Neural network-based atomic gravimeter interference fringe optimization method and device

Abstract

The present application relates to the field of quantum precision measurement, and provides an atomic gravimeter interference fringe optimization method and device based on a neural network, comprising: acquiring a plurality of vibration time sequence signals, training the neural network using the plurality of vibration time sequence signals to obtain a pre-optimized neural network; inputting the vibration time sequence signals into the pre-optimized neural network to obtain a predicted parasitic phase; acquiring original interference signals that are time-aligned with each vibration time sequence signal, compensating the corresponding original interference signals according to the predicted parasitic phase to obtain compensated interference signals; fitting the compensated interference signals to obtain compensated interference fringes, acquiring waveform differences between fitting waveform curves corresponding to the compensated interference fringes and standard cosine curves corresponding to ideal interference fringes, and optimizing the pre-optimized neural network with the aim of minimizing the waveform differences to obtain an optimized neural network, wherein the optimized neural network can compensate for more noise sources to achieve the purpose of optimizing the interference fringes.

Description

Technical Field

[0001] This invention belongs to the field of quantum precision measurement technology, and more specifically, relates to a method and device for optimizing interference fringes of an atomic gravimeter based on neural networks. Background Technology

[0002] As a core physical quantity in geophysics, high-precision measurement of gravitational acceleration is of great significance in both scientific research and practical applications. With the iterative development of gravity measurement technology, atomic gravimeters, due to their absolute measurement characteristics, high sensitivity, and good long-term stability, have become the core equipment for next-generation high-precision gravity measurements and have broad application prospects. However, in actual measurement work, atomic gravimeters are inevitably affected by various noise sources, including mirror vibration, laser parameter fluctuations, and external magnetic field interference. Among these, mirror vibration noise has the most significant impact on interference fringes.

[0003] Traditional optimization methods for interferometric fringes in atomic gravimeters mainly fall into two categories: The first relies on active and passive vibration isolation systems for physical suppression, reducing noise interference through hardware. However, these systems are complex and generally expensive. The second method uses collected vibration data combined with sensitivity functions for algorithmic compensation. However, sensitivity functions only have piecewise linear expression capabilities, approximating the linear correspondence between vibration and parasitic phase under ideal conditions, and cannot fit the nonlinear effects of vibration transmission in real-world environments. Furthermore, both methods assume that noise other than mirror vibration has been reduced to a negligible level, only correcting the parasitic phase introduced by mirror vibration noise during the interference phase. They cannot effectively compensate for the parasitic phases corresponding to other noises, resulting in limited compensation and restricting the measurement accuracy of atomic gravimeters.

[0004] Therefore, overcoming the shortcomings of the existing technology is an urgent problem to be solved in this technical field. Summary of the Invention

[0005] The problem that this invention aims to solve is that existing noise compensation schemes only compensate for the parasitic phase introduced by the vibration of the reflector, while ignoring the parasitic phase caused by other noises such as laser fluctuations and magnetic field interference, which limits the measurement accuracy of the atomic gravimeter.

[0006] Firstly, a neural network-based method for optimizing interferometric fringes in an atomic gravimeter is provided, including: Multiple vibration time-series signals are acquired and used to train a neural network to obtain a pre-optimized neural network; each vibration time-series signal corresponds to one atomic interference process. The vibration time-series signal is input into a pre-optimized neural network to obtain the predicted parasitic phase; The original interference signal is time-aligned with each vibration timing signal. The original interference signal is then compensated according to the predicted parasitic phase to obtain the compensated interference signal. The differentiable cosine fitting module is embedded into the pre-optimized neural network, and the compensation interference fringes are obtained by fitting the compensation interference signal through the differentiable cosine fitting module. The waveform difference between the fitted waveform curve corresponding to the compensated interference fringes and the standard cosine curve corresponding to the ideal interference fringes is obtained. The pre-optimized neural network is optimized with the goal of minimizing the waveform difference to obtain the optimized neural network.

[0007] Furthermore, the waveform differences between the fitted waveform curve corresponding to the compensated interference fringes and the standard cosine curve corresponding to the ideal interference fringes include: The parameters of the fitted waveform are obtained from the fitted waveform curve; Standard waveform parameters are obtained based on the standard cosine curve; The total loss is determined based on the fitted waveform parameters and the standard waveform parameters. The pre-optimized neural network is then optimized based on the total loss to obtain the optimized neural network.

[0008] Furthermore, the fitted waveform parameters include the fitted amplitude and the fitted phase, and the standard waveform parameters include the standard amplitude and the standard phase; the total loss is determined based on the fitted waveform parameters and the standard waveform parameters, including: Determine the fitting phase uncertainty based on the fitting amplitude and fitting phase; Determine the standard phase uncertainty based on the standard amplitude and standard phase; The amplitude loss is obtained from the fitted amplitude and the standard amplitude, and the phase uncertainty loss is obtained from the fitted phase uncertainty and the standard phase uncertainty. The total loss is obtained by weighted summation of the amplitude loss and the phase uncertainty loss.

[0009] Furthermore, the method also includes: The total loss is determined using a second loss function, the expression of which is: ; in, For the total loss, As the first hyperparameter, For amplitude loss, This is the second hyperparameter. This represents the loss due to phase uncertainty.

[0010] Furthermore, acquiring multiple vibration timing signals includes: Before atomic interferometry, vibration information from an atomic gravimeter is collected to obtain a forward-spreading vibration signal; During atomic interferometry, vibration information from an atomic gravimeter is collected to obtain intermediate vibration signals; After atomic interferometry, vibration information from an atomic gravimeter is collected to obtain a backward-spreading vibration signal; By sequentially splicing forward-expanding vibration signals, intermediate vibration signals, and backward-expanding vibration signals in chronological order, a vibration timing signal is obtained.

[0011] Furthermore, the neural network is trained using multiple vibration time-series signals to obtain a pre-optimized neural network, which includes: The theoretical parasitic phase corresponding to the vibration time series signal is solved by using a sensitivity function; Using theoretical parasitic phase as a supervision label and multiple vibration time series signals as input, the neural network is trained to obtain a pre-optimized neural network.

[0012] Furthermore, the method also includes: The neural network is trained using the first loss function, which is expressed as follows: ; in, This is the first loss; The predicted parasitic phase corresponds to the i-th vibration time sequence signal; is the theoretical parasitic phase corresponding to the i-th vibration timing signal; N is the number of vibration timing signals used in one round of training.

[0013] Furthermore, the vibration timing signal is input into a pre-optimized neural network, including: After normalizing the vibration time sequence signal, it is then input into the pre-optimized neural network.

[0014] In a second aspect, a neural network-based atomic gravimeter interferometric fringe optimization device is provided, comprising at least one processor and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the processor to perform the neural network-based atomic gravimeter interferometric fringe optimization method of the first aspect.

[0015] Thirdly, the present invention also provides a non-volatile computer storage medium storing computer-executable instructions that, when executed by one or more processors, cause the processors to execute the neural network-based atomic gravimeter interferometer fringe optimization method of the first aspect.

[0016] Fourthly, a chip is provided, comprising: a processor and an interface for calling and running a computer program stored in a memory, executing the neural network-based atomic gravimeter interferometric fringe optimization method of the first aspect.

[0017] Fifthly, a computer program product containing instructions is provided, which, when executed on a computer or processor, causes the computer or processor to perform the neural network-based atomic gravimeter interferometric fringe optimization method of the first aspect.

[0018] In a sixth aspect, a neural network-based atomic gravimeter interferometric fringe optimization system is provided, comprising a neural network-based atomic gravimeter interferometric fringe optimization device as described in the second aspect, and using a neural network-based atomic gravimeter interferometric fringe optimization method as described in the first aspect.

[0019] Unlike existing technologies, the present invention has at least the following beneficial effects: In this invention, a first-stage supervised training is performed on the neural network to initialize and stabilize its parameters. Then, a second-stage optimization training is conducted using a standard cosine curve as the learning target, gradually adjusting the network parameters to make the fitted waveform curve approximate the standard cosine curve, thereby minimizing interference and ultimately obtaining an optimized neural network. In practical use, the optimized neural network is directly used to perform phase compensation on the interference signal from the atomic gravimeter, ensuring that the compensated interference signal is essentially a clean, interference-free signal. This allows the fitted interference fringes to closely match the actual measurement, achieving the goal of optimizing the interference fringes and improving the measurement accuracy of the atomic gravimeter. Attached Figure Description

[0020] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments of the present invention will be briefly described below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0021] Figure 1 This is a flowchart of a neural network-based method for optimizing interferometric fringes in an atomic gravimeter, provided in an embodiment of the present invention. Figure 2 This is a flowchart of the optimized neural network trained in an atomic gravimeter interferometric fringe optimization method based on a neural network provided in an embodiment of the present invention. Figure 3a This is a flowchart of another method for optimizing interferometric fringes of an atomic gravimeter based on a neural network, provided in an embodiment of the present invention. Figure 3b This is a flowchart of another method for optimizing interferometric fringes of an atomic gravimeter based on a neural network, provided in an embodiment of the present invention. Figure 4This is a graph showing the change in loss value during the pre-optimization neural network training process in an atomic gravimeter interferometric fringe optimization method based on a neural network provided in an embodiment of the present invention. Figure 5 This is a graph showing the change of the optimal loss value calculated based on a sensitivity function, provided by an embodiment of the present invention. Figure 6 This is a waveform diagram of vibration compensation based on a sensitivity function in existing technologies; Figure 7 This is a vibration compensation waveform diagram based on a neural network provided in an embodiment of the present invention; Figure 8 This is a graph showing the change in loss value during the training process of the optimized neural network in an atomic gravimeter interferometric fringe optimization method based on a neural network, as provided in an embodiment of the present invention. Figure 9 This is a graph of the change in the optimal loss value during the training process of an optimized neural network, provided by an embodiment of the present invention. Figure 10 This is a comparison diagram of a vibration compensation waveform based on an optimized neural network and a vibration compensation waveform based on a sensitivity function, provided in an embodiment of the present invention. Figure 11 This is a comparison chart of phase uncertainty corrected based on an optimized neural network and phase uncertainty corrected based on a sensitivity function, provided by an embodiment of the present invention. Figure 12 This is a comparison chart of the Allan deviation between the optimized neural network and the sensitivity function in an atomic gravimeter interferometric fringe optimization method based on a neural network provided in an embodiment of the present invention. Figure 13 This is a schematic diagram of the structure of an atomic gravimeter interference fringe optimization device based on a neural network, provided in an embodiment of the present invention. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0023] Unless the context otherwise requires, throughout the specification and claims, the term "comprising" is interpreted as openly inclusive, meaning "including, but not limited to." In the description of the specification, terms such as "one embodiment," "some embodiments," "exemplary embodiment," "example," "specific example," or "some examples" are intended to indicate that a particular feature, structure, material, or characteristic associated with that embodiment or example is included in at least one embodiment or example of this disclosure. The illustrative representations of the above terms do not necessarily refer to the same embodiment or example. Furthermore, a particular feature, structure, material, or characteristic may be included in any suitable manner in any one or more embodiments or examples; that is, although they may be incorporated in embodiments or examples using the above terms for reasons such as order and position, it does not limit them to be incorporated in combination by a single embodiment or example.

[0024] In the description of this invention, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined with "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of embodiments of this disclosure, unless otherwise stated, "a plurality of" means two or more. Furthermore, for example, the description may use the prefix "A" or "B" to describe the same type of nouns as two independent entities. In this case, the corresponding features defined with "A" and "B" are used only to distinguish between similar entities and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features.

[0025] In the description of this invention, the expression “A and / or B” (where A and B are used to formally represent specific features) will be used. The corresponding expression includes the following three combinations: only A, only B, and a combination of A and B.

[0026] As used in this invention, “about,” “approximately,” or “approximately” includes the stated value and the average value within an acceptable range of deviation from a particular value, wherein the acceptable range of deviation is determined by those skilled in the art taking into account the measurement under discussion and the error associated with the measurement of the particular quantity (i.e., the limitations of the measurement system).

[0027] Furthermore, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0028] To more clearly illustrate the technical solution of the embodiments of the present invention, a brief introduction to the basic working mechanism of the atomic gravimeter is given before introducing the technical solution. The atomic gravimeter uses Raman laser to split, reflect, and combine atomic wave packets. Atoms undergo free evolution along two coherent paths, and the gravitational field causes a fixed optical path difference between the matter waves corresponding to the two coherent paths. As the atoms evolve freely, the phase difference accumulates continuously, and interference fringes are formed when the two matter waves converge again.

[0029] The expression for interference fringes is: ; in, Let be the relative population of the atomic group at the ground state energy level, A be the contrast of the interference fringes, C be the DC bias, ω be the angular frequency, and x be the chirp rate. This is the phase difference caused by the atomic interference process.

[0030] The expression for interference fringes reveals a definite mathematical correspondence between them and gravitational acceleration. Gravitational acceleration can be derived by analyzing the interference fringes. However, atomic gravimeters are susceptible to various noise sources during operation, and these noise disturbances generate parasitic phases. These parasitic phases, superimposed on the interference signal, cause fringe shifts, resulting in systematic and random errors in the calculated gravitational acceleration. Therefore, it is essential to compensate for the parasitic phases caused by noise to improve the accuracy of gravitational acceleration measurements.

[0031] In existing sensitivity function compensation schemes, the expression for the sensitivity function is:

[0032] in, For effective rabi frequency, For the time of free evolution of atoms, Let t be the duration of the laser pulse, and t be the current time. In practical applications, the duration of the laser pulse... This is usually much smaller than the free evolution time T of an atom.

[0033] From the expression of the sensitivity function, it can be seen that the sensitivity function It can be regarded as a piecewise linear function, which can only describe the linear mapping relationship between vibration and parasitic phase. It can only compensate for the vibration of the mirror, but cannot compensate for other noises under real working conditions, which restricts the further improvement of the accuracy of atomic gravitational acceleration measurement.

[0034] With the continuous development of neural networks and their widespread application in numerous scientific and engineering fields, their significant advantages in data feature extraction and complex mapping relationship representation have been fully verified. Neural networks possess strong nonlinear fitting and adaptive learning capabilities, enabling them to automatically mine potential statistical regularities and intrinsic structures from high-dimensional, noisy data. This characteristic makes neural networks a promising candidate for noise suppression and waveform correction tasks in interferometric signals. Furthermore, training neural networks only requires computer programming, sufficient computing power, and hyperparameter adjustment, avoiding the high cost of active and passive vibration isolation systems. Therefore, this invention introduces neural networks into the field of atomic interferometric signal correction, improving the environmental adaptability and measurement accuracy of atomic gravimeters.

[0035] From a theoretical perspective, under conditions free from external noise interference, the interference fringes output by an atomic gravimeter are standard cosine curves. Therefore, this invention innovatively departs from the traditional approach of compensating only for mirror vibration. Instead, it uses a neural network as the compensation model, sequentially performing a first stage of supervised training and a second stage of optimized training. In the first stage, the theoretical parasitic phase calculated by the sensitivity function is used as the supervisory label for training, allowing the compensation performance of the pre-optimized neural network to approximate that of the sensitivity function. In the second stage, the overall waveform morphology of the interference fringes is used as the optimization target for the neural network, achieving compensation for noise other than mirror vibration.

[0036] In summary, traditional compensation methods relying on sensitivity functions can only provide a linear approximation of vibrations, making them unsuitable for scenarios with multiple noise coupling effects. This invention utilizes neural networks to learn the nonlinear mapping relationship between vibration and phase, achieving adaptive differentiated correction. This method eliminates the need for additional monitoring of physical quantities such as laser phase noise and magnetic field fluctuations, implicitly suppressing parasitic phases formed by the superposition of multiple noise sources. It overcomes the limitations of sensitivity function compensation, significantly reduces phase uncertainty, improves interference fringe contrast, and enhances measurement stability under long-term observation conditions of the atomic gravimeter.

[0037] The technical solutions of the embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0038] Example 1: To address the aforementioned problems, this embodiment provides a neural network-based method for optimizing interferometric fringes in an atomic gravimeter, such as... Figure 1 As shown, the method includes steps 101 to 105, wherein step 101 corresponds to the first stage of supervised training, and steps 102 to 105 correspond to the second stage of optimization training.

[0039] Step 101: Acquire multiple vibration time-series signals, and use the multiple vibration time-series signals to train the neural network to obtain a pre-optimized neural network.

[0040] The vibration time-series signals are acceleration time-domain sequences or velocity time-domain sequences collected along the time axis, covering the entire process of a single atomic interference. Each vibration time-series signal corresponds to one atomic interference process, and the vibration time-series signals mainly reflect the vibration state of the mirror. The vibration time-series signals are used as samples to train the neural network.

[0041] In one implementation, a high-sensitivity accelerometer is used to acquire the acceleration vibration information of a Raman mirror to obtain a vibration timing signal. Since the vibration of the Raman mirror has the most significant impact on the interference fringes, the high-sensitivity accelerometer can be placed near the Raman mirror. The high-sensitivity accelerometer maintains strict timing synchronization and alignment with the atomic interference process of the atomic gravimeter during the acquisition of vibration information.

[0042] In one implementation, the vibration time-series signal is normalized before being input into a pre-optimized neural network for the first stage of supervised training. The purpose of normalization is to ensure that the data format of the vibration time-series signal meets the data format requirements of the neural network. During supervised training, the theoretical parasitic phase calculated by the sensitivity function is used as the supervision label to obtain a stable parameter initialization state, enabling the compensation performance of the pre-optimized neural network to approximate the compensation performance of the sensitivity function.

[0043] The training stop condition for supervised training is that the number of training rounds is greater than the preset number of rounds or the loss value is lower than the preset value.

[0044] In one implementation, step 101 specifically includes: using a sensitivity function to solve for the theoretical parasitic phase corresponding to the vibration time series signal; using the theoretical parasitic phase as a supervision label and multiple vibration time series signals as inputs to train the neural network to obtain a pre-optimized neural network.

[0045] Specifically, a first loss function can be used to train the neural network. The expression for the first loss function is: ; in, This is the first loss; Let i be the predicted parasitic phase corresponding to the i-th vibration time sequence signal; is the theoretical parasitic phase corresponding to the i-th vibration timing signal; N is the number of vibration timing signals used in one round of training.

[0046] The final trained pre-optimized neural network meets the following requirements:

[0047] in, The predicted parasitic phase corresponding to a certain vibration time series signal. For a certain vibration timing signal, For sensitivity function, For neural network parameters, For neural network expressions, This is the theoretical parasitic phase corresponding to a certain vibration time sequence signal.

[0048] Step 102: Input the vibration timing signal into the pre-optimized neural network to obtain the predicted parasitic phase.

[0049] Multiple normalized vibration time-series signals are sequentially input into a pre-optimized neural network to obtain the predicted parasitic phase of each vibration time-series signal. This predicted parasitic phase can compensate for the interference caused by the vibration of the mirror.

[0050] It should be noted that, in order to reduce the amount of data collected, the samples in steps 101 and 102 can be shared. That is, the same vibration time series signal can be used for the first stage of supervised training and the second stage of optimization training, respectively. Of course, the more data, the better the training effect of the neural network. Therefore, without considering the amount of data collected, vibration time series signals collected in different time periods can be used to train the neural network in steps 101 and 102. The specific choice can be made according to the actual situation.

[0051] Step 103: Obtain the original interference signal that is time-aligned with each vibration timing signal, and compensate the corresponding original interference signal according to the predicted parasitic phase to obtain the compensated interference signal.

[0052] When compensating for the original interference signal, it is necessary to strictly ensure timing alignment.

[0053] Step 104: Embed the differentiable cosine fitting module into the pre-optimized neural network, and use the differentiable cosine fitting module to fit multiple consecutive compensation interference signals to obtain compensation interference fringes.

[0054] In this embodiment, the differentiable cosine fitting module is embedded into the computation flow of the pre-optimized neural network. It is differentiable throughout the process and can backpropagate gradients. During training, the network parameters can be updated normally without computational gaps.

[0055] Step 105: Obtain the waveform difference between the fitted waveform curve corresponding to the compensated interference fringes and the standard cosine curve corresponding to the ideal interference fringes. Optimize the pre-optimized neural network with the goal of minimizing the waveform difference to obtain the optimized neural network.

[0056] Among them, the ideal interference fringes are the interference fringes output by the atomic gravimeter under conditions of no external noise interference.

[0057] In the second stage of optimization training, the shape of the waveform curve is used as the training objective to make the fitted waveform curve corresponding to the compensation interference fringes as close as possible to the standard cosine curve.

[0058] The angular frequency of the interference fringes is uniquely determined by inherent hardware parameters such as the equivalent wave vector of the Raman light and the free evolution time of atoms. These are known fixed physical constants and are independent of various interferences such as environmental vibrations, magnetic field disturbances, and laser phase noise. Therefore, in the second stage of training, in order to reduce the amount of fitting and improve efficiency, in the preferred embodiment, the angular frequency can be fixed to the theoretical prior value first, and then the compensation interference signal can be fitted to obtain the compensation interference fringes. This minimizes the waveform difference between the compensation fitting waveform curve and the standard cosine curve, thereby achieving the purpose of optimizing the pre-optimized neural network.

[0059] In a preferred embodiment, since the angular frequency ω has already been configured as a theoretical prior value, it is only necessary to determine the interference fringe contrast A (hereinafter also referred to as amplitude) and phase difference. With a DC bias C, the fitted waveform curve corresponding to the interference fringes can be obtained.

[0060] In this embodiment, the amplitude A and phase difference are solved using the least squares method. By applying a DC bias C, the fitted waveform curve corresponding to the interference fringes can be obtained. The expression for the least squares method is as follows:

[0061] Where N is the number of compensation interference signals required in a single operation; For the chirping rate, Let tof be the i-th compensated interference signal.

[0062] The Gauss-Newton (GN) and Levenberg-Marquardt (LM) methods are used to continuously adjust the parameter vector. Perform iterative updates to minimize the result of the least squares method. During the iterative update process:

[0063] Where k represents the number of iterations; It is the parameter vector at the k-th iteration. ; It is the parameter vector in the (k+1)th round after the update; is the damping factor; I is the identity matrix.

[0064] Wherein, the residual vector r consists of N residuals composition, For the residual of the i-th compensated interference signal, .

[0065] in, Let J be each row of the Jacobian matrix. .

[0066] The amplitude A and phase difference that are minimized by the least squares method result. Substituting the DC bias C into the aforementioned expression for the interference fringes, the fitted waveform curve can be obtained.

[0067] Combination Figure 2 Step 105 specifically includes the following steps: Step 201: Obtain the fitted waveform parameters based on the fitted waveform curve.

[0068] The fitted waveform parameters include the fitted amplitude and the fitted phase, that is, the amplitude and phase obtained using the least squares method. The fitted amplitude is the fitted interference fringe contrast.

[0069] Step 202: Obtain the standard waveform parameters based on the standard cosine curve.

[0070] The standard waveform parameters include standard amplitude and standard phase; the standard amplitude and standard phase are obtained by theoretical calculation.

[0071] Step 203: Determine the total loss based on the fitted waveform parameters and the standard waveform parameters, and optimize the pre-optimized neural network based on the total loss to obtain the optimized neural network.

[0072] First, determine the fitted phase uncertainty based on the fitted amplitude and fitted phase; then determine the standard phase uncertainty based on the standard amplitude and standard phase. The fitted phase uncertainty and the standard phase uncertainty are calculated in the same way, and can both be determined using the following expression for phase uncertainty: ; in, Let J be the phase uncertainty; J is the Jacobian matrix. This is the standard estimate of the residuals; , r is the residual vector, and N is the number of compensation interference signals used in a single fitting.

[0073] Then, the amplitude loss is obtained based on the fitted amplitude and the standard amplitude, and the phase uncertainty loss is obtained based on the fitted phase uncertainty and the standard phase uncertainty.

[0074] Obtain the amplitude difference between the fitted amplitude and the standard amplitude, and calculate the square of the amplitude difference to obtain the amplitude loss; obtain the phase uncertainty difference between the fitted phase uncertainty and the standard phase uncertainty, and calculate the square of the phase uncertainty difference to obtain the phase uncertainty loss.

[0075] Finally, the magnitude loss and phase uncertainty loss are weighted and summed to obtain the total loss.

[0076] Specifically, the total loss can be determined using a second loss function, the expression of which is: ; in, For the total loss, As the first hyperparameter, For amplitude loss, This is the second hyperparameter. For phase uncertainty loss, the first hyperparameter Second hyperparameter All can be adjusted according to the actual situation.

[0077] In the second stage of optimization training, the simplistic approach of using pointwise error (such as mean square error) as the sole optimization objective was abandoned. Instead, the learning direction of the network was simultaneously constrained from two dimensions: waveform morphology and phase accuracy. This ensured that the fitted cosine curve covered as many sampling points as possible along the vertical axis (amplitude), minimizing phase estimation uncertainty and thus achieving higher statistical confidence in the fitting result. The neural network directly used the quality of the final phase extraction (including waveform coverage and phase uncertainty) as the basis for calculating the loss function, realizing a collaborative learning mechanism where "correction serves fitting, and fitting guides correction."

[0078] During actual training, the inventors discovered that if only vibration information collected during the atomic interferometry process is selected for phase compensation—that is, if only vibration signals within the interference period are used for phase compensation—vibration information before and after the interference is lost, failing to maximize the optimization of compensation performance. This is because there is a time lead or lag effect between the vibration information measured within the interference period and the actual vibration acting on the mirror. If only vibration information within the interference period is extracted, the trend information of vibration changes before and after the interference is lost. Furthermore, the neural network cannot learn the temporal delay characteristics of the sensor-mirror system, resulting in a large deviation in the parasitic phase of the vibration predicted by the neural network. To enable the vibration timing signal to more accurately reflect the actual vibration, step 101 specifically includes the following steps: Before atomic interferometry, vibration information from an atomic gravimeter is collected to obtain a forward-spreading vibration signal. During atomic interferometry, vibration information from an atomic gravimeter is collected to obtain an intermediate vibration signal. After atomic interferometry, vibration information from an atomic gravimeter is collected to obtain a backward-spreading vibration signal. The forward-spreading vibration signal, intermediate vibration signal, and backward-spreading vibration signal are then spliced ​​together in chronological order to obtain a vibration timing signal.

[0079] In one implementation, the final spliced ​​vibration time-series signal can have a dimension of 8000, of which the intermediate vibration signal, which strictly matches the timing within the atomic interference period, has a dimension of 7102, corresponding to the vibration acceleration sequence acquired within a 160ms interference duration at a sampling frequency of 50kHz. By supplementing and extending sampling points at the front and back ends of the 7102-dimensional intermediate vibration signal, the vibration change information before and after the interference is incorporated into the input vibration time-series signal. This allows the neural network to fully learn the lead or lag characteristics between the vibration sensor and the reflector, improving the prediction accuracy of the parasitic phase of the vibration.

[0080] The input dimension of the corresponding neural network is also set to 8000. The structure of the neural network is shown in Table 1 below.

[0081] Table 1. Structure of Neural Networks

[0082] It is worth noting that the neural network of the present invention can be any one of the following neural networks with one-dimensional data input: one-dimensional convolutional neural network (1D-CNN), recurrent neural network (RNN), long short-term memory network (LSTM), one-dimensional residual network (ResNet-1D), and fully-connected neural network (FCNN).

[0083] In this invention, a first-stage supervised training is performed on the neural network to initialize and stabilize its parameters. Then, a second-stage optimization training is conducted using a standard cosine curve as the learning target, gradually adjusting the network parameters to make the fitted waveform curve approximate the standard cosine curve, thereby minimizing interference and ultimately obtaining an optimized neural network. In practical use, the optimized neural network is directly used to perform phase compensation on the interference signal from the atomic gravimeter, ensuring that the compensated interference signal is essentially a clean, interference-free signal. This allows the fitted interference fringes to closely match the actual measurement, achieving the goal of optimizing the interference fringes and improving the measurement accuracy of the atomic gravimeter.

[0084] Example 2: Based on the aforementioned Embodiment 1, this embodiment trains a fully connected neural network and verifies the training effect.

[0085] See Figure 3a and Figure 3b During training, one epoch constitutes one training round; each round has a batch size of 20, meaning 20 independent vibration timing signals are selected per round; each vibration timing signal contains 8000 sampling points. This invention consists of a first stage of supervised training and a second stage of optimization training.

[0086] The first stage of supervised training yields a pre-optimized neural network: The cleaned and normalized vibration time-series signal is fed into the neural network, and the network's forward computation outputs a predicted parasitic phase. The predicted parasitic phase is compared with pre-set supervision labels to calculate the first loss. Backpropagation is performed based on the first loss, and the network weight parameters are updated using gradient descent. This process is iterated until the network converges, completing the first stage of supervised training and obtaining the pre-optimized neural network. The effectiveness of the pre-optimized neural network is then validated using a test set. The first stage relies solely on the supervision labels to construct the first loss function, completing the initial learning of network parameters and providing a parameter foundation for the second stage of optimization training.

[0087] The pre-optimized neural network is further optimized through a second stage of training: Twenty sets of 8000-dimensional vibration time-series signals are input into the pre-optimized neural network in each batch, and the network predicts the corresponding parasitic phase. Phase compensation is performed on the original interference signal using the predicted parasitic phase, followed by cosine fitting to solve for the fitting amplitude, phase, and DC bias, resulting in compensated interference fringes. The total loss value is calculated based on the fitted waveform parameters corresponding to the 20 sets of samples. The network parameters are updated again using backpropagation of the total loss. The epoch iteration is repeated continuously. Training stops when the performance of the pre-optimized neural network reaches the set requirements, resulting in the optimized neural network. Finally, a test set is used to verify the compensation effect of the optimized neural network. In this second stage, instead of relying solely on supervised labels, a second loss function is constructed using waveform parameters to constrain network learning and improve phase compensation accuracy.

[0088] See Figure 4 and Figure 5 ,exist Figure 4 and Figure 5 The horizontal axis represents the number of training rounds, and the vertical axis represents the loss value. Figure 4 The graph shows how the training loss value changes with each training round during the first phase of training. Figure 5 The graph shows how the optimal loss value, determined based on the sensitivity function, changes with the number of training epochs. From Figure 4 and Figure 5As can be seen, a pre-optimized neural network was obtained after 6000 training rounds. The compensation performance of the pre-optimized neural network is close to that of the sensitivity function. In the first 100 rounds, the training loss value was rapidly converged. From the 100th to the 1000th round, it entered the fine-tuning stage. From the 1000th to the 6000th round, the training loss gradually stabilized at 0.0015.

[0089] The actual generalization ability of the pre-optimized neural network was verified on a 3-hour test set. The average loss on the test set was 0.0016, indicating that the pre-optimized neural network did not exhibit overfitting and had good generalization ability.

[0090] Converting the average loss into the prediction bias of a single sample provides a more intuitive understanding of the prediction accuracy of the pre-optimized neural network. The conversion process is as follows: an average loss of 0.0016 corresponds to a root mean square error of approximately 0.04, meaning the prediction bias between the parasitic phase output of the pre-optimized neural network and the supervision label is approximately ±0.04 radians. Furthermore, based on the fundamental physical relationships of an atomic gravimeter, the prediction bias can be converted into chirp rate bias. Chirp rate bias can be used to assess the impact of phase error on the final gravity measurement result. The conversion result is as follows: the chirp rate bias corresponding to the prediction bias is approximately ±1.26.

[0091] in, For chirp rate deviation; The value represents the prediction bias; 0.071 represents the time for free evolution of atoms, in seconds.

[0092] By converting between the prediction bias and the chirp rate bias described above, the chirp rate corresponding to the compensated interference signal is obtained, thereby determining the waveform curve corresponding to the compensated interference signal, such as... Figure 7 As shown.

[0093] The following is combined Figure 6 and Figure 7 This demonstrates that the compensation performance of the pre-optimized neural network approximates the compensation performance of the sensitivity function. Figure 6 The image shown is a waveform obtained by compensating using a sensitivity function. Figure 6 and Figure 7 In the figure, the vertical axis is tof(time) (of-flight) refers to atomic flight The detected atomic population signal; the horizontal axis chirp represents the Raman laser chirp rate; discrete dots represent the compensated interference signal; the solid line represents the cosine fitting result. Combined with... Figure 6 and Figure 7It can be seen that the waveform curve obtained by the pre-optimized neural network correction is basically consistent with the waveform curve obtained by the sensitivity function correction, proving that the compensation performance of the pre-optimized neural network is close to the compensation performance of the sensitivity function, and has reached the compensation performance requirements of the first stage.

[0094] The following is combined Figures 8-12 This demonstrates the effectiveness of optimizing the compensation effect of the neural network. Figure 8 This graph shows how the loss value changes with each training epoch during the second phase of training. Figure 9 The graph shows how the optimal loss value for the second stage changes with the number of training epochs. Figure 8 and Figure 9 In the diagram, the horizontal axis represents the number of training epochs, and the vertical axis represents the loss value. From... Figure 8 and Figure 9 As can be seen, the training loss rapidly decreased from 0.0105 to 0.0016 in the first 500 training rounds, a decrease of over 80%. After 1000 training rounds, the training loss value entered a stable period. In the curve of the training loss value change, several discrete spikes and outliers are normal phenomena and do not affect the overall training results; combined with Figure 8 and Figure 9 As can be seen, the gap between the training loss value and the optimal loss value gradually narrows.

[0095] The conversion formula from the first round of training is still used to convert the loss value into chirp rate bias in order to obtain the fitted waveform curve after further compensation by the optimized neural network (i.e., Figure 10 The cosine curve in (2), where, Figure 10 The circular dots in the diagram represent the interference signal after further compensation through optimized neural networks. Figure 10 The square points in the diagram represent the interference signal after compensation by the sensitivity function. These square points are then fitted into a cosine curve 1.

[0096] Compared to Figure 7 , Figure 10 The interference signal, after further compensation through optimized neural network, is basically closely surrounding its corresponding cosine curve, with significantly reduced dispersion and effective reduction of phase uncertainty of interference fringes. By separating two points on the same horizontal coordinate (i.e., the two sampling points boxed in the figure), they are distributed in different positions according to the correct interference fringe trajectory, and the correction direction shows differences related to vibration characteristics. The optimized interference fringes correspond to larger amplitudes and smaller phase uncertainties, thus having higher contrast and signal-to-noise ratio.

[0097] Figure 11 The comparison results of the sensitivity function correction method and the optimized neural network correction method on phase uncertainty are presented. Figure 11In the graph, the horizontal axis represents the sample sequence number, and the vertical axis represents the phase uncertainty. Curve 1 represents the correction method using a sensitivity function, and curve 2 represents the correction method using an optimized neural network. Figure 11 As can be seen, the phase uncertainty of the sensitivity function correction method exhibits a large fluctuation range with the increase of the sample sequence number. The phase uncertainty deviates significantly from the mean at multiple sample sequence numbers, and the curve fluctuates dramatically. In contrast, the curve corresponding to the optimized neural network is generally stable with relatively smaller fluctuations, demonstrating superior consistency and robustness. The above comparison intuitively illustrates to a certain extent that the method provided in Embodiment 1 can effectively suppress vibration noise and other noise, further ensuring the stability of phase compensation.

[0098] like Figure 12 The figure shows a comparison of Allan bias between the sensitivity function correction method and the optimized neural network correction method. Curve A represents the sensitivity function correction method, and curve B represents the optimized neural network correction method. Figure 12 The horizontal axis represents integration time, and the vertical axis represents Allan deviation; from Figure 12 As can be seen, the Allan bias curves of both methods show a rapid decreasing trend with the increase of integration time. Furthermore, over the entire time range, the Allan bias of the optimized neural network is always less than that of the sensitivity function correction method at the same integration time. This further illustrates that the optimization neural network correction method is more effective in reducing Allan bias and improving long-term stability.

[0099] Example 3: like Figure 13 The diagram shown is a schematic representation of a neural network-based atomic gravimeter interferometric fringe optimization device according to an embodiment of the present invention. This neural network-based atomic gravimeter interferometric fringe optimization device includes one or more processors 41 and a memory 42.

[0100] Processor 41 and memory 42 can be connected via a bus or other means. Figure 13 Taking the example of a connection between China and Israel via a bus.

[0101] The memory 42, as a non-volatile computer-readable storage medium, can be used to store non-volatile software programs and non-volatile computer-executable programs, such as the neural network-based atomic gravimeter interferometric fringe optimization method in the above embodiment. The processor 41 executes the neural network-based atomic gravimeter interferometric fringe optimization method by running the non-volatile software program and instructions stored in the memory 42.

[0102] Memory 42 may include high-speed random access memory, and may also include non-volatile memory, such as at least one disk storage device, flash memory device, or other non-volatile solid-state storage device. In some embodiments, memory 42 may optionally include memory remotely located relative to processor 41, which can be connected to processor 41 via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0103] The program instructions / modules are stored in memory 42 and, when executed by one or more processors 41, execute the neural network-based atomic gravimeter interferometric fringe optimization method described in the above embodiments.

[0104] This invention also provides a computer storage medium storing computer program instructions; when executed by a processor, the computer program instructions implement the neural network-based atomic gravimeter interferometric fringe optimization method provided in this invention.

[0105] Those skilled in the art will readily understand that the above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing interferometric fringes in an atomic gravimeter based on a neural network, characterized in that, include: Multiple vibration time-series signals are acquired, and the neural network is trained using the multiple vibration time-series signals to obtain a pre-optimized neural network; wherein each vibration time-series signal corresponds to one atomic interference process; The vibration timing signal is input into the pre-optimized neural network to obtain the predicted parasitic phase; Obtain the original interference signal that is time-aligned with each of the vibration timing signals, and compensate the corresponding original interference signal according to the predicted parasitic phase to obtain the compensated interference signal; The differentiable cosine fitting module is embedded in the pre-optimized neural network, and the differentiable cosine fitting module is used to fit multiple consecutive compensation interference signals to obtain compensation interference fringes. The waveform difference between the fitted waveform curve corresponding to the compensated interference fringes and the standard cosine curve corresponding to the ideal interference fringes is obtained. The pre-optimized neural network is optimized with the goal of minimizing the waveform difference to obtain the optimized neural network.

2. The method for optimizing interferometric fringes of an atomic gravimeter according to claim 1, characterized in that, The waveform difference between the fitted waveform curve corresponding to the compensated interference fringes and the standard cosine curve corresponding to the ideal interference fringes includes: The fitted waveform parameters are obtained based on the fitted waveform curve. The standard waveform parameters are obtained based on the standard cosine curve. The total loss is determined based on the fitted waveform parameters and the standard waveform parameters. The pre-optimized neural network is then optimized based on the total loss to obtain an optimized neural network.

3. The method for optimizing interferometric fringes of an atomic gravimeter according to claim 2, characterized in that, The fitted waveform parameters include fitted amplitude and fitted phase, and the standard waveform parameters include standard amplitude and standard phase; determining the total loss based on the fitted waveform parameters and the standard waveform parameters includes: The fitting phase uncertainty is determined based on the fitting amplitude and the fitting phase. The standard phase uncertainty is determined based on the standard amplitude and the standard phase. The amplitude loss is obtained based on the fitted amplitude and the standard amplitude, and the phase uncertainty loss is obtained based on the fitted phase uncertainty and the standard phase uncertainty. The total loss is obtained by weighted summation of the amplitude loss and the phase uncertainty loss.

4. The method for optimizing interferometric fringes of an atomic gravimeter according to claim 2, characterized in that, The method further includes: The total loss is determined using a second loss function, the expression of which is: ； in, For the total loss, As the first hyperparameter, For the amplitude loss, This is the second hyperparameter. This refers to the phase uncertainty loss.

5. The method for optimizing interferometric fringes of an atomic gravimeter according to claim 1, characterized in that, The acquisition of multiple vibration timing signals includes: Before atomic interferometry, vibration information from the atomic gravimeter is collected to obtain a forward-spreading vibration signal; During atomic interference, vibration information from the atomic gravimeter is collected to obtain intermediate vibration signals; After atomic interferometry, vibration information from the atomic gravimeter is collected to obtain a backward-spreading vibration signal; By sequentially splicing the forward-expanding vibration signal, the intermediate vibration signal, and the backward-expanding vibration signal in chronological order, a vibration timing signal is obtained.

6. The method for optimizing interferometric fringes of an atomic gravimeter according to claim 1, characterized in that, The step of training the neural network using multiple vibration time-series signals to obtain a pre-optimized neural network includes: The theoretical parasitic phase corresponding to the vibration time sequence signal is solved using a sensitivity function; Using the theoretical parasitic phase as a supervision label and multiple vibration time-series signals as inputs, the neural network is trained to obtain a pre-optimized neural network.

7. The method for optimizing interferometric fringes of an atomic gravimeter according to claim 6, characterized in that, The method further includes: The neural network is trained using a first loss function, the expression of which is: ； in, This is the first loss; The predicted parasitic phase corresponds to the i-th vibration timing signal; The theoretical parasitic phase corresponds to the i-th vibration timing signal; N is the number of vibration timing signals used in one round of training.

8. The method for optimizing interferometric fringes of an atomic gravimeter according to claim 1, characterized in that, The step of inputting the vibration timing signal into the pre-optimized neural network includes: The vibration time sequence signal is normalized and then input into the pre-optimized neural network.

9. A neural network-based interferometric fringe optimization device for atomic gravimeters, characterized in that, The method includes at least one processor and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the processor for performing the neural network-based atomic gravimeter interferometric fringe optimization method according to any one of claims 1-8.

10. A non-volatile computer storage medium, characterized in that, The computer storage medium stores computer program instructions that, when executed by one or more processors, cause the processors to perform the neural network-based atomic gravimeter interferometric fringe optimization method as described in any one of claims 1-8.

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