of sepsis in the next 5 hours; 3. Intervention guidance: SBGSHAP outputs key feature SHAP values, such as C-reactive protein > 80 mg / L (SHAP=0.35), lactate > 3.5 mmol / L (SHAP=0.22), to clarify the priority intervention direction.

[0055] Application Results: (1) Significantly Extended Warning Window: Sepsis risk prediction results can be output 5 hours earlier. Compared with the average warning time of 3.8 hours of the existing mainstream prediction models, the warning window is extended by 31.6%, providing sufficient time for clinicians to initiate early intervention measures such as fluid resuscitation and antibiotic use, effectively reducing the risk of sepsis progression; (2) Highly Targeted Intervention Guidance: Based on the SHAP-based graph interpretation module (SBGSHAP), key predictive indicators for early sepsis can be quantitatively identified—among which, when C-reactive protein > 80 mg / L, the contribution to risk prediction (SHAP value) reaches 0.35, and the contribution (SHAP value) when lactate > 3.5 mmol / L reaches 0.22. The two are the strongest risk-related indicators, which help doctors prioritize inflammation control and tissue hypoxia improvement, avoid wasting diagnostic and treatment resources on non-critical indicators, and improve treatment efficiency; (3) Patient prognosis is significantly improved: simulated clinical intervention experiment verification, based on the early warning results and interpretation basis of the present invention, the treatment plan is formulated, the average intensive care days of sepsis patients are shortened by 1.5 days, the exposure time of patients in the ICU is reduced, and the risk of adverse outcomes caused by long-term bed rest and cross-infection is indirectly reduced, and the success rate of treatment is improved.

[0056] The above verification shows that the present invention has the following beneficial effects: (I) Economic Effects: Reducing Medical Costs and Improving Resource Utilization Efficiency: 1. Reducing Medical Expenses: Taking ICU applications as an example, this invention reduces the number of days patients require intensive care by providing early warnings. Experimental simulations show that the average ICU stay per patient can be shortened by 1.5 days. Based on the average daily cost of 8,000 yuan for ICUs in China, a single patient can save 12,000 yuan in medical expenses. If this invention is promoted in ICUs of tertiary hospitals nationwide, the annual savings in medical expenses could reach several billion yuan. 2. Reducing Equipment Costs: The lightweight alternative solution of this invention is compatible with existing wearable devices (such as smartwatches and dynamic electrocardiographs), eliminating the need to purchase additional dedicated monitoring equipment and reducing equipment investment for primary healthcare institutions and patients. Compared with dedicated medical monitoring equipment (average price > 5,000 yuan), this invention can reduce equipment costs by more than 90%.

[0057] (II) Social Impact: Improving Accessibility to Medical Services and Safeguarding Public Health: 1. Supporting Primary Healthcare: In primary hospitals in remote areas, this invention can enable primary care physicians to obtain IMTS prediction capabilities at the same level as tertiary hospitals through a "terminal device data collection + cloud model prediction" model, solving the problem of a lack of professional monitoring equipment and technical personnel at the primary level. Experiments show that the "accuracy rate of high-risk patient referral" in primary hospitals that have deployed this invention has increased by 35%, avoiding missed diagnoses and over-referrals. 2. Responding to Public Health Events: In the prevention and control of large-scale infectious diseases (such as influenza), this invention can achieve early warning at the community level through IMTS monitoring of signals such as fever and blood oxygen. For example, in a simulated virus transmission scenario, this invention can identify the gathering of people with abnormal respiratory function in the community 48 hours in advance, buying time for response and helping to detect and control public health events early.

[0058] In summary, through innovative technical solutions, this invention achieves significant results in terms of technical performance, clinical application, and economic and social aspects, providing a practical solution for AI-driven clinical decision support systems, and possesses extremely high promotional value and application prospects.

[0059] 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 preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for predicting physiological irregularities in time series based on graph-based frequent differential equations, characterized by: Includes the following steps: S1. Collect raw, unstructured physiological IMTS time series containing missing values ​​and preprocess the raw, unstructured physiological IMTS time series. S2. The preprocessed unstructured physiological IMTS time series is transformed into a structured sparse bipartite graph. The sparse bipartite graph includes nodes and edges connecting the nodes, and the nodes include time nodes and channel nodes. S3. The node and edge features in the structured sparse bipartite graph are continuously evolved using the constant differential equation of the God and solved by numerical integration to obtain the node embedding and edge embedding. S4. Map the edge embeddings to time series predicted values; S5. Based on the sparse bipartite graph and time series predictions, calculate the contribution of each node and edge to the prediction results and generate a visualization report. Step S4 specifically includes the following steps: S41. Target Time Localization and Edge Matching: Predict the target time based on user input. Matching time nodes of the original unstructured physiological IMTS time series In, with The two nearest moments , The corresponding edge-evolved embeddings , ;in, ; S42. Temporal interpolation of edge embedding: The target time is calculated using a linear interpolation method. Corresponding edge embedding : ； S43, Lightweight Decoding Mapping: Embedding edges at the target time step using a single-layer MLP. Mapped to the final physiological signal prediction value : ； In the formula, Indicates decoder operation; Represents the Sigmoid function; and All represent decoder parameters; S44, Denormalization Reduction: This involves performing a denormalization operation to restore the original state. It is restored to the true physiological signal unit.

2. The physiological irregularity time series prediction method based on graph-based frequent differential equations according to claim 1, characterized in that: The original unstructured physiological IMTS time series described in step S1 is in the form of ,in, Indicates the first The timestamp of the next sample; Indicates the first The channel observations of the second sampling, and , Indicates the total number of channels; Preprocessing includes missing value interpolation, normalization, and time interval segmentation.

3. The physiological irregularity time series prediction method based on graph-based frequent differential equations according to claim 1, characterized in that: The structured sparse bipartite graph described in step S2 ,in, Represents a set of nodes, and , Indicates a time point. , This indicates the sampling time of the physiological IMTS time series, and time nodes with missing values ​​are marked as query nodes. ; Indicates a channel node. , Monitoring indicators representing physiological IMTS time series; Denotes an edge, and when time The channel has valid observations. At the same time, construct the observation edge At this point, the edge features are initialized to The normalized value; when time When the channel has a missing value, construct a query edge. At this point, the edge features are initialized to the mean of the historical observations of that channel.

4. The physiological irregularity time series prediction method based on graph-based frequent differential equations according to claim 3, characterized in that: Step S3 specifically includes the following steps: S31. Initial embedding encoding of nodes and edges: Embedding encoding is performed on the time nodes, channel nodes and edges of the sparse bipartite graph to transform discrete features into high-dimensional vectors to adapt to the calculation of the neural ordinary differential equation. S32. Define continuous-time evolution equations: Construct NODE evolution equations for nodes and edges respectively to capture the dynamic interaction and feature change patterns of nodes and edges over time. S33. Numerical integration to solve the evolution results: The Runge-Kutta method is used to numerically integrate the evolution equation to obtain the node embedding and edge embedding at any time.

5. The physiological irregularity time series prediction method based on graph-based frequent differential equations according to claim 4, characterized in that: In step S31, for time nodes : Uses sinusoidal encoding to convert timestamps Mapped to a high-dimensional vector , The embedding dimension is represented by the following encoding formula: ； ； In the formula, and Representing time nodes The first in the initial embedding vector peacekeeping Dimensional element value; Indicates time node The initial embedding vector; Indicates the dimension of the embedding vector; For channel nodes One-hot encoding is used, mapped as ,in, Indicates channel node The initial embedding vector; For the edge The initial edge features are concatenated with the embeddings of the corresponding time nodes and channel nodes to obtain the following initial edge embeddings: ； In the formula, Representing an edge The initial embedding vector; This represents a vector concatenation operation; Representing an edge The initial eigenvalues; In step S32, the time node evolution equation is as follows: ； In the formula, This represents a multilayer perceptron for a node; Represents a multilayer perceptron Network parameters; Indicates time node At any moment Real-time embedding features; The evolution equations for channel nodes are as follows: ； In the formula, Indicates channel node At any moment Real-time embedding features; The edge evolution equation is as follows: ； In the formula, This represents a multilayer perceptron for edges; Represents a multilayer perceptron Network parameters; Representing an edge At any moment Real-time embedding features; In step S33, time node At any moment t Embedding features The expression is: ； In the formula, Indicates time node At the initial moment The embedding vector; Indicates time node In the integral variable Real-time embedding vector at each moment; Channel Node At any moment t Embedding features The expression is: ； In the formula, Indicates channel node At the initial moment The embedding vector; Indicates channel node In the integral variable Real-time embedding vector at each moment; side At any moment The embedding feature expression is: 。 6. The method for predicting physiological irregularities in time series based on graph-based frequent differential equations according to claim 5, characterized in that: Step S5 specifically includes the following steps: S51. Definition of Feature Set: A sparse bipartite graph... All time nodes, channel nodes, and edges are used as explanatory features to obtain the feature set. ; S52, SHAP value calculation: Based on the Shapley value principle of game theory, traversing feature subsets. Calculate the effect of each feature on the prediction result Marginal contribution: ； ； ； In the formula, , and Representing time nodes Channel nodes and edge The SHAP value; Factorial operation representing the number of elements in a set; , and They represent the feature subsets respectively Add time nodes Channel nodes and edge The predicted value after; S53. Key Feature Filtering: Sort by absolute SHAP value, filter nodes and edges corresponding to each set SHAP value from front to back, and output SHAP value bar chart visualization results. At the same time, associate clinical information to generate a natural language interpretation report.

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