System modeling method, device and equipment based on multi-time scale characteristics, and medium
By employing a system modeling approach using deep collaborative networks and neural differential equations, we can identify and model slow and fast variables in complex systems, solving the problem of unknown dynamic equations and achieving accurate prediction of system states.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- TSINGHUA UNIVERSITY
- Filing Date
- 2025-04-18
- Publication Date
- 2026-07-07
AI Technical Summary
Existing technologies struggle to effectively identify and model slow and fast variables when the dynamic equations of complex systems are unknown, leading to inaccurate system state predictions.
By employing a system modeling method based on multi-timescale characteristics, deep collaborative networks and neural differential equations are used to identify and model slow and fast variables, including acquiring sample trajectory data, analyzing feature representations, determining initial values, and training until the system meets preset conditions.
It achieves accurate prediction of system state when the dynamic equations are unknown, and can accurately predict the values at future times after inputting parameters.
Smart Images
Figure CN120561839B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of data processing technology, and in particular to a system modeling method, apparatus, device and medium based on multi-timescale characteristics. Background Technology
[0002] Complex systems are prevalent in fields such as geophysics, neuroscience, and molecular biology. The states of these systems typically evolve in high-dimensional space, but their long-term evolution is usually determined by only a few slow variables. The interaction of these slow variables with other fast variables determines the dynamic behavior of the system across multiple time scales and is key to analyzing and predicting the behavior of complex systems; such complex systems are also called multi-timescale dynamical systems. For example, in climate systems, slow variables can be used to predict long-term climate change, while fast variables describe short-term weather fluctuations; in neural systems, slow variables can reflect long-term neural activity patterns, while fast variables capture instantaneous neuronal responses. However, for most real-world complex systems, their dynamic equations are unknown. How to effectively identify and model slow and fast variables, and thus achieve accurate prediction of the system's state, remains an open problem.
[0003] The challenge in studying multi-timescale dynamical systems lies in the fact that the dynamic equations of many complex real-world systems are unknown, and they involve multiple coupled timescales. Traditional manual analysis-based methods struggle to handle these complexities. Multi-timescale dynamical models, such as the Van Der Pol oscillator, the FitzHugh-Nagumo model, and the Hodgkin-Huxley model, typically rely on known dynamic equations. These models describe the coupling relationships between slow and fast variables in explicit equation form. However, for most real-world systems, the dynamic equations are difficult to obtain directly. Even with the introduction of tools such as singular perturbation theory and trajectory optimization in subsequent research, traditional methods still exhibit significant limitations when dealing with the complex nonlinear dynamics of real-world systems. These methods rely on known system dynamic descriptions or require simplification and assumptions about the system's intrinsic mechanisms, thus limiting their application in unknown or highly complex systems. Therefore, for complex systems with significant multi-timescale characteristics (multi-timescale dynamical systems), there is an urgent need for a solution that can effectively identify and model slow and fast variables and accurately predict the system state even when the dynamic equations are unknown. Summary of the Invention
[0004] This application provides a system modeling method, apparatus, device, and medium based on multi-timescale characteristics. The method of this application can effectively identify and model slow and fast variables when the dynamic equations of a complex system (target system) with significant multi-timescale characteristics are unknown. This enables the modeled target system to accurately predict the system state. For example, after inputting a certain parameter, the value of that parameter at a certain time in the future can be accurately predicted, thereby effectively solving the problems in related technologies.
[0005] This application provides a system modeling method based on multi-timescale characteristics, including the following steps:
[0006] The target system to be modeled and the target parameters in the target system are determined. The target system is used to predict the state values of the target parameters at any time. The target system is a climate system with unknown dynamic equations, and the target parameters are climate-related parameters.
[0007] Obtain sample trajectory data of the target parameter changing over time;
[0008] The sample trajectory data is analyzed to obtain the feature representation of the target parameter at multiple different time scales;
[0009] Based on multiple feature representations, the initial values of the slow variable and the fast variable corresponding to the target parameter are determined. The slow variable represents the change trend of the target parameter on a scale greater than or equal to a preset time period, and the fast variable represents the change trend of the target parameter on a scale less than the preset time period.
[0010] The target system is trained based on the initial values of the slow variables, the initial values of the fast variables, the neural ordinary differential equations corresponding to the slow variables, and the neural ordinary differential equations corresponding to the fast variables, until the target system meets the preset conditions.
[0011] According to the system modeling method based on multi-timescale characteristics provided in this application, determining the initial values of the slow variables and fast variables corresponding to the target parameters based on multiple feature representations includes:
[0012] Determine the intrinsic dimension value corresponding to each of the aforementioned features, and obtain the trajectory of the change of the intrinsic dimension value over time;
[0013] Based on the change trajectory, a feature representation containing only slow variables is determined, and the time scale corresponding to the feature representation containing only slow variables is the preset duration.
[0014] Decode the feature representation containing only slow variables to obtain the value of the slow variables at the initial time. The value of the slow variables at the initial time is the initial value of the slow variables, and the initial time is determined according to the time scale corresponding to the feature representation containing only slow variables.
[0015] The difference between the value corresponding to the initial time in the sample trajectory data and the initial value of the slow variable is determined as the initial value of the fast variable.
[0016] According to the system modeling method based on multi-timescale characteristics provided in this application, the target system includes a deep cooperative network. The deep cooperative network is used to fuse the values of the slow variable and the fast variable at different times. The training of the target system based on the initial values of the slow variable, the initial values of the fast variable, the neural ordinary differential equation corresponding to the slow variable, and the neural ordinary differential equation corresponding to the fast variable includes:
[0017] The slow variable is analyzed based on its initial value and the corresponding neural ordinary differential equation to obtain the predicted value of the slow variable at a preset time.
[0018] Based on the initial value of the fast variable, the corresponding neural ordinary differential equation, the deep collaborative network, and the initial value of the slow variable, the fast variable is analyzed to obtain the predicted value of the fast variable at the preset time.
[0019] Based on the predicted values corresponding to the slow variable and the predicted values corresponding to the fast variable, the predicted state value of the target parameter at the preset time is determined;
[0020] The target system is trained using a first loss function based on the actual state value and the predicted state value of the target parameters at the preset time.
[0021] Wherein, the first loss function is The The predicted state value of the target parameter at the preset time. The target parameter represents the actual state value at the preset time.
[0022] According to the system modeling method based on multi-timescale characteristics provided in this application, the target system further includes a first encoder. The step of training the target system using a first loss function based on the true state value and the predicted state value of the target parameters at a preset time includes:
[0023] A second loss function is determined based on the first loss function, and the target system is trained with the goal of minimizing the value of the second loss function. The formula is as follows (1):
[0024] (1)
[0025] in, , Denotes the first loss function. Indicates the preset time. This represents the predicted value of the slow variable at the preset time. This represents the predicted state value of the target parameter at the preset time. This refers to the first encoder. Indicates feature splicing, This represents a feature representation that contains only slow variables among multiple feature representations. , These are the weighting coefficients.
[0026] According to the system modeling method based on multi-timescale characteristics provided in this application, the neural ordinary differential equation corresponding to the slow variable is as follows (2), and the neural ordinary differential equation corresponding to the fast variable is as follows (3):
[0027] (2)
[0028] (3)
[0029] in, Indicates the preset time. Indicates the initial time. Indicates the slow variable at time t. The predicted value, Indicates the slow variable at time t. The true value, Indicates the slow variable at time ( The predicted value of ) Represents the fast variable at time t. The predicted value, Represents the fast variable at time t. The true value, Indicates the fast variable at time ( The predicted value of ) Indicates the slow variable at time ( The predicted value of ) This represents the deep neural network corresponding to the slow variable. This represents the deep neural network corresponding to the fast variable. express The integration time step used and The ratio of the integration time step used.
[0030] According to the system modeling method based on multi-timescale characteristics provided in this application, the target system includes a preset neural network, which includes a second encoder. The analysis of the sample trajectory data to obtain the feature representation of the target parameters at multiple different timescales includes:
[0031] The sample trajectory data is input into the second encoder of the preset neural network to obtain the feature representation of the target parameter at multiple different time scales. The preset neural network is pre-trained using the third loss function shown in the following formula (4):
[0032] (4)
[0033] in, This represents the third loss function. This indicates taking the average value. Representing time scale The corresponding encoder, Forward prediction loss represents the encoder's loss based on the current state value. Output Predicted state value at time 1 and The true state value at any given moment The error, The backward prediction loss is represented by the encoder based on... State value at time Output Predicted state value at time 1 and The true state value at any given moment The error, Hyperparameters that balance the importance of forward prediction loss and backward prediction loss It is an auxiliary network used to perform forward prediction. It is an auxiliary network used to perform backward prediction. "" indicates function composition.
[0034] According to the system modeling method based on multi-timescale characteristics provided in this application, after the target system meets preset conditions, the method further includes:
[0035] The target parameters and target time are input into the target system to obtain the predicted value of the target parameters at the target time.
[0036] This application also provides a system modeling device based on multi-timescale characteristics, including the following modules:
[0037] The first determining module is used to determine the target system to be modeled and the target parameters in the target system. The target system is used to predict the state values of the target parameters at any time. The target system is a climate system with unknown dynamic equations, and the target parameters are climate-related parameters.
[0038] The acquisition module is used to acquire sample trajectory data of the target parameter changing over time;
[0039] The analysis module analyzes the sample trajectory data to obtain the feature representation of the target parameter at multiple different time scales;
[0040] The second determining module is used to determine the initial values of the slow variable and the fast variable corresponding to the target parameter based on the multiple feature representations. The slow variable represents the change trend of the target parameter on a scale greater than or equal to a preset time period, and the fast variable represents the change trend of the target parameter on a scale less than the preset time period.
[0041] The training module is used to train the target system based on the initial values of the slow variables, the initial values of the fast variables, the neural ordinary differential equations corresponding to the slow variables, and the neural ordinary differential equations corresponding to the fast variables, until the target system meets preset conditions.
[0042] This application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement a system modeling method based on multi-timescale characteristics as described above.
[0043] This application also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements a system modeling method based on multi-timescale characteristics as described above.
[0044] This application also provides a computer program product, including a computer program that, when executed by a processor, implements a system modeling method based on multi-timescale characteristics as described above.
[0045] The method of this application first determines the target system to be modeled and the target parameters as inputs to the target system. The target system is used to predict the state value of the target parameters at any time. Next, sample trajectory data of the target parameters changing over time is acquired. The sample trajectory data is analyzed to obtain the feature representations of the target parameters at multiple different time scales. Then, based on the multiple feature representations, the initial values of the slow variables and fast variables corresponding to the target parameters are determined. The slow variables represent the changing trend of the target parameters at scales greater than or equal to a preset time length, and the fast variables represent the changing trend of the target parameters at scales less than a preset time length. Finally, the target system is trained based on the initial values of the slow variables, the initial values of the fast variables, the neural network constant differential equations corresponding to the slow variables, and the neural network constant differential equations corresponding to the fast variables, until the target system meets preset conditions. This method effectively identifies and models slow and fast variables in complex systems (target systems) with significant multi-time-scale characteristics when the dynamic equations are unknown. This allows the modeled target system to accurately predict the system state; for example, after inputting a parameter, the value of that parameter at a future time can be accurately predicted, thus effectively solving problems in related technologies. Attached Figure Description
[0046] To more clearly illustrate the technical solutions in this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0047] Figure 1 This is a flowchart illustrating a system modeling method based on multi-timescale characteristics according to an embodiment of this application;
[0048] Figure 2 This is a schematic diagram illustrating a plurality of feature representations according to an embodiment of this application;
[0049] Figure 3 This is a schematic diagram illustrating the modeling process of a target system according to an embodiment of this application;
[0050] Figure 4 This is a flowchart illustrating the modeling process of a target system according to an embodiment of this application;
[0051] Figure 5 This is a structural block diagram of a system modeling device based on multi-timescale characteristics, as shown in one embodiment of this application;
[0052] Figure 6 This is a schematic diagram of the physical structure of an electronic device according to an embodiment of this application. Detailed Implementation
[0053] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0054] Figure 1 This is a flowchart illustrating a system modeling method based on multi-timescale characteristics, as shown in an embodiment of this application. (Refer to...) Figure 1 The system modeling method based on multi-timescale characteristics in this application may include the following steps:
[0055] Step 101: Determine the target system to be modeled and the target parameters in the target system. The target system is used to predict the state values of the target parameters at any time. The target system is a climate system with unknown dynamic equations, and the target parameters are climate-related parameters.
[0056] In this application, a system can be considered a multi-timescale dynamical system if it possesses the following characteristics: unknown dynamic equations, unclear coupling relationships between slow and fast variables, system states (the changes in parameters over time) typically evolve in a high-dimensional space, the long-term evolution of the system state is usually determined only by a few slow variables, and the interaction between slow variables and other fast variables determines the dynamic behavior of the system at multiple time scales. The target system in this application is a multi-timescale dynamical system. For example, the target system could be a climate system, an urban traffic flow system, a FHN (FitzHugh-Nagumo) system in neuroscience, or an NTL9 protein folding system in molecular biology. Regardless of the application field, the methods described in this application can be used to predict the parameters. The target system can include multiple parameters. Taking a climate system as an example, parameters affecting climate prediction could include sea surface temperature, sea level height, soil moisture, greenhouse gas concentration, etc., all of which can serve as parameters within the climate system. When it is necessary to predict the sea surface temperature at a future time, the target parameter is sea surface temperature. When it is necessary to predict the sea level height at a future point in time, the target parameter is the sea level height.
[0057] In this application, system status is used express, This represents a parameter in the target system, such as sea surface temperature.
[0058] Step 102: Obtain sample trajectory data of target parameters changing over time.
[0059] In this application, modeling the target system mainly refers to identifying and modeling the slow and fast variables of the target parameters in the target system, so that the modeled target system can predict the future state of the target parameters. To model the target system, it is necessary to obtain trajectory data of the target parameters changing over time as sample trajectory data. For example, when the target parameter is sea surface temperature, sample trajectory data of sea surface temperature changing over time can be obtained; similarly, when the target parameter is sea level height, sample trajectory data of sea level height changing over time can be obtained.
[0060] After obtaining the sample trajectory data, it can be preprocessed, such as by removing missing or duplicate values, to improve the quality of the data. The specific preprocessing steps can be configured according to actual needs.
[0061] Step 103: Analyze the sample trajectory data to obtain the feature representation of the target parameters at multiple different time scales.
[0062] Specifically, the target system includes a preset neural network, which includes a second encoder. Step 103 may include:
[0063] The sample trajectory data is input into the second encoder of a pre-defined neural network to obtain feature representations of the target parameters at multiple different time scales. The pre-defined neural network is pre-programmed with a third loss function as shown in the following formula. What was obtained from training:
[0064]
[0065] in, This represents the third loss function. This indicates taking the average value. Representing time scale The corresponding encoder is the second encoder. Forward prediction loss represents the encoder's loss based on the current state value. Output Predicted state value at time 1 and The true state value at any given moment The error, The backward prediction loss is represented by the encoder based on... State value at time Output Predicted state value at time 1 and The true state value at any given moment The error, Hyperparameters that balance the importance of forward prediction loss and backward prediction loss It is an auxiliary network used to perform forward prediction. It is an auxiliary network used to perform backward prediction. " indicates that the function conforms to the specified condition.
[0066] In this application, the modeling process of the target system is divided into two stages: a dynamic analysis stage and a prediction stage. In the dynamic analysis stage, a multi-timescale structure of the target system's dynamics is extracted using a self-supervised learning method. The theory underlying the dynamic analysis stage is that if a representation vector can accurately predict the future or past state of the system at a given timescale, then it should include all variables slower than that timescale. The goal of the dynamic analysis stage is to find a suitable timescale. This achieves the separation of slow and fast variables, and uses self-supervised learning to extract the feature representations corresponding to the slow variables.
[0067] In this application, given sample trajectory data of the target parameters, inputting this sample trajectory data into a preset neural network can yield feature representations of the target parameters at multiple different time scales. .
[0068] The preset neural network includes a pre-trained second encoder. After inputting sample trajectory data, the preset neural network uses an encoder. Obtain feature representations of the target parameters at multiple different time scales. .
[0069] Taking the climate system as an example, assuming that the parameters in the climate system include four parameters: sea surface temperature, sea level height, soil moisture, and greenhouse gas concentration. If the target parameter is sea surface temperature, the sample trajectory data corresponding to the sea surface temperature is input into the encoder. Next, if the time scale... include , ... , Therefore, for each time scale, a corresponding encoder is required. Obtain the corresponding feature representation That is, through the encoder Obtain the characteristic representation corresponding to sea surface temperature via encoder Obtain the characteristic representation corresponding to sea surface temperature via encoder Obtain the characteristic representation corresponding to sea surface temperature This continues until the feature representations corresponding to each time scale are obtained.
[0070] For example, if the time scale =10s, so firstly, the sample trajectory data is sampled at 10s intervals to generate a sparse time series. For example, the sampled data would correspond to ocean temperatures at 0s, 10s, 20s, ... 100s. Then, the encoder... Each sampled state point is mapped to a low-dimensional latent vector. For example, the ocean temperatures corresponding to 0s, 10s, 20s, ..., 100s are uniformly mapped to a low-dimensional latent vector as a feature representation. For example, if the time scale =20s, so firstly, the sample trajectory data is sampled at 20s intervals to generate a sparse time series. For example, the sampled data would correspond to ocean temperatures at 0s, 20s, 40s...100s. Then, the encoder... Each sampled state point is mapped to a low-dimensional latent vector. For example, the ocean temperatures corresponding to 0s, 20s, 40s...100s are uniformly mapped to a low-dimensional latent vector as a diagnostic representation. .
[0071] Similarly, if the target parameter is sea level height, the sample trajectory data corresponding to the sea level height is input into the encoder. This also allows us to obtain characteristic representations of sea level height at multiple different time scales.
[0072] In this application, the network parameters in the pre-defined neural network are optimized based on the mutual prediction signals of the system state at different time intervals. As an asynchronous mutual information prediction task, this application simplifies the backward prediction task to focus only on the effective information in the system state.
[0073] The target loss function in the pre-defined neural network middle, The loss corresponding to the forward prediction represents the encoder output. Through auxiliary network Predicting future states The error. The loss corresponding to backward prediction is represented by the future state. Through auxiliary network Reverse calculation of the current representation The error. Indicates that the encoder is applied first. Processing input Then input the results into the auxiliary network. .
[0074] exist In the middle, only calculation and The error, rather than the calculation and The error is due to the fact that this application only focuses on the valid information in the system state during backward prediction, while System status Valid information.
[0075] To ensure the compactness of the feature representation, this application employs an adaptive embedding dimension search method. This method is a data-driven technique designed to automatically determine the optimal embedding dimension based on system dynamics, ensuring the compactness of the feature representation. The compactness. This application analyzes different feature representations... By considering the dimensional changes, we can find the minimum representation dimension of the slow variable.
[0076] Specifically, this application uses feature representations at multiple different time scales. Perform intrinsic dimension estimation, calculate its complexity on low-dimensional manifolds, and plot the intrinsic dimension as a function of the manifold. The change curve of the feature representation can be used to obtain the intrinsic dimension of the feature representation over time. A changing function is called a dynamic ID. When Increase to At this time, the ID tends to stabilize. The corresponding intrinsic dimension is the smallest representation dimension of the slow variable, and The optimal time scale corresponds to the slow variable. Therefore, the dynamic ID function is used to describe the target system from a dynamic perspective, finding a suitable time scale to generate feature representations that only include the slow variable. The output of the pre-defined neural network can include the optimal time scale and the corresponding feature representation.
[0077] Specifically, the target parameter is sea surface temperature, and the time scale includes... , ... , For example. For , ... , Each of them Obtain the previously obtained feature representation , , , The intrinsic dimensions were estimated separately, and the results were obtained. One intrinsic dimension estimate. Then, with... Plot a dynamic ID curve with the intrinsic dimension estimate (ID) on the y-axis and the x-axis on the y-axis. Analyzing the dynamic ID curve reveals that when... Increase to When the ID curve stabilizes (e.g., the ID change is less than the threshold), then... Corresponding representation The process includes only slow variables, such as... Figure 2 As shown. Figure 2 This is a schematic diagram illustrating a plurality of feature representations in one embodiment of this application.
[0078] Step 104: Based on multiple feature representations, determine the initial values of the slow variable and the fast variable corresponding to the target parameter. The slow variable represents the trend of change of the target parameter on a scale greater than or equal to a preset time period, and the fast variable represents the trend of change of the target parameter on a scale less than a preset time period.
[0079] Specifically, step 104 may include:
[0080] Step 1041: Determine the intrinsic dimension value corresponding to each feature representation, and obtain the trajectory of the intrinsic dimension value change over time.
[0081] The trajectory of the intrinsic dimension value over time is the dynamic ID curve mentioned earlier.
[0082] Step 1042: Determine the feature representation containing only slow variables based on the change trajectory. The time scale corresponding to the feature representation containing only slow variables is a preset duration. The initial time is determined based on the time scale corresponding to the feature representation containing only slow variables.
[0083] Following the previous example, in the dynamic ID curve, when Increase to At this point, the ID curve tends to stabilize. Corresponding feature representation Includes only slow variables, i.e. The most suitable time scale for feature representations containing only slow variables. For the preset duration, the initial time It can be based on the most suitable time scale Sure.
[0084] In this application, the sample trajectory data is actually a superposition of the trajectories corresponding to the slow variable and the trajectories corresponding to the fast variable. For example, in the sample trajectory data, time... The corresponding value is 1, and the slow variable is at time 1. The corresponding value is 0.9, so the fast variable at time... The corresponding value should be 0.1.
[0085] Step 1043: Decode the feature representation containing only slow variables to obtain the value of the slow variables at the initial time. The value of the slow variables at the initial time is the initial value of the slow variables.
[0086] Step 1044: Determine the initial value of the fast variable as the difference between the initial value of the sample trajectory data corresponding to the initial time and the initial value of the slow variable.
[0087] Figure 3 This is a schematic diagram illustrating the modeling process of a target system according to an embodiment of this application. Figure 3 In the modeling process shown, time 0-time After the sample trajectory data between points is input into a preset neural network, the preset neural network obtains the most suitable time scale and feature representation containing only slow variables corresponding to the target parameters through the encoder. Then, after intervals from time 0 at this most suitable time scale, the following is obtained: ,time This can be the initial time for making predictions.
[0088] The pre-defined neural network also includes a decoder. The feature representation containing only the slow variable is input into this decoder for decoding, allowing the slow variable to be obtained at the initial time step. value Sample trajectory data at time The value and The difference is the value of the fast variable at the initial time. value .
[0089] Step 105: Train the target system based on the initial values of the slow variables, the initial values of the fast variables, the neural ordinary differential equations corresponding to the slow variables, and the neural ordinary differential equations corresponding to the fast variables, until the target system meets the preset conditions.
[0090] In this application, the target system includes a deep cooperative network, which is used to fuse the values of slow variables and fast variables at different time points. Accordingly, step 105 may include:
[0091] Step 1051: Analyze the slow variable based on its initial value and the corresponding neuronormal differential equation to obtain the predicted value of the slow variable at the preset time.
[0092] The neural ordinary differential equation corresponding to the slow variable is as follows:
[0093]
[0094] in, Indicates the preset time. Indicates the initial time. Indicates the slow variable at time t. The predicted value, Indicates the slow variable at time t. The true value, Indicates the slow variable at time ( The predicted value of ) This represents the deep neural network corresponding to the slow variable.
[0095] Step 1052: Based on the initial value of the fast variable, the corresponding neural ordinary differential equation, the deep collaborative network, and the initial value of the slow variable, analyze the fast variable to obtain the predicted value of the fast variable at the preset time.
[0096] The corresponding ordinary differential equations for the fast variables are as follows:
[0097]
[0098] in, Represents the fast variable at time t. The predicted value, Represents the fast variable at time t. The true value, Indicates the fast variable at time ( The predicted value of ) Indicates the slow variable at time ( The predicted value of ) This represents the deep neural network corresponding to the fast variable. express The integration time step used and The ratio of the integration time step used.
[0099] Step 1053: Determine the predicted state value of the target parameter at the preset time based on the predicted values of the slow variable and the fast variable.
[0100] In this application, the predicted state value of the target parameter at a preset time is the sum of the predicted values of the slow variable and the fast variable at the preset time.
[0101] Step 1054: Train the target system using the first loss function based on the actual and predicted state values of the target parameters at preset times;
[0102] Wherein, the first loss function is , The predicted state value of the target parameter at a preset time. The target parameter represents the actual state value at a preset time. For the target parameter at time The predicted state value, For the target parameter in The actual state value.
[0103] In this application, the target system also includes a first encoder. Accordingly, step 1054 may include:
[0104] A second loss function is determined based on the first loss function, and the target system is trained with the goal of minimizing the value of the second loss function. The second loss function... The formula is as follows:
[0105]
[0106] in, , Denotes the first loss function. This represents the predicted value of the slow variable at a preset time. This represents the predicted state value of the target parameter at a preset time. Indicates the first encoder, Indicates feature splicing, This represents a feature representation that contains only slow variables among multiple feature representations. , These are the weighting coefficients.
[0107] Step 105 corresponds to the prediction stage in the modeling process of the target system in this application. The prediction stage of this application will be described in detail below.
[0108] First, the principle of multi-timescale dynamics used in this application is as follows: for complex systems with multi-timescale characteristics, there exists a pair of mappings. and This makes the system state It can be decomposed into slow variables and fast variables And reconstruct the system state through these variables, that is and The dynamics of slow and fast variables can be expressed in the following form:
[0109]
[0110]
[0111] in, The time-scale difference factor. It is a small parameter that describes the difference in time scale between slow and fast variables. Representing slow variables The evolution rate is much slower than that of fast variables. The smaller the time scale, the more significant the separation. The drift term function represents the deterministic evolutionary trend of the slow variable. The coefficient of the diffusion term represents the intensity of random disturbances in the slow variable. Function and All elements are . and It is an independent standard Brownian motion.
[0112] In this application, neural differential equations are a tool for modeling the dynamics of complex systems using deep learning. They combine the numerical modeling capabilities of traditional Ordinary Differential Equations (ODEs) with the nonlinear expressive power of deep neural networks to describe the interactions between slow and fast variables in complex systems. Specifically, the neural differential equations used in this application consist of two parts: 1) Differential equations for slow variables: used to describe the dynamics of slow variables, in the form of: ,in 1) A deep neural network used to approximate the evolution of slow variables; 2) Differential equations for fast variables: used to describe the dynamics of fast variables, in the form of: ,in It is also a deep neural network that captures the rapid changes in fast variables.
[0113] The encoder in the target system of this application includes and The decoder includes and Among them, the most suitable time scale obtained in the dynamic analysis phase. Corresponding encoder The parameters in the encoder are used in the prediction phase. The initialization parameters in the file. The initial extraction of slow variable information is performed in D dimensions. Will The initially extracted D-dimensional slow variables are compressed into dimension. and These are the corresponding decoders, used to map the encoder's output back to the encoder's input dimension. In this application, the decoder used in the preset neural network is... .
[0114] Reference Figure 3 In slow dynamics, the value of the slow variable at the initial moment... First, through the encoder and right Encode, where, In This represents latent spatial feature concatenation, which involves merging the outputs of two encoders along their dimensions to obtain... Next, Input slow variable The dynamic equation right Obtain the slow variable At any moment Predicted value Next, Input Decoder and The slow variables are decoded sequentially. System state prediction values .in, For the deep neural network mentioned above .
[0115] The above and Figure 3 The transformation process between integral expressions in the text is as follows:
[0116] make ,Right now ,when hour, ,when hour, .Will Substitution ,get ,remember (Scaling by time scale) (Establishing sign consistency) then the integral equation becomes .
[0117] In this application, slow variables are... The part corresponding to the modeling of the constant differential equation (ODE) of God. Figure 3 Slow ODE in the context of fast variables The part corresponding to the modeling of the constant differential equation (ODE) of God. Figure 3 The fast ODE in the middle.
[0118] Fast variables in this application The dynamic equation ,and Figure 3 The transformation process between integral expressions in the equation is as follows: Let ,Right now ,when hour, ,when hour, .Will Substitution Then it becomes ,Right now .
[0119] In this application, slow ODE and fast ODE are modeled through a cooperative network. This is implemented to fuse information from slow and fast variables at different times, thereby capturing their interactions.
[0120] According to Haken's slave principle, fast variables can be explicitly represented as functions of slow variables, thus simplifying the dynamic modeling of the system. To achieve this principle, fast ODEs need to be expressed as functions of fast variables. and slow variables As input, slow ODEs only require slow variables. Furthermore, the evolution rate of slow variables is much slower than that of fast variables, thus allowing for coarser time steps. Integrating is performed, while fast ODE uses a finer time step. The ratio is To fuse coarse-grained slow variable information with fine-grained fast variable information, this application proposes an improved attention mechanism called the "slow-fast attention mechanism." This mechanism is used in cooperative networks to combine the values of slow and fast variables at different time points, thereby ensuring accurate modeling and prediction of system dynamics.
[0121] Reference Figure 3 In the fast ODE, firstly... and Input collaborative network ,get ,Will Substitution ,get Next, and Input collaborative network , get new Then the new Substitution ,get Next, and Input collaborative network , get new Then the new Substitution ,get Similarly, through collaborative networks By fusing fast and slow variables, the time step is ultimately obtained. Predicted values of fast variables .
[0122] Finally, the time System state prediction values of slow variables With time System state prediction values of fast variables Add them together to get the time. The final system state prediction value.
[0123] To enable the proposed deep collaborative network to effectively model complex systems across multiple time scales, the modeling of the entire target system employs a phased, joint optimization process. This ensures effective dimensionality reduction of the system state, accurate separation of slow and fast variables, and precise prediction of long-term changes in the system state. The modeling process includes:
[0124] In the dynamics analysis phase, a self-supervised learning method is used to perform an encoder task based on the mutual prediction of system states at different time intervals. Pre-training is necessary. During this process, the target system is trained according to the self-supervised loss function. Optimization is performed to ensure a reasonable separation of slow and fast variables in the system and to obtain feature representations of the target parameters at multiple different time scales.
[0125] Next, in the prediction phase, the parameters obtained from the dynamics analysis phase are used to jointly optimize the entire deep cooperative network. Decomposition mapping. (via encoder) and Implementation) and inverse mapping (via decoder) and In the implementation, the network parameters are optimized using a reconstruction loss function to ensure accurate decomposition of slow and fast variables from the original system state. Reconstruction Loss Function Decoder required and Slow variables are extracted to approximate the original system state as closely as possible, ensuring information consistency between slow and fast variables, thereby preserving the dynamic characteristics of the system to the greatest extent and reconstructing the loss function. Specifically:
[0126]
[0127] in, This represents the predicted value of the slow variable at a preset time. This represents the predicted value of the target parameter at a preset time.
[0128] After initial optimization, all parameters in the target system, including slow variable ODE, fast variable ODE, and cooperative network, are optimized by minimizing the prediction error of the system state. The parameters in the table. The loss function at this point. for ,in, Represents the target parameter at future time. Predicted value Compared with actual value The error. At this point, the loss function... It includes error measures for both long-term and short-term predictions of system state to ensure accurate state predictions across different time scales.
[0129] Finally, the loss function The objective is to minimize the value of , and the gradient descent optimization algorithm is used to update the parameters of each network to obtain the final target system, which meets the preset conditions (e.g., The target system whose value is less than a certain threshold. and It can be set according to actual needs.
[0130] Figure 4 This is a flowchart illustrating the modeling process of a target system according to an embodiment of this application. (Refer to...) Figure 4 The modeling process of this application includes the following steps: 1) Dynamics analysis stage. A self-supervised learning method is adopted, based on the mutual prediction task of system states at different time intervals. Based on the sample trajectory data of the input target parameters, feature representations of the target parameters at multiple different time scales are extracted. Time scale analysis and slow variable dimension analysis are performed on multiple feature representations (see previous text for details) to determine the most suitable time scale for separating the slow and fast variables of the target parameters and the minimum representation dimension of the slow variables. 2) Prediction stage. In this stage, a physics-inspired neural network model is used to model the dynamics of the slow and fast variables. By constructing neural ordinary differential equations for the slow and fast variables, and using a fast-slow attention mechanism to fuse the information of the fast and slow variables, the dynamics model of the target system is achieved.
[0131] In conjunction with the above embodiments, in one implementation, after the target system meets preset conditions, the method of this application may further include:
[0132] By inputting the target parameters and target time into the target system, the predicted values of the target parameters at the target time are obtained.
[0133] After obtaining the modeled target system, the target system can be used to predict the value of the target parameter at a future time (target time). For example, by modeling the climate system based on historical ocean temperature trajectory data from October 1, 2010 to March 1, 2025, the climate system can be used to predict the ocean temperature value at a future time after March 1, 2025.
[0134] In summary, the method of this application first determines the target system to be modeled and the target parameters as inputs to the target system. The target system is used to predict the state value of the target parameters at any given time. Next, sample trajectory data of the target parameters changing over time is acquired. The sample trajectory data is analyzed to obtain the feature representations of the target parameters at multiple different time scales. Then, based on these feature representations, the initial values of the slow and fast variables corresponding to the target parameters are determined. The slow variables represent the changing trend of the target parameters at scales greater than or equal to a preset time duration, and the fast variables represent the changing trend of the target parameters at scales less than a preset time duration. Finally, the target system is trained based on the initial values of the slow and fast variables, the corresponding neural frequent differential equations of the slow and fast variables, and the corresponding neural frequent differential equations of the fast variables, until the target system meets preset conditions. This method effectively identifies and models slow and fast variables in complex systems (target systems) with significant multi-time-scale characteristics when the dynamic equations are unknown. This allows the modeled target system to accurately predict the system state; for example, after inputting a parameter, the value of that parameter at a future time can be accurately predicted, thus effectively solving problems in related technologies.
[0135] The system modeling apparatus based on multi-timescale characteristics provided in this application is described below. The system modeling apparatus based on multi-timescale characteristics described below and the system modeling method based on multi-timescale characteristics described above can be referred to in correspondence.
[0136] Figure 5 This is a structural block diagram of a system modeling device based on multi-timescale characteristics, as shown in an embodiment of this application. (Refer to...) Figure 5 The system modeling apparatus 500 of this application may include:
[0137] The first determining module 501 is used to determine the target system to be modeled and the target parameters in the target system, wherein the target system is used to predict the state value of the target parameters at any time.
[0138] The acquisition module 502 is used to acquire sample trajectory data of the target parameter changing over time;
[0139] Analysis module 503 analyzes the sample trajectory data to obtain the feature representation of the target parameter at multiple different time scales;
[0140] The second determining module 504 is used to determine the initial values of the slow variable and the fast variable corresponding to the target parameter based on the multiple feature representations, wherein the slow variable represents the change trend of the target parameter on a scale greater than or equal to a preset time period, and the fast variable represents the change trend of the target parameter on a scale less than the preset time period.
[0141] The training module 505 is used to train the target system based on the initial values of the slow variables, the initial values of the fast variables, the neural ordinary differential equations corresponding to the slow variables, and the neural ordinary differential equations corresponding to the fast variables, until the target system meets preset conditions.
[0142] According to the system modeling apparatus 500 based on multi-timescale characteristics provided in this application, the second determining module 504 includes:
[0143] The first determining submodule is used to determine the intrinsic dimension value corresponding to each of the feature representations, and to obtain the trajectory of the change of the intrinsic dimension value over time.
[0144] The second determining submodule is used to determine a feature representation containing only slow variables based on the change trajectory, wherein the time scale corresponding to the feature representation containing only slow variables is the preset duration.
[0145] The decoding submodule is used to decode the feature representation containing only slow variables to obtain the value of the slow variables at the initial time. The value of the slow variables at the initial time is the initial value of the slow variables, and the initial time is determined according to the time scale corresponding to the feature representation containing only slow variables.
[0146] The third determining submodule is used to determine the difference between the value corresponding to the initial time in the sample trajectory data and the initial value of the slow variable as the initial value of the fast variable.
[0147] According to the system modeling apparatus 500 based on multi-timescale characteristics provided in this application, the target system includes a deep collaborative network, which is used to fuse the values of the slow variable and the fast variable at different times. The training module 505 includes:
[0148] The first analysis submodule is used to analyze the slow variable based on the initial value of the slow variable and the corresponding neural ordinary differential equation to obtain the predicted value of the slow variable at a preset time.
[0149] The second analysis submodule is used to analyze the fast variable based on the initial value of the fast variable, the corresponding neural ordinary differential equation of the fast variable, the deep collaborative network, and the initial value of the slow variable, to obtain the predicted value of the fast variable at the preset time.
[0150] The fourth determining submodule is used to determine the predicted state value of the target parameter at the preset time based on the predicted value corresponding to the slow variable and the predicted value corresponding to the fast variable.
[0151] The first training submodule is used to train the target system using a first loss function based on the actual state value and the predicted state value of the target parameters at the preset time.
[0152] Wherein, the first loss function is The The predicted state value of the target parameter at the preset time. The target parameter represents the actual state value at the preset time.
[0153] According to the system modeling apparatus 500 based on multi-timescale characteristics provided in this application, the target system further includes a first encoder, and the first training submodule includes:
[0154] The second training submodule is used to determine a second loss function based on the first loss function, and to train the target system with the objective of minimizing the value of the second loss function. The second loss function... The formula is as follows (1):
[0155] (1)
[0156] in, , Denotes the first loss function. Indicates the preset time. This represents the predicted value of the slow variable at the preset time. This represents the predicted state value of the target parameter at the preset time. This refers to the first encoder. Indicates feature splicing, This represents a feature representation that contains only slow variables among multiple feature representations. , These are the weighting coefficients.
[0157] According to the system modeling device 500 based on multi-timescale characteristics provided in this application, the neural ordinary differential equation corresponding to the slow variable is as follows: (2), and the neural ordinary differential equation corresponding to the fast variable is as follows: (3).
[0158] (2)
[0159] (3)
[0160] in, Indicates the preset time. Indicates the initial time. Indicates the slow variable at time t. The predicted value, Indicates the slow variable at time t. The true value, Indicates the slow variable at time ( The predicted value of ) Represents the fast variable at time t. The predicted value, Represents the fast variable at time t. The true value, Indicates the fast variable at time ( The predicted value of ) Indicates the slow variable at time ( The predicted value of ) This represents the deep neural network corresponding to the slow variable. This represents the deep neural network corresponding to the fast variable. express The integration time step used and The ratio of the integration time step used.
[0161] According to the system modeling device 500 based on multi-timescale characteristics provided in this application, the target system includes a preset neural network, the preset neural network includes a second encoder, and the analysis module 503 includes:
[0162] The input submodule is used to input the sample trajectory data into the second encoder of the preset neural network to obtain the feature representation of the target parameter at multiple different time scales. The preset neural network is pre-trained using the third loss function shown in the following formula (4):
[0163] (4)
[0164] in, This represents the third loss function. This indicates taking the average value. Representing time scale The corresponding encoder, Forward prediction loss represents the encoder's loss based on the current state value. Output Predicted state value at time 1 and The true state value at any given moment The error, The backward prediction loss is represented by the encoder based on... State value at time Output Predicted state value at time 1 and The true state value at any given moment The error, Hyperparameters that balance the importance of forward prediction loss and backward prediction loss It is an auxiliary network used to perform forward prediction. It is an auxiliary network used to perform backward prediction. "" indicates function composition.
[0165] According to the system modeling apparatus 500 based on multi-timescale characteristics provided in this application, the apparatus 500 further includes:
[0166] The input module is used to input the target parameters and the target time into the target system to obtain the predicted value of the target parameters at the target time.
[0167] Figure 6 This is a schematic diagram of the physical structure of an electronic device according to an embodiment of this application, as shown below. Figure 6 As shown, the electronic device may include: a processor 610, a communications interface 620, a memory 630, and a communication bus 640, wherein the processor 610, the communications interface 620, and the memory 630 communicate with each other via the communication bus 640. The processor 610 can call logical instructions in the memory 630 to execute a system modeling method based on multi-timescale characteristics, the method including:
[0168] The target system to be modeled and the target parameters in the target system are determined. The target system is used to predict the state values of the target parameters at any time. The target system is a climate system with unknown dynamic equations, and the target parameters are climate-related parameters.
[0169] Obtain sample trajectory data of the target parameter changing over time;
[0170] The sample trajectory data is analyzed to obtain the feature representation of the target parameter at multiple different time scales;
[0171] Based on multiple feature representations, the initial values of the slow variable and the fast variable corresponding to the target parameter are determined. The slow variable represents the change trend of the target parameter on a scale greater than or equal to a preset time period, and the fast variable represents the change trend of the target parameter on a scale less than the preset time period.
[0172] The target system is trained based on the initial values of the slow variables, the initial values of the fast variables, the neural ordinary differential equations corresponding to the slow variables, and the neural ordinary differential equations corresponding to the fast variables, until the target system meets the preset conditions.
[0173] Furthermore, the logical instructions in the aforementioned memory 630 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.
[0174] On the other hand, this application also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer is able to execute the system modeling method based on multi-timescale characteristics provided by the above methods, the method including:
[0175] Determine the target system to be modeled and the target parameters in the target system, wherein the target system is used to predict the state values of the target parameters at any time;
[0176] Obtain sample trajectory data of the target parameter changing over time;
[0177] The sample trajectory data is analyzed to obtain the feature representation of the target parameter at multiple different time scales;
[0178] Based on multiple feature representations, the initial values of the slow variable and the fast variable corresponding to the target parameter are determined. The slow variable represents the change trend of the target parameter on a scale greater than or equal to a preset time period, and the fast variable represents the change trend of the target parameter on a scale less than the preset time period.
[0179] The target system is trained based on the initial values of the slow variables, the initial values of the fast variables, the neural ordinary differential equations corresponding to the slow variables, and the neural ordinary differential equations corresponding to the fast variables, until the target system meets the preset conditions.
[0180] Furthermore, this application also provides a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, is implemented to perform the system modeling methods based on multi-timescale characteristics provided by the methods described above, the method comprising:
[0181] Determine the target system to be modeled and the target parameters in the target system, wherein the target system is used to predict the state values of the target parameters at any time;
[0182] Obtain sample trajectory data of the target parameter changing over time;
[0183] The sample trajectory data is analyzed to obtain the feature representation of the target parameter at multiple different time scales;
[0184] Based on multiple feature representations, the initial values of the slow variable and the fast variable corresponding to the target parameter are determined. The slow variable represents the change trend of the target parameter on a scale greater than or equal to a preset time period, and the fast variable represents the change trend of the target parameter on a scale less than the preset time period.
[0185] The target system is trained based on the initial values of the slow variables, the initial values of the fast variables, the neural ordinary differential equations corresponding to the slow variables, and the neural ordinary differential equations corresponding to the fast variables, until the target system meets the preset conditions.
[0186] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.
[0187] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.
[0188] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application 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. Such 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 this application.
Claims
1. A system modeling method based on multi-timescale characteristics, characterized in that, include: The target system to be modeled and the target parameters in the target system are determined. The target system is used to predict the state values of the target parameters at any time. The target system is a climate system with unknown dynamic equations. The target parameters are climate-related parameters, including sea surface temperature, sea level height, soil moisture and greenhouse gas concentration. The target system includes a deep cooperative network. Obtain sample trajectory data of the target parameter changing over time; The sample trajectory data is analyzed to obtain the feature representation of the target parameter at multiple different time scales; Based on multiple feature representations, the initial values of the slow variable and the fast variable corresponding to the target parameter are determined. The slow variable represents the change trend of the target parameter on a scale greater than or equal to a preset time period, and the fast variable represents the change trend of the target parameter on a scale less than the preset time period. The deep collaborative network is used to fuse the values of the slow variable and the fast variable at different times. The target system is trained based on the initial values of the slow variables, the initial values of the fast variables, the neural ordinary differential equations corresponding to the slow variables, and the neural ordinary differential equations corresponding to the fast variables, until the target system meets preset conditions, including: The slow variable is analyzed based on its initial value and the corresponding neural ordinary differential equation to obtain the predicted value of the slow variable at a preset time. Based on the initial value of the fast variable, the corresponding neural ordinary differential equation, the deep collaborative network, and the initial value of the slow variable, the fast variable is analyzed to obtain the predicted value of the fast variable at the preset time. Based on the predicted values corresponding to the slow variable and the predicted values corresponding to the fast variable, the predicted state value of the target parameter at the preset time is determined; The target system is trained using a first loss function based on the actual state value and the predicted state value of the target parameters at the preset time. Wherein, the first loss function is , The predicted state value of the target parameter at the preset time. The target parameter represents the actual state value at the preset time. For the target parameter at time The predicted state value, For the target parameter at time The actual state value.
2. The system modeling method according to claim 1, characterized in that, The step of determining the initial values of the slow variable and the fast variable corresponding to the target parameter based on multiple feature representations includes: Determine the intrinsic dimension value corresponding to each of the aforementioned features, and obtain the trajectory of the change of the intrinsic dimension value over time; Based on the change trajectory, a feature representation containing only slow variables is determined, and the time scale corresponding to the feature representation containing only slow variables is the preset duration. Decode the feature representation containing only slow variables to obtain the value of the slow variables at the initial time. The value of the slow variables at the initial time is the initial value of the slow variables, and the initial time is determined according to the time scale corresponding to the feature representation containing only slow variables. The difference between the value corresponding to the initial time in the sample trajectory data and the initial value of the slow variable is determined as the initial value of the fast variable.
3. The system modeling method according to claim 2, characterized in that, The target system further includes a first encoder, wherein training the target system using a first loss function based on the true state value and the predicted state value of the target parameters at a preset time includes: A second loss function is determined based on the first loss function, and the target system is trained with the goal of minimizing the value of the second loss function. The formula is as follows (1): （1） in, , Denotes the first loss function. Indicates the preset time. This represents the predicted value of the slow variable at the preset time. This represents the predicted state value of the target parameter at the preset time. This refers to the first encoder. Indicates feature splicing, This represents a feature representation that contains only slow variables among multiple feature representations. , These are the weighting coefficients.
4. The system modeling method according to any one of claims 1-3, characterized in that, The neural constant differential equation corresponding to the slow variable is as follows: (2) The neural constant differential equation corresponding to the fast variable is as follows: (3) （2） （3） in, Indicates the preset time. Indicates the initial time. Indicates the slow variable at time t. The predicted value, Indicates the slow variable at time t. The true value, Indicates the slow variable at time ( The predicted value of ) Represents the fast variable at time t. The predicted value, Represents the fast variable at time t. The true value, Indicates the fast variable at time ( The predicted value of ) Indicates the slow variable at time ( The predicted value of ) This represents the deep neural network corresponding to the slow variable. This represents the deep neural network corresponding to the fast variable. express The integration time step used and The ratio of the integration time step used.
5. The system modeling method according to claim 1, characterized in that, The target system includes a preset neural network, which includes a second encoder. The analysis of the sample trajectory data to obtain feature representations of the target parameters at multiple different time scales includes: The sample trajectory data is input into the second encoder of the preset neural network to obtain the feature representation of the target parameter at multiple different time scales. The preset neural network is pre-trained using the third loss function shown in the following formula (4): （4） in, This represents the third loss function. This indicates taking the average value. Representing time scale The corresponding encoder, Forward prediction loss represents the encoder's loss based on the current state value. Output Predicted state value at time 1 and The true state value at any given moment The error, The backward prediction loss is represented by the encoder based on... State value at time Output Predicted state value at time 1 and The true state value at any given moment The error, Hyperparameters that balance the importance of forward prediction loss and backward prediction loss It is an auxiliary network used to perform forward prediction. It is an auxiliary network used to perform backward prediction. "" indicates function composition.
6. The system modeling method according to claim 1, characterized in that, After the target system meets the preset conditions, the method further includes: The target parameters and target time are input into the target system to obtain the predicted value of the target parameters at the target time.
7. A system modeling device based on multi-timescale characteristics, characterized in that, include: The first determining module is used to determine the target system to be modeled and the target parameters in the target system. The target system is used to predict the state values of the target parameters at any time. The target system is a climate system with unknown dynamic equations. The target parameters are climate-related parameters, including sea surface temperature, sea level height, soil moisture and greenhouse gas concentration. The target system includes a deep cooperative network. The acquisition module is used to acquire sample trajectory data of the target parameter changing over time; The analysis module analyzes the sample trajectory data to obtain the feature representation of the target parameter at multiple different time scales; The second determining module is used to determine the initial values of the slow variable and the fast variable corresponding to the target parameter based on the multiple feature representations. The slow variable represents the change trend of the target parameter on a scale greater than or equal to a preset time, and the fast variable represents the change trend of the target parameter on a scale less than the preset time. The deep collaborative network is used to fuse the values of the slow variable and the values of the fast variable at different times. The training module is used to train the target system based on the initial values of the slow variables, the initial values of the fast variables, the neural ordinary differential equations corresponding to the slow variables, and the neural ordinary differential equations corresponding to the fast variables, until the target system meets the preset conditions. The training module includes: The first analysis submodule is used to analyze the slow variable based on the initial value of the slow variable and the corresponding neural ordinary differential equation to obtain the predicted value of the slow variable at a preset time. The second analysis submodule is used to analyze the fast variable based on the initial value of the fast variable, the corresponding neural ordinary differential equation of the fast variable, the deep collaborative network, and the initial value of the slow variable, to obtain the predicted value of the fast variable at the preset time. The fourth determining submodule is used to determine the predicted state value of the target parameter at the preset time based on the predicted value corresponding to the slow variable and the predicted value corresponding to the fast variable. The first training submodule is used to train the target system using a first loss function based on the actual state value and the predicted state value of the target parameters at the preset time. Wherein, the first loss function is , The predicted state value of the target parameter at the preset time. The target parameter represents the actual state value at the preset time. For the target parameter at time The predicted state value, For the target parameter at time The actual state value.
8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the system modeling method based on multi-timescale characteristics as described in any one of claims 1 to 6.
9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the system modeling method based on multi-timescale characteristics as described in any one of claims 1 to 6.