Anesthesia brain state evaluation method based on deep learning EEG data model inversion

By constructing a deep learning-based EEG data model and combining it with a neuron swarm model, the subjectivity and lag issues of traditional anesthesia depth assessment methods were resolved, enabling real-time and accurate assessment of the anesthetized brain state and improving the accuracy and reliability of the assessment.

CN120392007BActive Publication Date: 2026-03-27RES INST OF ZHEJIANG UNIV TAIZHOU +1
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Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-04-03
Publication Date
2026-03-27

AI Technical Summary

Technical Problem

Traditional methods for assessing the depth of anesthesia rely on experience and physiological indicators, which are subjective and lagging. Existing EEG signal monitoring equipment lacks neurophysiological understanding and is difficult to assess the state of the anesthetized brain in real time and accurately.

Method used

We construct a deep learning-based EEG data model, combined with a neuron swarm model, and invert the anesthesia brain state from EEG signals by training a deep learning model in the parameter space of the model. This includes constructing a neuron swarm model, generating a training dataset, designing a deep learning model structure, and applying it to actual EEG data for parameter inversion and anesthesia depth assessment.

Benefits of technology

It enables real-time and accurate assessment of the state of the brain under anesthesia, improving the accuracy and reliability of the assessment, better reflecting brain activity, and reducing the risk of misjudgment.

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Abstract

The application discloses an EEG data model inversion anesthetic brain state evaluation method based on deep learning. First, a neuron group model suitable for an anesthetic state is constructed, which is based on a Jansen-Rit model, covers multiple neuron groups and has specific dynamic equations. Then, a model parameter value range is determined, a combination is generated by sampling and simulated EEG signals are generated to construct a training set. Then, a deep learning model is designed for training to learn a parameter mapping relationship. In actual application, after EEG signals of a subject are collected and preprocessed, the trained model is inputted to invert parameters, and then an anesthetic depth index ADI is calculated to evaluate an anesthetic brain state. The method has high accuracy in evaluating an anesthetic depth and provides an effective means for anesthetic monitoring.
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Description

TECHNICAL FIELD

[0001] The present application relates to the field of biomedical engineering, neuroscience and anesthesia monitoring, and particularly relates to an EEG data model inversion anesthesia brain state evaluation method based on deep learning. BACKGROUND

[0002] Traditional anesthesia depth evaluation methods mainly rely on the experience of anesthetists and the physiological indicators of subjects, such as heart rate, blood pressure, etc. These methods have certain subjectivity and hysteresis, and may not accurately reflect the brain state of the subject.

[0003] Electroencephalogram (EEG) as a non-invasive neuroelectrophysiological monitoring method can record the electrical activity of the cerebral cortex in real time and is considered an effective tool for evaluating anesthesia depth. At present, there are some anesthesia depth monitoring devices based on EEG signals, such as Bispectral Index (BIS) monitors. However, these devices are mostly based on empirical formulas and statistical methods, lacking a deep understanding of the neurophysiological mechanisms, and may produce misjudgments in certain situations.

[0004] Neural Mass Model (NMM) is a mathematical model that describes brain activity from a neurophysiological perspective, which can simulate the collective dynamic behavior of a large number of neuron groups. By adjusting the model parameters, EEG signals under different brain states can be simulated. However, traditional model parameter estimation methods, such as optimization algorithms, have high computational complexity and are prone to local optimization, making it difficult to meet the needs of real-time monitoring.

[0005] In recent years, deep learning has made remarkable achievements in signal processing and pattern recognition. Using deep learning models to extract features from EEG signals and perform classification and regression analysis has become a research hotspot. However, combining deep learning with neural mass models to invert model parameters from EEG signals and evaluate anesthesia brain states remains a challenge. SUMMARY

[0006] The purpose of the present application is to overcome the shortcomings of the prior art and provide an EEG data model inversion anesthesia brain state evaluation method based on deep learning.

[0007] The present application is implemented as follows: an EEG data model inversion anesthesia brain state evaluation method based on deep learning, comprising the following steps:

[0008] Step S1, constructing a neural mass model suitable for electroencephalogram activity under anesthesia state;

[0009] Step S2, determine the value range of the model parameters, generate a plurality of parameter combinations; generate simulated EEG signals according to the parameter combinations to form a training data set;

[0010] Step S3, design and train a deep learning model of the model parameter space to learn the parameter mapping relationship from the simulated EEG signals;

[0011] Step S4, apply the trained deep learning model of the model parameter space to the actual EEG data for model parameter inversion;

[0012] Step S5, according to the estimated model parameters, calculate the depth of anesthesia index to realize real-time evaluation of the anesthetic brain state;

[0013] Preferably, in step S1, the neuron group model suitable for brain electrical activity under anesthesia state takes the Jansen-Rit model as the basis, and is composed of excitatory neuron group and inhibitory neuron group, including pyramidal cell group PC, excitatory intermediate neuron group EI and inhibitory intermediate neuron group II.

[0014] Preferably, in step S1, the model dynamics equation of the neuron group model suitable for brain electrical activity under anesthesia state includes post-synaptic membrane potential transfer function, average firing rate of neuron group, and state equation:

[0015] The post-synaptic membrane potential transfer function includes post-synaptic membrane potential response functions h e (t) and h i (t) of excitatory neuron group and inhibitory neuron group, which are specifically as follows:

[0016]

[0017] Wherein, A and B are excitatory synaptic gain and inhibitory synaptic gain respectively; a and b are the inverse of the time constant of excitatory neuron group and inhibitory neuron group; t represents time; exp() represents natural exponential function;

[0018] The average firing rate function is:

[0019] The average firing rate S(v) of neuron group converts the post-synaptic membrane potential v into the average pulse density of action potential:

[0020]

[0021] Wherein, e0 is the maximum discharge rate, v0 is the membrane potential corresponding to the half-maximum discharge rate, and r is the slope parameter;

[0022] The state equation is specifically as follows:

[0023]

[0024] Where y1 is the membrane potential of the pyramidal cell group, y2 and y3 are the membrane potentials of the excitatory neuron group and the inhibitory neuron group, respectively, y4, y5, and y6 are the derivatives of y1, y2, and y3, respectively, i.e., the rate of change of their membrane potentials, p(t) is the external input, C1 and C2 represent the average connection coefficients of the input and output excitatory circuits, respectively, and C3 and C4 represent the average connection coefficients of the input and output inhibitory circuits, respectively. Let x be the derivative.

[0025] Preferably, in step S2, each parameter is randomly selected within the range of model parameter values ​​to generate multiple parameter combinations; the parameters selected in different parameter combinations are different from each other.

[0026] The model parameters include excitatory synaptic gain A, inhibitory synaptic gain B, reciprocal of the time constant of the excitatory neuron group a, reciprocal of the time constant of the inhibitory neuron group b, average connection coefficient C1 for entering the excitatory circuit, average connection coefficient C2 for exiting the excitatory circuit, average connection coefficient C3 for entering the inhibitory circuit, and average connection coefficient C4 for exiting the inhibitory circuit.

[0027] Preferably, in step S2, for each set of parameter combinations, the dynamic equations are numerically integrated to generate the corresponding simulated EEG signal:

[0028] V i (t)=y 2i (t)-y 3i (t) Equation (5)

[0029] Where y 2i (t), y 3i (t) represents the membrane potential of the excitatory neuron group and the inhibitory neuron group in the i-th simulated EEG;

[0030] Preferably, in step S2, the training dataset is formed by simulated EEG signals and corresponding model parameters;

[0031] Preferably, in step S2, the simulated EEG signal needs to be preprocessed before it is input into the deep learning model in the model parameter space;

[0032] Preferably, in step S3, the deep learning model in the model parameter space includes an input layer, a convolutional layer, a pooling layer, a recurrent layer, and a fully connected layer;

[0033] The input layer receives EEG signals;

[0034] The convolutional layer employs a one-dimensional convolutional neural network (CNN) with multiple convolutional kernels to extract local temporal features from the input.

[0035] The pooling layer uses maximum pooling to reduce the feature dimension of the output of the convolution layer;

[0036] The recurrent layer adopts a long short-term memory network layer to capture long-term dependencies of time series of the output of the pooling layer;

[0037] The fully connected layer expands the features extracted by the recurrent layer and maps them to a model parameter space to obtain estimated model parameters

[0038] The output layer outputs the estimated model parameters

[0039] The loss function of the deep learning model of the model parameter space is as follows:

[0040]

[0041] Where θ i represents the true value of the model parameter.

[0042] Preferably, step S4 is specifically:

[0043] Collecting the EEG signal of the patient, and pre-processing the EEG signal;

[0044] Inputting the pre-processed EEG signal segment into the trained deep learning model of the model parameter space to obtain estimated model parameters

[0045] Preferably, step S5 is specifically:

[0046] According to the estimated model parameters, the anesthetic depth index ADI is calculated:

[0047]

[0048] Where w1, w2, and w3 are weight coefficients.

[0049] According to the anesthetic depth index ADI, the anesthetic depth is divided into different grades.

[0050] The beneficial effects of the present application at least include the following:

[0051] The present application is based on EEG data and a neuron group model, and calculates the anesthetic depth index by deep learning from the EEG signal, which can effectively improve the evaluation accuracy and more accurately reflect the anesthetic brain state.

[0052] The neuron group model used in the present application describes brain activity from the perspective of neurophysiology, can simulate EEG signals under different brain states, and realizes model parameter inversion combined with deep learning, deeply integrates neurophysiological mechanisms, and enhances evaluation reliability.

[0053] The deep learning model structure designed in the application is reasonable, features are extracted and parameter spaces are mapped by using convolution layers, pooling layers, recurrent layers and full connection layers, calculation efficiency is improved while ensuring parameter estimation accuracy, and anesthesia brain state can be evaluated in real time. BRIEF DESCRIPTION OF DRAWINGS

[0054] In order to more clearly illustrate the technical solutions of the present application, the drawings needed in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application, and other drawings can also be obtained according to these drawings without creative labor for those skilled in the art.

[0055] Figure 1 is a flow chart of the anesthesia brain state evaluation method provided by the embodiment of the present application.

[0056] Figure 2 is a model structure diagram of a neuron group model suitable for electroencephalogram activity under anesthesia.

[0057] Figure 3 is a comparison diagram of each parameter and bis, (a) is a correlation diagram of parameters related to excitatory connection and bis, (b) is a correlation diagram of parameters related to inhibitory connection and bis, (c) is a correlation diagram of excitatory synaptic gain and bis, (d) is a correlation diagram of inhibitory synaptic gain and bis, (e) is a correlation diagram of excitatory time constant and bis, and (f) is a correlation diagram of inhibitory time constant and bis.

[0058] Figure 4 is a SVM classification result in binary classification, (a) is a classification result of the model, and (b) is a true reference. DETAILED DESCRIPTION

[0059] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application.

[0060] As shown in Figure 1 , the present application provides an EEG data model inversion anesthesia brain state evaluation method, the brain state evaluation here is not for therapeutic or diagnostic purposes, and the method comprises the following steps:

[0061] Step S1, constructing a neuron group model suitable for electroencephalogram activity under anesthesia;

[0062] Step S2, determining the value range of the model parameters, generating a plurality of parameter combinations; generating simulated EEG signals according to the parameter combinations to form a training data set;

[0063] Step S3, design and train a deep learning model of model parameter space to learn the parameter mapping relationship from the simulated EEG signal; Step S4, apply the trained deep learning model of model parameter space to the actual EEG data for model parameter inversion;

[0064] Step S5, according to the estimated model parameters, calculate the anesthesia depth index (ADI) to realize real-time evaluation of the anesthesia brain state;

[0065] Specifically, in step S1, a neuron group model suitable for electroencephalogram activity under anesthesia is constructed, such as Figure 2 Jansen-Rit model. The model describes the interaction between the cortical excitatory neuron group, the inhibitory neuron group and the thalamic input, and can simulate the generation process of the EEG signal. It is composed of excitatory neuron group and inhibitory neuron group, including pyramidal cells (PC), excitatory interneurons (EI) and inhibitory interneurons (II).

[0066] The model dynamics equation of the neuron group model suitable for electroencephalogram activity under anesthesia includes the postsynaptic membrane potential transfer function, the average firing rate of the neuron group, and the state equation:

[0067] The postsynaptic membrane potential transfer function includes the postsynaptic membrane potential response functions h e (t) and h i (t) of the excitatory neuron group and the inhibitory neuron group, which are as follows:

[0068]

[0069] Wherein, A and B are the excitatory synaptic gain and the inhibitory synaptic gain, respectively; a and b are the inverse of the time constant of the excitatory neuron group and the inhibitory neuron group; t represents the time; exp() represents the natural exponential function;

[0070] The average firing rate function is:

[0071] The average firing rate S(v) of the neuron group is represented by the Sigmoid function:

[0072]

[0073] Wherein, e0 is the maximum firing rate, v0 is the membrane potential corresponding to the half maximum firing rate, and r is the slope parameter;

[0074] The state equation is as follows:

[0075]

[0076] where y1 is the membrane potential of the pyramidal cell population, y2 and y3 are the membrane potentials of the excitatory and inhibitory neuron populations, respectively, y4, y5, y6 are the derivatives of y1, y2, y3, i.e., the rates of change of their membrane potentials, p(t) is the external input, and C1-C4 are the connection strength coefficients, C1 and C2 represent the average connection coefficients of the excitatory loop and the inhibitory loop, respectively, and C3 and C4 represent the average connection coefficients of the excitatory loop and the inhibitory loop, respectively. denotes the derivative of x;

[0077] Specifically, step S2 is specifically:

[0078] 2.1 Parameter setting

[0079] According to the influence of anesthesia on neuronal activity, the value range of the model parameters is set. The value range of the excitatory synaptic gain A is 3-8 mV; the value range of the inhibitory synaptic gain B is 20-100 mV. The value range of the time constant a, b is 50-100 s; the value range of the coupling coefficient C1, C2 is 0.8-1.2. Other parameters such as the maximum firing rate e0, the membrane potential v0 corresponding to the half-maximum firing rate, and the slope parameter r are fixed at 2.5 s, 6 mV, and 0.56 mV, respectively.

[0080] 2.2 Simulation data generation

[0081] The Latin hypercube sampling method is used to generate N sets of parameter combinations θ i = {A i ,B i ,a i ,b i ,C 1i ,C 2i}, where i = 1, 2, …, N. For each set of parameters, the fourth-order Runge-Kutta method is used to numerically integrate the dynamic equation, with a time step of Δt = 0.001 s and a total time of T = 10 s, to generate the corresponding simulated EEG signal:

[0082] V i (t) = y 2i (t) - y 3i (t).

[0083] where y 2i (t), y 3i (t) represent the membrane potentials of the excitatory and inhibitory neuron populations in the i-th simulated EEG;

[0084] The simulated EEG signal is pre-processed, including band-pass filtering (0.5 Hz to 45 Hz) to remove low-frequency drift and high-frequency noise, standardization (zero mean, unit variance) to eliminate dimensional influence, and signal segmentation (e.g., 5 seconds per segment, sampling rate 256 Hz). The training data set is formed from the simulated EEG signal and the corresponding model parameters.

[0085] Specifically, step S3 is specifically:

[0086] 3.1 Training data preparation

[0087] The training data consists of simulated EEG signal segments and corresponding model parameters. The input data is an EEG signal segment with a shape of (T, 1), T = 1280 (corresponding to a signal length of 5 seconds, sampling rate 256 Hz); the target output is the corresponding model parameters θ = {A, B, a, b, C1, C2}.

[0088] 3.2 Model structure design

[0089] A deep learning model capable of extracting features from EEG signals and mapping to the model parameter space is designed. The specific structure of the model includes an input layer, a convolutional layer, a pooling layer, a recurrent layer, and a fully connected layer. The input layer accepts EEG signal segments; the convolutional layer uses a one-dimensional convolutional neural network (CNN) with multiple convolutional kernels to extract local temporal features; the pooling layer uses max-pooling to reduce the feature dimension; the recurrent layer adds a long short-term memory network (LSTM) layer to capture the long-term dependence of time series; the fully connected layer expands the extracted features and maps them to the model parameter space; and the output layer outputs the estimated model parameters A linear activation function is used.

[0090] 3.3 Model training

[0091] The deep learning model in the model parameter space uses mean squared error (MSE) as the loss function:

[0092]

[0093] where θ i represents the true value of the model parameters.

[0094] The Adam optimizer is used, with an initial learning rate of 0.001 and a batch size of 32. To prevent overfitting, a Dropout layer with a proportion of 0.5 is used, and the loss of the validation set is monitored during training, using an early stopping strategy. When the validation set loss no longer decreases for a certain number of periods (e.g., 10 epochs), training is stopped. After multiple iterations of training, the model's parameter estimation mean squared error on the test set reaches a low level, and the estimation accuracy of each parameter is high.

[0095] In particular, step S4 is specifically:

[0096] 4.1 EEG data acquisition and preprocessing

[0097] During the operation of anesthesia, the EEG signal of the patient is collected using a high-precision EEG device with a sampling rate of 256Hz. The EEG signal is filtered (0.5Hz to 45Hz) to remove low-frequency and high-frequency noise, and the independent component analysis (ICA) method is used to remove artifacts such as electrooculogram and electromyogram. The continuous EEG signal is segmented according to a 5-second window, and the overlapping part can be set to 50% to increase the amount of data and improve the time resolution.

[0098] 4.2 Parameter inversion

[0099] The preprocessed EEG signal segment is input into the trained deep learning model to obtain the estimated model parameters Since the model is trained on simulated data, to adapt to actual data, model fine-tuning may be needed, which re-trains part of the model layers using a small amount of labeled actual data to improve the accuracy of the estimate.

[0100] In particular, step S5 is specifically:

[0101] According to the estimated model parameters, the anesthesia depth index (ADI) is calculated:

[0102]

[0103] where w1, w2, w3 are weight coefficients that can be determined by clinical data. The determination of the weight coefficients requires the use of a certain number of clinical samples to establish a regression model using the actual anesthesia depth (such as the BIS index or clinical score) and the estimated model parameters.

[0104] According to the value of ADI, set threshold values τ1, τ2, τ3 to divide the anesthesia depth into different levels:

[0105] Awake: ADI ≥ τ1.

[0106] Light anesthesia: τ2 ≤ ADI < τ1.

[0107] Suitable anesthesia: τ3 ≤ ADI < τ2.

[0108] Deep anesthesia: ADI < τ3.

[0109] By analyzing the change of ADI over time, the anesthesia depth can be evaluated in real time.

[0110] The embodiment also provides an anesthesia brain state evaluation device, comprising:

[0111] a data acquisition module responsible for acquiring EEG signals and preprocessing them;

[0112] a narcotized brain state evaluation module responsible for inputting the EEG signals into a deep learning model with trained model parameters, performing model parameter inversion, calculating the narcotic depth index according to the estimated model parameters, and realizing real-time evaluation of the narcotized brain state.

[0113] In addition, the present embodiment carries out experimental research on the EEG data model inversion narcotized brain state evaluation method based on deep learning, aiming to verify its effectiveness and reliability in the field of anesthesia monitoring.

[0114] The data of the present embodiment is derived from the public database VitalDB (http: / / vitaldb.net / data-bank). In order to verify the correlation between the estimated parameters and the clinical narcotic depth index, the Pearson correlation coefficient between the key parameters and the BIS index is calculated, as shown in Figure 3 (a)- Figure 3 (f). The results show that the correlation coefficient between the excitatory synaptic gain A and the BIS index reaches 0.85, with a significant positive correlation. This further proves that the excitatory parameter can be used as an important indicator for evaluating narcotic depth.

[0115] In the four-classification task, the overall accuracy of the model is about 80%, and the main misclassification occurs between the "light anesthesia period" and the "recovery period", which may be due to the similar physiological characteristics in these two states.

[0116] In order to improve the classification accuracy, the classification task is simplified to a two-classification task of "awake period" and "moderate anesthesia period", as shown in Figure 4 (a)- Figure 4 (b), the classification accuracy is more than 95%, indicating that the model can accurately distinguish between significantly different anesthesia states.

[0117] The above is the preferred embodiment of the present application, it should be noted that for those skilled in the art, without departing from the principles of the present application, can make a number of improvements and refinements, these improvements and refinements are also considered to be within the scope of protection of the present application.

Claims

1. A method for assessing anesthetized brain state by inverting EEG data models based on deep learning, characterized in that... Includes the following steps: Step S1: Construct a neuronal population model suitable for brain electrical activity under anesthesia; Step S2: Determine the range of values ​​for the model parameters and generate multiple parameter combinations; generate simulated EEG signals based on the parameter combinations to form a training dataset; Step S3: Design and train a deep learning model for the model parameter space to learn parameter mapping relationships from simulated EEG signals; Step S4: Apply the trained deep learning model in the parameter space to the actual EEG data to perform model parameter inversion; Step S5: Calculate the anesthesia depth index based on the estimated model parameters to achieve real-time assessment of the anesthetized brain state. In step S1, the neuronal group model applicable to brain electrical activity under anesthesia is based on the Jansen-Rit model and consists of excitatory neuronal groups and inhibitory neuronal groups, including pyramidal cell group PC, excitatory interneuron group EI and inhibitory interneuron group II. The model dynamics equations describing the neuronal population model applicable to EEG activity under anesthesia include the postsynaptic membrane potential transfer function, the average firing rate of the neuronal population, and the equation of state. The postsynaptic membrane potential transfer function includes the postsynaptic membrane potential response functions of excitatory neuronal groups and inhibitory neuronal groups. and The details are as follows: Equation (1) Equation (2) in, and These are the excitatory synaptic gain and the inhibitory synaptic gain, respectively. and It is the reciprocal of the time constants of the excitatory neuron group and the inhibitory neuron group; Indicates time; Represents the natural exponential function; Average firing rate function: Average firing rate of a group of neurons Postsynaptic membrane potential The average pulse density converted into action potential; Equation (3) in, For the maximum discharge rate, This represents the membrane potential corresponding to half-maximum discharge rate. The slope parameter; The state equations are as follows: Equation (4) in, This represents the membrane potential of the pyramidal cell population. and These are the membrane potentials of excitatory and inhibitory neuronal groups, respectively. , , They are respectively the corresponding , , The derivative of the membrane potential, i.e., the rate of change of its membrane potential. For external input, and These represent the average connectivity coefficients of the input and output excitatory circuits, respectively. and These represent the average connection coefficients of the input and output inhibitory loops, respectively; Step S4 specifically involves: acquiring the patient's EEG signal and preprocessing the EEG signal; inputting the preprocessed EEG signal fragment into a deep learning model in the trained model parameter space to obtain the estimated model parameters. , Step S5 specifically involves calculating the depth of anesthesia index (ADI) based on the estimated model parameters. Equation (7) in, These are the weighting coefficients; Anesthesia depth is classified into different levels based on the Anesthesia Depth Index (ADI).

2. The method according to claim 1, characterized in that, In step S2, each parameter is randomly selected within the range of model parameter values ​​to generate multiple parameter combinations; the parameters selected in different parameter combinations are different from each other. The model parameters include excitatory synaptic gain. Inhibitory synaptic gain The reciprocal of the time constant of excitatory neuronal groups The reciprocal of the time constant of the inhibitory neuron group Average connectivity coefficients of the circuits connected to excitatory circuits Average connectivity coefficient of excitatory circuits Average connection coefficient of the inhibitory loop Average connection coefficient of the outgoing inhibitory loop .

3. The method according to claim 2, characterized in that, In step S2, for each set of parameters, the dynamic equation is numerically integrated to generate the corresponding simulated EEG signal: Equation (5) in , This represents the membrane potential of the excitatory and inhibitory neuron groups in the k-th simulated EEG.

4. The method according to claim 1, characterized in that, In step S2, the training dataset is formed by simulated EEG signals and corresponding model parameters.

5. The method according to claim 1, characterized in that, In step S2, the simulated EEG signal needs to be preprocessed before it is input into the deep learning model in the model parameter space.

6. The method according to claim 1, characterized in that, In step S3, the deep learning model in the model parameter space includes an input layer, a convolutional layer, a pooling layer, a recurrent layer, a fully connected layer, and an output layer. The input layer receives EEG signals; The convolutional layer employs a one-dimensional convolutional neural network (CNN) with multiple convolutional kernels to extract local temporal features from the input. The pooling layer uses max pooling to reduce the feature dimension of the convolutional layer's output. The recurrent layer uses a long short-term memory network layer to capture the long-term dependencies of the time series in the output of the pooling layer; The fully connected layer unfolds the features extracted by the recurrent layer and maps them to the model parameter space to obtain the estimated model parameters. ; The output layer outputs the estimated model parameters. ; The loss function of the deep learning model in the model parameter space is as follows: Equation (6) in This represents the true values ​​of the model parameters.

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