Atomic clock aging prediction method based on feature fusion and quantum constraint learning

Abstract

The invention relates to the technical field of precision timing instrument testing, in particular to an atomic clock aging prediction method based on feature fusion and quantum constraint learning. According to the atomic clock aging prediction method based on multi-modal feature fusion and quantum constraint learning provided by the invention, a multi-modal tensor fusion means is adopted, and a time domain microwave probe signal, a space domain atomic cloud density distribution signal and a frequency domain lambda stripe signal are collected at the same time for feature extraction, so that the completeness of the features is improved; during nonlinear modeling, a Bloch equation constraint is adopted to ensure that a network model accords with a quantum physics rule. According to the method, the atomic clock aging feature expression effect can be improved through an artificial intelligence means, the defect of overfitting caused by purely depending on training data is effectively avoided, the atomic clock aging prediction model better conforms to the physical law, the atomic clock aging prediction precision is improved, and the prediction model complexity is optimized.

Description

Technical Field

[0001] The present application relates to the technical field of precision timing instrument testing, and in particular to an atomic clock aging prediction method based on feature fusion and quantum constrained learning. Background Art

[0002] As a high-precision time and frequency benchmark, the long-term stability and lifespan of atomic clocks directly affect the reliability in key areas such as navigation, communications, and deep space exploration.

[0003] Existing aging status assessment technologies for atomic clocks (such as rubidium and cesium atomic clocks) mainly accumulate frequency drift data of atomic clocks through accelerated aging experiments or natural aging monitoring (6-12 months) to establish empirical models. Statistical models (such as multivariate linear regression and support vector machines) or physical models (such as quantum noise theory models) are usually used to analyze the impact of environmental disturbances such as temperature and magnetic fields on aging. Then, based on threshold alarms (such as Allan variance exceeding the limit) or spectrum analysis (FFT detection of abnormal harmonics), early signs of frequency drift are identified.

[0004] Traditional atomic clock aging status assessment technology has the following three major pain points: (1) It relies on long-term physical experiments and has poor timeliness. Traditional methods require continuous aging experiments lasting up to 6-12 months to collect frequency drift data, resulting in a long R&D cycle and high costs. In the design of new atomic clocks, repeated experiments seriously slow down the iteration efficiency and cannot meet the needs of real-time life assessment. (2) It is difficult to model the nonlinear relationship between environment and aging. Atomic clock aging is affected by the coupling of multiple parameters such as temperature, magnetic field, and power supply noise. Its nonlinear dynamic characteristics are difficult to accurately characterize through traditional mathematical models (such as linear regression and polynomial fitting). Existing methods ignore environmental dynamic interference, resulting in large long-term prediction errors. (3) Data overfitting is a key challenge that may cause the model to fail in practical applications. Overfitting models perform well on training data, but the prediction error for new data is significantly increased. Atomic clock aging data usually has high noise and complex nonlinear characteristics. Overfitting training data (such as short-term fluctuations or measurement noise) will cause the model to fail to capture the true long-term aging trend (such as frequency drift). Relying on overfitting models may trigger unnecessary calibration or replacement operations, increasing operation and maintenance costs. For example, satellite atomic clocks are extremely expensive to maintain, and incorrect predictions can directly impact mission lifespan. Overfitting can mask data quality issues (such as sensor errors and uneven sampling intervals), causing researchers to overlook the importance of data preprocessing. Overfitted models perform well on the training data, but prediction errors on new data increase significantly.

[0005] Therefore, those skilled in the art are committed to developing an atomic clock aging prediction method that can realize environment-aging nonlinear relationship modeling and better represent the real physical degradation laws (such as the frequency drift of rubidium clocks or the cavity aging of hydrogen masers). Summary of the Invention

[0006] This application provides an atomic clock aging prediction method based on feature fusion and quantum constrained learning. Through a multimodal feature fusion architecture, cross-dimensional correlation features are extracted, and a neural network constrained by Bloch quantum physics is used to construct an environment-aging nonlinear model to solve the technical problem of real-time aging prediction of atomic clocks.

[0007] The specific implementation methods of this application are now introduced as follows.

[0008] The present embodiment provides an atomic clock aging prediction method based on feature fusion and quantum constrained learning, comprising the following steps:

[0009] Synchronously collect time-domain microwave probe signals, spatial-domain atomic cloud density distribution, and frequency-domain Ramsey fringe signals; construct a three-dimensional space-time-frequency tensor input matrix X∈R^(T×S×N), where T is the time step, S is the spatial grid point, and N is the number of frequency channels;

[0010] A 3D convolutional neural network is used to extract deep features of the three-dimensional tensor and output a feature map F∈R^(k×d), where k is the number of time segments and d is the feature dimension.

[0011] Construct a dual-channel GRU network. The main channel inputs the feature F and outputs the predicted frequency offset Δω. The auxiliary channel embeds the Bloch equation constraint to calculate the differential constraint terms of the Hamiltonian H and the wave function ψ. Define the hybrid loss function:

[0012] Among them, L MSE is the mean square error term, is the constraint term of the Bloch equation, H is the Hamiltonian of the system, which describes the internal energy level structure of the atomic clock and the effect of the external field. is the reduced Planck constant; α and β are weight parameters used to balance the contributions of the two losses. If β>α, the model will more strictly obey the physical laws, but may reduce the ability to fit the data. Otherwise, it will rely more on the data and may deviate from the physical constraints.

[0013] Establish the environmental stress transfer function: dω / dt=K·∫[f(T(t))·g(P(t))·h(E(t))]dt+λ∫ω_hist(t-τ)dτ, where K is the stress coupling coefficient, λ is the historical aging memory factor, f(T(t)) is the temperature stress function, g(P(t)) is the pressure stress function, and h(E(t)) is the electromagnetic field stress function;

[0014] A lightweight model is deployed on the atomic clock edge computing unit to output aging prediction values in real time. A dynamic calibration threshold is set. When the predicted aging rate exceeds the dynamic calibration threshold, an active compensation signal is triggered to the servo system.

[0015] In one possible implementation, the time attention weight W_t, the spatial attention weight W_s, and the frequency attention weight W_f are applied in parallel to the three-dimensional tensor input matrix; the fusion feature is generated by cross-correlation calculation Where σ is the Sigmoid activation function.

[0016] In one possible embodiment, the time-domain microwave probe signal is acquired using a lock-in amplifier or a high-speed ADC in a specific time window of the microwave pulse, and the signal-to-noise ratio is improved by accumulating multiple repeated pulse sequences.

[0017] In a possible embodiment, the spatial atomic cloud density distribution is acquired by using absorption imaging or fluorescence imaging.

[0018] In one possible embodiment, the steps for collecting frequency-domain Ramsey fringe signals are as follows: precisely control the frequency of the microwave source to scan near the atomic transition frequency, with the step frequency interval being smaller than the fringe width; after the secondarily separated microwave field interacts with the atoms, measure the proportion of atoms in the excited state by detecting lasers or electronic methods; repeat the experiment multiple times for each scanning frequency point to calculate the probability of atomic state population; fit the Ramsey fringes and extract the center frequency.

[0019] In one possible embodiment, the temperature stress function f(T(t)) is fitted using an Arrhenius model or a polynomial, f(T(t))=exp(-Ea / kBT(t)), where Ea is the activation energy and kB is the Boltzmann constant, or The coefficient a i Calibrated by experimental data.

[0020] In one possible implementation, the pressure stress function g(P(t))=b0+b1P(t)+b2P 2 (t).

[0021] In one possible implementation, the pressure stress function is simplified to a linear response according to the influence of pressure, g(P(t))=b0+b1P(t).

[0022] In one possible implementation, the electromagnetic field stress function h(E(t))=c0||E(t)||+c1||E(t)|| 2 , where E(t) is the electromagnetic field strength.

[0023] In one possible implementation, the calibration threshold is a 3σ historical mean.

[0024] On the one hand, this solution avoids underfitting by enriching the learning and data processing capabilities of the neural network nonlinear model, while also increasing detailed features by integrating time-space frequency feature types. On the other hand, by adding quantum constraint regularization terms to the neural network learning model to avoid data overfitting, the learning model has both data and physical interpretation capabilities.

[0025] The beneficial effects of this application include extracting cross-domain correlations through multimodal spatiotemporal feature fusion, improving model generalization through the use of quantum physics-constrained neural networks, and achieving high-precision aging verification of atomic clocks. This solution, through cross-modal correlation modeling and the embedding of physical laws, addresses the bottleneck issue of aging assessment for atomic sensors in complex environments.

[0026] The beneficial effects of this application are also reflected in: multimodal tensor fusion improves feature completeness; Bloch equation constraints ensure that the network model conforms to the laws of quantum physics. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and, together with the description, serve to explain the principles of the present application.

[0028] Figure 1 :Flowchart of atomic clock aging prediction in existing technology;

[0029] Figure 2 : Flowchart of atomic clock aging prediction based on multimodal feature fusion and quantum constrained learning adopted in Example 1 of this solution;

[0030] Figure 3 : Schematic diagram of underfitting, best fit, and overfitting of machine learning data;

[0031] Figure 4 : Schematic diagram of underfitting, best fit, and overfitting model complexity for machine learning data.

[0032] The above drawings illustrate specific embodiments of the present application, which will be described in more detail below. These drawings and the textual description are not intended to limit the scope of the present application in any way, but rather to illustrate the concepts of the present application to those skilled in the art by reference to specific embodiments. DETAILED DESCRIPTION

[0033] Exemplary embodiments will be described in detail herein, with examples illustrated in the accompanying drawings. In the following description, when referring to the drawings, identical numerals in different figures represent identical or similar elements, unless otherwise indicated. The embodiments described in the following exemplary embodiments are not intended to represent all embodiments consistent with the present application. Rather, they are merely examples of apparatus and methods consistent with certain aspects of the present application, as detailed in the appended claims.

[0034] The following specific embodiments describe in detail the technical solution of the present application and how the technical solution of the present application solves the above-mentioned technical problems. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be repeated in some embodiments. The embodiments of the present application will be described below in conjunction with the accompanying drawings.

[0035] Example 1

[0036] In order to clearly understand the technical solution of Example 1 of the present application, the solution of the prior art is first introduced in detail.

[0037] The aging of atomic clocks is primarily manifested as long-term drift in their output frequency. Causes include: slight changes in atomic transition frequencies (such as energy level shifts in cesium or rubidium atomic clocks), external environmental interference (temperature and magnetic field fluctuations), and performance degradation of hardware components (such as oscillators and lasers).

[0038] Atomic clock aging prediction involves using specific algorithms and techniques to predict the performance changes of atomic clocks over time, particularly changes in their frequency stability and accuracy. Atomic clock aging is primarily due to physical changes in internal components and the influence of the external environment, leading to frequency drift and decreased accuracy.

[0039] Atomic clocks use the transition frequency between atomic energy levels to keep time. This frequency is extremely stable and provides an extremely precise standard for time measurement. The core of an atomic clock lies in a specific type of atom (such as cesium or rubidium), whose electrons will transition between different energy levels when exposed to electromagnetic radiation. By measuring this transition frequency, an atomic clock can achieve high-precision time measurement. However, over time, the internal components of an atomic clock (such as crystal oscillators, electronic components, etc.) will change, resulting in a decrease in frequency stability and accuracy. This is the aging phenomenon of the atomic clock.

[0040] Deep neural networks are an effective prediction method. By simulating the way the human brain processes information, they are able to learn and predict complex nonlinear mapping relationships. In atomic clock error prediction, deep neural networks can analyze historical data to capture the underlying characteristics of atomic clock performance changes, thereby predicting future performance changes. Furthermore, the convolutional layers in deep neural networks reduce the number of model parameters through parameter sharing, improving computational efficiency and further optimizing prediction accuracy.

[0041] Ramsey fringes are interference patterns produced by split-oscillation field technology (interaction between two microwave pulses separated by a time interval) and their key functions include: Frequency sensitivity: The central peak of the fringes corresponds to the intrinsic transition frequency of the atoms, and frequency drift will directly manifest as a shift in the center of the fringes. High resolution: The narrow linewidth of the fringes (inversely proportional to the interaction time) can detect extremely small frequency changes (e.g., on the order of 10^-16). Aging indicator: Long-term monitoring of the shift in the center position of the fringes can quantify the aging trend of the atomic clock.

[0042] Practical Application Effects: Calibration Benchmark: Ramsey fringes are used to correct the local oscillator frequency in real time to compensate for aging drift. Fault Warning: Distortions in fringe shape (such as contrast loss and linewidth variations) may indicate hardware degradation (such as unstable microwave power).

[0043] Ramsey fringes serve as both a high-precision frequency scale and a diagnostic profile for the hardware's condition in atomic clock aging prediction. When used as AI features, their physical parameters (center frequency, linewidth, etc.) are converted into quantifiable aging indicators through signal processing and machine learning. Combining physical models with data-driven approaches enables cross-scale predictions, from microscopic quantum effects to macroscopic performance degradation.

[0044] In the world of machine learning and deep learning, we always hope that the model can not only fit the training data well, but also have excellent generalization ability to unknown data. However, the reality is always full of challenges, and the model may fall into the dilemma of overfitting or underfitting.

[0045] Underfitting: When a model fails to capture the underlying trends in the data. Underfitting occurs when a model performs poorly on the training, validation, and test sets. This typically means the model lacks sufficient power to capture the characteristics of the data, or that the features of the training examples are insufficiently extracted. Causes of underfitting: Insufficient model complexity: The model lacks sufficient power to fit the data. Insufficient feature extraction: Too few features are extracted from the training examples, resulting in a poor fit for the model.

[0046] Overfitting: When the model overfits the training data. Overfitting means that the model performs well on the training set but performs poorly on the test set. This is usually because the model overfits the training data, resulting in a decrease in the ability to generalize to unknown data. Manifestation of overfitting: The training error and test error begin to separate after reaching a certain critical point. The model performs well on the training set but performs poorly on the test set. Ways to solve overfitting: Increase training data: Although increasing data is usually helpful in solving underfitting, it has limited effect on overfitting. Reduce model complexity: For example, reduce the number of hidden layers and hidden units of the neural network, or use a simpler algorithm. Add regularization constraints: Regularization is to prevent the model from overfitting by increasing the regularization parameter or introducing a regularization term to limit the complexity of the model.

[0047] The current existing atomic clock aging prediction technology uses Figure 1 The process shown generally involves collecting data from atomic clock frequency signals and using machine learning to make predictions based on this data. However, its drawbacks include limited feature representation of the collected data, resulting in a lack of comprehensive and detailed features for modeling. Furthermore, in nonlinear modeling (typically neural network models), the mean square error (MSE) criterion is often used to establish constraints, which can lead to overfitting, resulting in complex models, inaccurate predictions, and violations of physical laws.

[0048] In view of this, the purpose of Example 1 of the present invention is to provide an atomic clock aging prediction method based on multimodal feature fusion and quantum constrained learning. On the one hand, the underfitting phenomenon is avoided by enriching the learning and data processing capabilities of the neural network nonlinear model, and detailed features are added by fusing time-space frequency feature types. On the other hand, the problem of data overfitting is avoided by adding quantum constrained regularization terms in the neural network learning model, so that the learning model has both data and physical interpretation capabilities. The steps of this method are as follows: Figure 2 Shown, including:

[0049] Step 1: Multimodal data acquisition and three-dimensional tensor construction.

[0050] 1.1Simultaneously acquire time-domain microwave probe signals, spatial atomic cloud density distribution (obtained through absorption imaging), and frequency-domain Ramsey fringe signals;

[0051] 1.2 Perform time alignment and normalization on the three types of signals to construct a three-dimensional space-time-frequency tensor input matrix X∈R^(T×S×N), where T is the time step, S is the spatial grid point, and N is the number of frequency channels.

[0052] Step 2: Cross-dimensional feature extraction.

[0053] 2.1 Design of spatiotemporal attention mechanism:

[0054] Apply temporal attention weights W_t, spatial attention weights W_s, and frequency attention weights W_f in parallel to the tensor input;

[0055] Generate fusion features through cross-correlation calculation: Where σ is the Sigmoid activation function;

[0056] 2.2 Use 3D convolutional neural network to extract deep features of tensor and output feature map F∈R^(k×d), where k is the number of time segments and d is the feature dimension.

[0057] Step 3: Temporal modeling of quantum physics constraints.

[0058] 3.1 Build a dual-channel GRU network (Gated Recurrent Unit, a variant of the recurrent neural network RNN):

[0059] The main channel input feature F, output predicted frequency offset Δω;

[0060] The auxiliary channel embeds the Bloch equation constraint to calculate the differential constraint terms of Hamiltonian H and wave function ψ;

[0061] 3.2 Define the hybrid loss function:

[0062] Among them, L MSE is the mean squared error term, which represents the mean squared error between the model prediction value and the actual aging data. It is the standard loss term in supervised learning. is the Bloch equation constraint, which requires that the output of the neural network (wave function ψ or its derivative) must approximately satisfy the dynamical equations of the quantum system. is the gradient of the wave function with respect to time or parameter (depending on the model input variable), H is the Hamiltonian of the system, which describes the internal energy level structure of the atomic clock and the effect of the external field. is the reduced Planck constant; the weight parameters α and β are used to balance the contribution of the two losses. If β>α, the model will obey the physical laws more strictly, but may reduce the ability to fit the data. Otherwise, it will rely more on the data and may deviate from the physical constraints.

[0063] Step 4: Establish the environmental stress transfer function:

[0064] dω / dt=K·∫[f(T(t))·g(P(t))·h(E(t))]dt+λ∫ω_hist(t-τ)dτ, where K is the stress coupling coefficient and λ is the historical aging memory factor.

[0065] Step 5: Online prediction and calibration.

[0066] 5.1 Deploy a lightweight model on the atomic clock edge computing unit to output aging prediction values in real time;

[0067] 5.2 Set the dynamic calibration threshold: When the predicted aging rate exceeds the 3σ historical mean, an active compensation signal is triggered to the servo system.

[0068] Example 1 solves the limitations of traditional single-modal monitoring by fusing space-time and frequency features with three-dimensional tensors; the basic equations of quantum mechanics are used as neural network constraints to ensure that the prediction results conform to physical laws.

[0069] In a possible improved embodiment of Example 1, the time-domain microwave probe signal is collected using a phase-locked amplifier or a high-speed ADC in a specific time window of the microwave pulse, and the signal-to-noise ratio is improved by accumulating multiple repeated pulse sequences.

[0070] In a possible improved embodiment of Example 1, the spatial atomic cloud density distribution is acquired by using absorption imaging or fluorescence imaging.

[0071] In a possible improved embodiment of Example 1, the steps for collecting the frequency-domain Ramsey fringe signal are as follows: by precisely controlling the frequency of the microwave source, scanning near the atomic transition frequency, and the step frequency interval must be smaller than the fringe width; after the secondarily separated microwave field interacts with the atoms, measuring the proportion of atoms in the excited state by detecting laser or electronic methods; repeating the experiment multiple times for each scanning frequency point, and statistically calculating the probability of the atomic state population; fitting the Ramsey fringes and extracting the center frequency.

[0072] In a possible improved embodiment of embodiment 1, the temperature stress function f(T(t)) adopts the Arrhenius model or polynomial fitting, f(T(t))=exp(-E a / k B T(t)), where E a is the activation energy, kB is the Boltzmann constant, or The coefficient a i Calibrated by experimental data.

[0073] In a possible improved embodiment of embodiment 1, the pressure stress function g(P(t))=b0+b1P(t)+b2P 2 (t).

[0074] In a possible improved embodiment of embodiment 1, the pressure stress function is simplified to a linear response according to the influence of pressure, g(P(t))=b0+b1P(t).

[0075] In a possible improved embodiment of embodiment 1, the electromagnetic field stress function h(E(t))=c0||E(t)||+c1||E(t)||2 , where E(t) is the electromagnetic field strength.

[0076] Through the above-mentioned embodiment 1 and its improved embodiments, the multimodal tensor fusion method is used to improve the completeness of the features; the Bloch equation constraint is used to ensure that the network model conforms to the laws of quantum physics; this method can improve the expression effect of the atomic clock aging features by means of artificial intelligence and effectively avoid the shortcomings of overfitting that exist when relying solely on training data (such as Figure 3 As shown), the atomic clock aging prediction model is more consistent with the physical laws (as shown Figure 4 ) to avoid unnecessary model complexity.

[0077] In the above-mentioned embodiment 1 and its various improved embodiments, the descriptions of each embodiment have their own emphasis. For parts not described in detail in a particular embodiment, please refer to the relevant descriptions of other embodiments. The technical features of the above-mentioned embodiments can be combined arbitrarily. To keep the description concise, not all possible combinations of the technical features in the above-mentioned embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0078] Those skilled in the art will readily appreciate other embodiments of the present application after considering the specification and practicing the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the present application that follow the general principles of the present application and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered as exemplary only, and the true scope and spirit of the present application are indicated by the following claims.

[0079] It should be understood that the present application is not limited to the exact structure described above and shown in the drawings, and that various modifications and changes may be made without departing from the scope thereof. The scope of the present application is limited only by the appended claims.

Claims

1. Atomic clock aging prediction method based on multimodal feature fusion and quantum constrained learning, characterized by: Including steps: Synchronously collect time-domain microwave probe signals, spatial-domain atomic cloud density distribution, and frequency-domain Ramsey fringe signals; construct a three-dimensional space-time-frequency tensor input matrix X∈R^(T×S×N), where T is the time step, S is the spatial grid point, and N is the number of frequency channels; A 3D convolutional neural network is used to extract deep features of the three-dimensional tensor and output a feature map F∈R^(k×d), where k is the number of time segments and d is the feature dimension. Construct a dual-channel GRU network. The main channel inputs the feature F and outputs the predicted frequency offset Δω. The auxiliary channel embeds the Bloch equation constraint to calculate the differential constraint terms of the Hamiltonian H and the wave function ψ. Define the hybrid loss function: Among them, L MSE is the mean square error term, is the constraint term of the Bloch equation, H is the Hamiltonian of the system, which describes the internal energy level structure of the atomic clock and the effect of the external field. is the reduced Planck constant; α and β are weight parameters used to balance the contributions of the two losses. If β>α, the model will more strictly follow the physical laws but reduce the ability to fit the data. Otherwise, it will rely more on the data and deviate from the physical constraints. Establish the environmental stress transfer function: dω / dt=K·∫[f(T(t))·g(P(t))·h(E(t))]dt+λ∫ω_hist(t-τ)dτ, where K is the stress coupling coefficient, λ is the historical aging memory factor, f(T(t)) is the temperature stress function, g(P(t)) is the pressure stress function, and h(E(t)) is the electromagnetic field stress function; A lightweight model is deployed on the atomic clock edge computing unit to output aging prediction values in real time. A dynamic calibration threshold is set. When the predicted aging rate exceeds the dynamic calibration threshold, an active compensation signal is triggered to the servo system.

2. The atomic clock aging prediction method based on multimodal feature fusion and quantum constrained learning according to claim 1 is characterized in that: Apply the time attention weight W_t, spatial attention weight W_s and frequency attention weight W_f in parallel on the three-dimensional tensor input matrix; generate fusion features through cross-correlation calculation Where σ is the Sigmoid activation function.

3. The atomic clock aging prediction method based on multimodal feature fusion and quantum constrained learning according to claim 1 is characterized in that: The time-domain microwave probe signal is acquired by using a lock-in amplifier or a high-speed ADC in a specific time window of the microwave pulse, and the signal-to-noise ratio is improved by accumulating multiple repeated pulse sequences.

4. The atomic clock aging prediction method based on multimodal feature fusion and quantum constrained learning according to claim 1 is characterized in that: The spatial atomic cloud density distribution is obtained by using absorption imaging or fluorescence imaging.

5. The atomic clock aging prediction method based on multimodal feature fusion and quantum constrained learning according to claims 1-4, characterized in that: The frequency-domain Ramsey fringe signal acquisition steps are as follows: precisely controlling the frequency of the microwave source to scan near the atomic transition frequency, with the step frequency interval being smaller than the fringe width; after the secondarily separated microwave field interacts with the atoms, measuring the proportion of atoms in the excited state using a detection laser or electronic method; repeating the experiment multiple times for each scanning frequency point to calculate the probability of atomic state population; and fitting the Ramsey fringes to extract the center frequency.

6. The atomic clock aging prediction method based on multimodal feature fusion and quantum constrained learning according to claims 1-4, characterized in that: The temperature stress function f(T(t)) is fitted by the Arrhenius model or polynomial, f(T(t))=exp(-E a / k B T(t)), where E a is the activation energy, k B is the Boltzmann constant, or The coefficient a i Calibrated by experimental data.

7. The atomic clock aging prediction method based on multimodal feature fusion and quantum constrained learning according to claims 1-4, characterized in that: The pressure stress function g(P(t))=b0+b1P(t)+b2P 2 (t).

8. The atomic clock aging prediction method based on multimodal feature fusion and quantum constrained learning according to claim 7 is characterized in that: The pressure stress function is simplified to a linear response according to the influence of pressure, g(P(t))=b0+b1P(t).

9. The atomic clock aging prediction method based on multimodal feature fusion and quantum constrained learning according to claims 1-4, characterized in that: The electromagnetic field stress function h(E(t))=c0‖E(t)‖+c1‖E(t)‖ 2 , where E(t) is the electromagnetic field strength.

10. The atomic clock aging prediction method based on multimodal feature fusion and quantum constrained learning according to claim 1 is characterized in that: The calibration threshold is the 3σ historical mean.

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