Physical field reconstruction methods, devices, equipment and media

Abstract

This application provides a method, apparatus, device, and medium for reconstructing a physical field. The method includes: acquiring observation data, a set of observed locations, and a set of unobserved locations; determining the posterior prediction variance corresponding to each unobserved location based on the observation data and the set of observed locations; determining the next observation location based on the posterior prediction variance corresponding to each unobserved location, and controlling a sensing platform to measure the next observation location; updating the observation data based on the measurement data corresponding to the next observation location, updating the set of observed locations and the set of unobserved locations based on the next observation location, and returning to the step: determining the posterior prediction variance corresponding to each unobserved location in the set of unobserved locations; and outputting the reconstruction result corresponding to the physical field if preset conditions are met. In this application, during the physical field reconstruction process, the next measurement location is dynamically selected based on the current observation data, improving the reconstruction accuracy of the physical field.

Description

Technical Field

[0001] This application relates to the field of physical field measurement technology, and in particular to a physical field reconstruction method, apparatus, equipment and medium. Background Technology

[0002] Physical fields are typically distributed in two-dimensional space, three-dimensional space, space-time combined space, or higher-dimensional space, such as sound velocity fields, temperature fields, salinity fields, pressure fields, flow velocity fields, concentration fields, and electromagnetic fields. In the field of physical field measurement technology, to completely measure all locations of a physical field, a large number of measuring instruments are required, consuming a significant amount of measurement time. Under the condition of limited measurement budget, the current mainstream technology is to reconstruct the physical field using a small amount of observational data.

[0003] In existing technologies, observation data is first obtained at some locations of the physical field through random sampling or sampling along a preset path. Then, based on the collected data, methods such as interpolation, matrix completion, tensor completion, or deep learning are used to predict the physical field values ​​at unobserved locations, thereby restoring the complete physical field and realizing physical field reconstruction.

[0004] However, the aforementioned random sampling or preset path sampling usually determines the measurement location before reconstruction. The sampling process and the reconstruction process are separate from each other, and it is impossible to dynamically select the next measurement location based on the current observation data. In other words, the measurement process of the physical field cannot be dynamically adjusted based on the existing observation results, which reduces the accuracy of the reconstruction of the physical field. Summary of the Invention

[0005] This application provides a physical field reconstruction method, apparatus, device, and medium that can improve the reconstruction accuracy of physical fields.

[0006] In a first aspect, embodiments of this application provide a physical field reconstruction method, the method comprising: Acquire observation data of the physical field on a multidimensional spatial grid, a set of observed locations, and a set of unobserved locations; the set of observed locations includes multiple observed locations, which are measured locations on the multidimensional spatial grid, and the set of unobserved locations includes multiple unobserved locations, which are unmeasured locations on the multidimensional spatial grid; Based on the observed data and the set of observed locations, the posterior prediction variance corresponding to each unobserved location in the set of unobserved locations is determined; the posterior prediction variance is used to characterize the observation weight of the unobserved location. Based on the posterior prediction variance corresponding to each unobserved location, the next observation location is determined, and the sensing platform is controlled to measure the next observation location. Update the observation data according to the measurement data corresponding to the next observation position, update the set of observed positions and the set of unobserved positions according to the next observation position, and return to the step: determine the posterior prediction variance corresponding to each unobserved position in the set of unobserved positions according to the observation data and the set of observed positions; Under the condition that the preset conditions are met, the reconstruction result corresponding to the physical field is output.

[0007] Optionally, determining the posterior prediction variance corresponding to each unobserved location in the unobserved location set based on the observed data and the observed location set includes: Based on the distribution of the physical field on the multidimensional spatial grid, the data structure of the physical field, and the dimension of the multidimensional spatial grid, a Bayesian tensor completion model is constructed; the Bayesian tensor completion model includes model parameters, noise parameters, and prior distribution. Based on the observed data, the model parameters, the noise parameters, and the prior distribution, determine the posterior sample; Based on the posterior sample, determine the posterior prediction variance corresponding to each unobserved location.

[0008] Optionally, determining the posterior sample based on the observed data, the model parameters, the noise parameters, and the prior distribution includes: The likelihood function is determined based on the observed data, the model parameters, and the noise parameters. Based on the likelihood function and the prior distribution, the posterior distribution is obtained; Posterior sampling is performed based on the posterior distribution to obtain posterior samples; the posterior sampling includes Markov chain Monte Carlo sampling, Gibbs sampling, Metropolis-Hastings sampling, Hamiltonian Monte Carlo sampling, importance sampling, and sequential Monte Carlo sampling.

[0009] Optionally, the determination of the likelihood function based on the observed data, the model parameters, and the noise parameters can be expressed by the following formula:

[0010] in, Represents the likelihood function. This represents the observation value at grid position i. Denotes the set of observations at time T. Let N represent the observed data, and N represent the normal distribution. Indicates noise parameters, This represents the physical field value at grid position i; The posterior distribution, obtained from the likelihood function and the prior distribution, can be expressed by the following formula:

[0011] in, Denotes the posterior distribution. Represents the likelihood function. Let d represent the prior distribution, and d represent the distribution with respect to the model parameters. Integrate the points.

[0012] Optionally, the determination of the posterior prediction variance corresponding to each unobserved location based on the posterior sample can be expressed by the following formula:

[0013] in, Let represent the posterior prediction variance corresponding to grid position i, and M represent the number of posterior samples. This represents the physical field value of the posterior sample m at grid position i.

[0014] Optionally, determining the next observation location based on the posterior prediction variance corresponding to each unobserved location includes: The unobserved location corresponding to the maximum a posteriori prediction variance is determined as the next observation location.

[0015] Optionally, the preset conditions include any one of the following: The number of measurements of the physical field reaches a first preset threshold; The ratio between the number of observed locations and the number of grids of the physical field on the multidimensional spatial grid reaches a second preset threshold. The number of times the observed data and the set of unobserved locations are updated reaches a third preset threshold.

[0016] Secondly, embodiments of this application provide a physical field reconstruction device, the device comprising: The acquisition module is used to acquire observation data of the physical field on a multidimensional spatial grid, a set of observed positions, and a set of unobserved positions; the set of observed positions includes multiple observed positions, which are measured positions on the multidimensional spatial grid; the set of unobserved positions includes multiple unobserved positions, which are unmeasured positions on the multidimensional spatial grid. The first determining module is used to determine the posterior prediction variance corresponding to each unobserved location in the unobserved location set based on the observation data and the observed location set; the posterior prediction variance is used to characterize the observation weight of the unobserved location. The second determining module is used to determine the next observation position based on the posterior prediction variance corresponding to each unobserved position, and to control the sensing platform to measure the next observation position. The update module is used to update the observation data according to the measurement data corresponding to the next observation position, update the set of observed positions and the set of unobserved positions according to the next observation position, and return to the step: determine the posterior prediction variance corresponding to each unobserved position in the set of unobserved positions according to the observation data and the set of observed positions; The output module is used to output the reconstruction result corresponding to the physical field when the preset conditions are met.

[0017] Thirdly, embodiments of this application provide an electronic device, including: a processor, a memory, and a program stored in the memory and executable on the processor, wherein the program, when executed by the processor, implements the steps of the method described in the first aspect.

[0018] Fourthly, embodiments of this application provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method described in the first aspect.

[0019] This application provides a physical field reconstruction method, including: acquiring observation data of the physical field on a multi-dimensional spatial grid, a set of observed positions, and a set of unobserved positions; determining the posterior prediction variance corresponding to each unobserved position in the unobserved position set based on the observation data and the set of observed positions; determining the next observation position based on the posterior prediction variance corresponding to each unobserved position, and controlling a sensing platform to measure the next observation position; updating the observation data based on the measurement data corresponding to the next observation position, updating the set of observed positions and the set of unobserved positions based on the next observation position, and returning to the step: determining the posterior prediction variance corresponding to each unobserved position in the unobserved position set based on the observation data and the set of observed positions; and outputting the reconstruction result of the physical field under preset conditions. In this application, the posterior prediction variance corresponding to each unobserved position is determined based on the observation data and the set of observed positions, and then the next observation position is determined based on the posterior prediction variance corresponding to each unobserved position, and the sensing platform is controlled to measure the next observation position. Thus, in the process of physical field reconstruction, the next measurement position is dynamically selected based on the current observation data, improving the reconstruction accuracy of the physical field. Attached Figure Description

[0020] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a flowchart of a physical field reconstruction method provided in an embodiment of this application; Figure 2 This is a schematic diagram illustrating an application scenario of a physical field reconstruction method provided in an embodiment of this application; Figure 3 This is a schematic diagram of the mean square error of physical field reconstruction using different sampling strategies; Figure 4 This is a schematic diagram of the application process of a physical field reconstruction method provided in an embodiment of this application; Figure 5 This is a schematic diagram of the structure of a physical field reconstruction device provided in an embodiment of this application; Figure 6 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0022] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0023] See Figure 1 , Figure 1 This is a flowchart of a physical field reconstruction method provided in an embodiment of this application, such as... Figure 1 As shown, the method includes the following steps: Step 101: Obtain the observation data of the physical field on the multidimensional spatial grid, the set of observed locations, and the set of unobserved locations.

[0024] In this step, the physical field can be discretized as a multidimensional tensor on a multidimensional spatial grid. This involves acquiring observation data, the set of observed locations, and the set of unobserved locations.

[0025] The aforementioned observation data represents data obtained by measuring the physical field through a sensing platform.

[0026] The aforementioned set of observed locations includes multiple observed locations, which are measured locations located on a multidimensional spatial grid.

[0027] The aforementioned set of unobserved locations includes multiple unobserved locations, which are unmeasured locations located on a multidimensional spatial grid.

[0028] Step 102: Based on the observation data and the observed location set, determine the posterior prediction variance corresponding to each unobserved location in the unobserved location set.

[0029] In this step, given the observed data and the set of observed locations, the posterior prediction variance for each unobserved location can be determined based on these data and locations. For detailed implementation methods, please refer to subsequent examples.

[0030] The aforementioned posterior prediction variance is used to characterize the uncertainty of the physical field values ​​at unobserved locations. The larger the posterior prediction variance, the greater the uncertainty of the physical field values ​​at unobserved locations.

[0031] Step 103: Determine the next observation position based on the posterior prediction variance corresponding to each unobserved position, and control the sensing platform to measure the next observation position.

[0032] Optionally, determining the next observation location based on the posterior prediction variance corresponding to each unobserved location includes: The unobserved location corresponding to the maximum a posteriori prediction variance is determined as the next observation location.

[0033] In this step, one optional implementation is to determine the unobserved position corresponding to the largest posterior prediction variance as the next observation position, that is, to determine the unobserved position with the greatest uncertainty of the physical field value as the next observation position.

[0034] It should be noted that the aforementioned sensing platforms include, but are not limited to, unmanned surface vessels, drones, mobile robots, gliders, buoys, and reconfigurable sensor arrays. After determining the next observation location, the coordinates of that location can be sent to the sensing platform to control the platform to measure the physical field at that location.

[0035] In its embodiments, motion constraints, measurement cost constraints, communication constraints, reachability constraints, or batch sampling constraints of the sensing platform can also be added to the process of determining the next observation location, and the unobserved location with the largest posterior prediction variance among the observation locations that satisfy the above constraints can be selected as the next observation location.

[0036] Step 104: Update the observation data according to the measurement data corresponding to the next observation position, update the set of observed positions and the set of unobserved positions according to the next observation position, and return to step: Determine the posterior prediction variance corresponding to each unobserved position in the set of unobserved positions according to the observation data and the set of observed positions.

[0037] In this step, after the sensing platform measures the next observation location, it generates measurement data. This measurement data is then incorporated into the existing observation data to update the observation data; the next observation location is defined as an observed location, thereby updating the set of observed locations and the set of unobserved locations.

[0038] After performing the above steps, the posterior prediction variance for each unobserved location is determined again based on the observed data and the set of observed locations.

[0039] Step 105: If the preset conditions are met, output the reconstruction result corresponding to the physical field.

[0040] In this step, if the preset conditions are met, it indicates that the reconstruction of the physical field is complete, and the complete physical field tensor reconstruction result is output. This reconstruction result can be the posterior mean, posterior median, maximum a posteriori estimate, or a result obtained from the statistics of multiple posterior samples.

[0041] Optionally, the preset conditions include any one of the following: The number of measurements of the physical field reaches a first preset threshold; The ratio between the number of observed locations and the number of grids of the physical field on the multidimensional spatial grid reaches a second preset threshold. The number of times the observed data and the set of unobserved locations are updated reaches a third preset threshold.

[0042] In one optional implementation, when the number of measurements of the physical field reaches a first preset threshold, it indicates that the reconstruction of the physical field is complete, and the reconstruction result corresponding to the physical field can be output. Here, the first preset threshold is a customizable threshold.

[0043] Another optional implementation is that when the observation ratio reaches a second preset threshold, it indicates that the reconstruction of the physical field has been completed, and the reconstruction result corresponding to the physical field can be output. Here, the observation ratio is the ratio between the number of observed locations and the number of grids in the multidimensional spatial grid of the physical field, and the second preset threshold is a customizable threshold.

[0044] Another alternative implementation involves updating the observed data and the set of unobserved locations (which can be understood as the number of iterations). When a third preset threshold is reached, it indicates that the reconstruction of the physical field is complete, and the reconstruction result corresponding to the physical field can be output. Here, the aforementioned third preset threshold is a customizable threshold.

[0045] In this embodiment, based on the observation data and the set of observed locations, the posterior prediction variance corresponding to each unobserved location is determined. Then, based on the posterior prediction variance corresponding to each unobserved location, the next observation location is determined, and the sensing platform is controlled to measure the next observation location. In this way, during the physical field reconstruction process, the next measurement location is dynamically selected based on the current observation data, thereby improving the reconstruction accuracy of the physical field.

[0046] Please see Figure 2 , Figure 2 This is a schematic diagram illustrating an application scenario of a physical field reconstruction method provided in an embodiment of this application. Figure 2 The application scenarios shown include physical field areas, sensing platforms, and data processing centers, wherein the data processing center applies the physical field reconstruction method provided in the embodiments of this application.

[0047] The physical field region is the object to be perceived and reconstructed, and can be discretized into a two-dimensional spatial grid, a three-dimensional spatial grid, a space-time joint grid, or a high-dimensional grid composed of spatial, temporal, and physical attribute dimensions. Among them, the locations for which observation data has been obtained constitute the set of observed locations, and the locations for which observation data has not been obtained constitute the set of unobserved locations.

[0048] The sensing platform can be a ship, unmanned surface vessel, mobile robot, buoy, glider, drone, fixed sensor array or reconfigurable sensor array, etc., used to collect observation data in a physical field area and send the observation data, measurement location, timestamp and sensor status information to the data processing center.

[0049] The data processing center, which can be a server, terminal device, edge computing device, or cloud computing platform, receives observation data, maintains the sets of observed and unobserved locations, constructs a Bayesian tensor completion model, performs posterior sampling, calculates the posterior prediction variance of unobserved locations, and generates the next measurement location and control commands. The data processing center sends the next measurement location and control commands to the sensing platform, which then moves, adjusts sensor states, or switches sampling channels accordingly to complete the next round of measurement.

[0050] The sensing platform collects observation data in the physical field area; the observation data is transmitted to the data processing center via a communication link; the data processing center determines the next measurement location based on the observation data and the Bayesian tensor completion model; and then feeds it back to the sensing platform, thereby realizing an active sensing closed loop.

[0051] To further illustrate the technical effects of the physical field reconstruction method provided in the embodiments of this application, please refer to... Figure 3 , Figure 3 This is a schematic diagram of the mean square error of physical field reconstruction using different sampling strategies.

[0052] Figure 3 In the graph, the horizontal axis represents the observation ratio, and the vertical axis represents the mean square error. The dashed line represents uniform random sampling, and the solid line represents the physical field reconstruction method provided in this application. The results show that as the observation ratio increases from 2% to 10%, the mean square error of the sampling method provided by this scheme decreases faster and is lower than that of uniform random sampling for most observation ratios. This indicates that selecting the next measurement location by using the posterior prediction variance can improve the reconstruction accuracy under a limited measurement budget.

[0053] Optionally, determining the posterior prediction variance corresponding to each unobserved location in the unobserved location set based on the observed data and the observed location set includes: Based on the distribution of the physical field on the multidimensional spatial grid, the data structure of the physical field, and the dimension of the multidimensional spatial grid, a Bayesian tensor completion model is constructed; the Bayesian tensor completion model includes model parameters, noise parameters, and prior distribution. Based on the observed data, the model parameters, the noise parameters, and the prior distribution, determine the posterior sample; Based on the posterior sample, determine the posterior prediction variance corresponding to each unobserved location.

[0054] In this embodiment, a suitable low-rank tensor parameterization form, such as Tucker decomposition or CP decomposition, can be selected based on the data structure of the physical field and application requirements to construct a Bayesian tensor completion model. Different tensor models correspond to different tensor decomposition parameters. The aforementioned Bayesian tensor completion model includes both the multidimensional correlation structure of the physical field and preserves the uncertainties in parameters and prediction results.

[0055] Furthermore, based on the observation data, model parameters, noise parameters, and prior distribution, the posterior sample is determined. For detailed implementation methods, please refer to subsequent examples.

[0056] After obtaining the posterior sample, the posterior prediction variance corresponding to each unobserved location is determined based on the posterior sample.

[0057] Optionally, the determination of the posterior prediction variance corresponding to each unobserved location based on the posterior sample can be expressed by the following formula:

[0058] in, Let represent the posterior prediction variance corresponding to grid position i, and M represent the number of posterior samples. This represents the physical field value of the posterior sample m at grid position i.

[0059] In this embodiment, the physical field is discretized as a multidimensional tensor, and a Bayesian low-rank tensor completion model is constructed based on a small number of initial observations. The predicted distribution of potential physical field values ​​at unobserved locations is obtained through posterior sampling, and the posterior prediction variance of the unobserved locations is used as the active perception evaluation value. The location with the most uncertainty in the current model is selected for subsequent measurement, that is, the unobserved location with the largest posterior prediction variance is determined as the next observation location. After the measurement is completed, the strategy data is incorporated into the observation data, the set of observed locations and the set of unobserved locations, thus forming a closed loop of "observation - modeling - uncertainty assessment - active measurement - reconstruction update".

[0060] Optionally, determining the posterior sample based on the observed data, the model parameters, the noise parameters, and the prior distribution includes: The likelihood function is determined based on the observed data, the model parameters, and the noise parameters. Based on the likelihood function and the prior distribution, the posterior distribution is obtained; Posterior sampling is performed based on the posterior distribution to obtain posterior samples; the posterior sampling includes Markov chain Monte Carlo sampling, Gibbs sampling, Metropolis-Hastings sampling, Hamiltonian Monte Carlo sampling, importance sampling, and sequential Monte Carlo sampling.

[0061] In this embodiment, the likelihood function can be determined based on the observation data, model parameters, and noise parameters.

[0062] Optionally, the determination of the likelihood function based on the observed data, the model parameters, and the noise parameters can be expressed by the following formula:

[0063] in, Represents the likelihood function. This represents the observation value at grid position i. Denotes the set of observations at time T. Let N represent the observed data, and N represent the normal distribution. Indicates noise parameters, This represents the physical field value at grid position i.

[0064] Furthermore, based on the likelihood function and the prior distribution, the posterior distribution is obtained.

[0065] Optionally, the posterior distribution obtained based on the likelihood function and the prior distribution can be expressed by the following formula:

[0066] in, Denotes the posterior distribution. Represents the likelihood function. Let d represent the prior distribution, and d represent the distribution with respect to the model parameters. Integrate the points.

[0067] After obtaining the posterior distribution, posterior sampling can be performed based on the posterior distribution to obtain posterior samples. The aforementioned posterior sampling methods include, but are not limited to, Markov chain Monte Carlo sampling, Gibbs sampling, Metropolis-Hastings sampling, Hamiltonian Monte Carlo sampling, importance sampling, and sequential Monte Carlo sampling.

[0068] For a better understanding of the overall technical solution, please refer to [link / reference]. Figure 4 ,like Figure 4 As shown, the initial observation data of the target physical field on a multi-dimensional spatial grid, the initial set of observation locations, and the set of unobserved candidate locations are first acquired. Specifically, the sensing platform or historical database provides the initial observation data of the target physical field on the multi-dimensional grid. The initial observations can come from random sampling, uniform sampling, historical observations, or a preset sampling scheme; the unobserved locations constitute the set of candidate measurement locations.

[0069] A Bayesian tensor completion model is constructed. Specifically, the latent physics field is represented as a low-rank tensor model, and tensor decomposition parameters, a noise model, and a prior distribution are set. This model not only characterizes the multidimensional correlation structure of the target physics field but also preserves the uncertainties of the parameters and prediction results.

[0070] Based on the current observation data, the posterior distribution is determined and multiple posterior samples are obtained. Specifically, a likelihood function is constructed using the current set of observation locations, their observation data, and the noise model, and the posterior distribution of the model parameters is obtained by combining it with the prior distribution; then, multiple posterior samples are obtained through methods such as MCMC, Gibbs sampling, Metropolis-Hastings, HMC, importance sampling, or SMC.

[0071] Calculate the posterior prediction variance for unobserved candidate locations. Specifically, for each candidate location, calculate the empirical posterior variance of the latent physics prediction based on the posterior samples; this variance characterizes the uncertainty of the current model regarding the physics value at that location.

[0072] The next measurement location is determined based on the posterior prediction variance, and new observation data is collected. Specifically, the candidate location with the largest posterior prediction variance is selected as the next measurement location; if there are constraints related to platform motion, energy consumption, path, or reachability, the candidate location with the largest variance is selected from the candidate set that satisfies the constraints. Subsequently, the sensing platform collects new observation data at this location.

[0073] Update the observation location set, observation data, and physics reconstruction results. Specifically, incorporate the new measurement locations and corresponding observations into the current observation set and observation data set; re-estimate the model posterior based on the updated data, and output or update the reconstructed tensor of the target physics field. Determine if the termination condition is met. Specifically, the termination condition may include reaching the measurement budget, reaching the preset number of iterations, or reaching the preset observation ratio. If the termination condition is not met, return to continue executing the active sensing iteration.

[0074] Output the target physics reconstruction result. Specifically, when the termination condition is met, output the complete physics tensor reconstruction result after termination. The reconstruction result can be the posterior prediction mean.

[0075] See Figure 5 , Figure 5 This is a schematic diagram of the structure of a physical field reconstruction device provided in an embodiment of this application, as shown below. Figure 5 As shown, the physics field reconstruction device 500 includes: The acquisition module 501 is used to acquire observation data of the physical field on a multidimensional spatial grid, a set of observed positions, and a set of unobserved positions; the set of observed positions includes multiple observed positions, which are measured positions located on the multidimensional spatial grid; the set of unobserved positions includes multiple unobserved positions, which are unmeasured positions located on the multidimensional spatial grid. The first determining module 502 is used to determine the posterior prediction variance corresponding to each unobserved location in the unobserved location set based on the observation data and the observed location set; the posterior prediction variance is used to characterize the observation weight of the unobserved location. The second determining module 503 is used to determine the next observation position based on the posterior prediction variance corresponding to each unobserved position, and control the sensing platform to measure the next observation position; The update module 504 is used to update the observation data according to the measurement data corresponding to the next observation position, update the set of observed positions and the set of unobserved positions according to the next observation position, and return to the step: determine the posterior prediction variance corresponding to each unobserved position in the set of unobserved positions according to the observation data and the set of observed positions; The output module 505 is used to output the reconstruction result corresponding to the physical field when the preset conditions are met.

[0076] Optionally, the first determining module 502 is specifically used for: Based on the distribution of the physical field on the multidimensional spatial grid, the data structure of the physical field, and the dimension of the multidimensional spatial grid, a Bayesian tensor completion model is constructed; the Bayesian tensor completion model includes model parameters, noise parameters, and prior distribution. Based on the observed data, the model parameters, the noise parameters, and the prior distribution, determine the posterior sample; Based on the posterior sample, determine the posterior prediction variance corresponding to each unobserved location.

[0077] Optionally, the first determining module 502 is further specifically used for: The likelihood function is determined based on the observed data, the model parameters, and the noise parameters. Based on the likelihood function and the prior distribution, the posterior distribution is obtained; Posterior sampling is performed based on the posterior distribution to obtain posterior samples; the posterior sampling includes Markov chain Monte Carlo sampling, Gibbs sampling, Metropolis-Hastings sampling, Hamiltonian Monte Carlo sampling, importance sampling, and sequential Monte Carlo sampling.

[0078] Optionally, the first determining module 502 is further specifically used for: Based on the observed data, the model parameters, and the noise parameters, the likelihood function can be determined using the following formula:

[0079] in, Represents the likelihood function. This represents the observation value at grid position i. Denotes the set of observations at time T. Let N represent the observed data, and N represent the normal distribution. Indicates noise parameters, This represents the physical field value at grid position i; The posterior distribution, obtained from the likelihood function and the prior distribution, can be expressed by the following formula:

[0080] in, Denotes the posterior distribution. Represents the likelihood function. Let d represent the prior distribution, and d represent the distribution with respect to the model parameters. Integrate the points.

[0081] Optionally, the first determining module 502 is further specifically used for: The determination of the posterior prediction variance for each unobserved location based on the posterior sample can be expressed by the following formula:

[0082] in, Let represent the posterior prediction variance corresponding to grid position i, and M represent the number of posterior samples. This represents the physical field value of the posterior sample m at grid position i.

[0083] Optionally, the second determining module 503 is specifically used for: The unobserved location corresponding to the maximum a posteriori prediction variance is determined as the next observation location.

[0084] The physical field reconstruction device 500 is capable of implementing the various processes applied to the physical field reconstruction method described above. The technical features correspond one-to-one and can achieve the same technical effect. To avoid repetition, it will not be described again here.

[0085] This application also provides an electronic device, including: a processor, a memory, and a program stored in the memory and executable on the processor. When the program is executed by the processor, it implements the various processes of the above-described physical field reconstruction method embodiments and achieves the same technical effect. To avoid repetition, it will not be described again here.

[0086] For details, see Figure 6 This application also provides an electronic device, including a bus 601, a transceiver 602, an antenna 603, a bus interface 604, a processor 605, and a memory 606.

[0087] exist Figure 6 In this document, a bus architecture (represented by bus 601) is used. Bus 601 may include any number of interconnected buses and bridges, linking various circuits including one or more processors represented by processor 605 and memory represented by memory 606. Bus 601 may also link various other circuits such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and therefore will not be described further herein. Bus interface 604 provides an interface between bus 601 and transceiver 602. Transceiver 602 may be a single element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices over a transmission medium. Data processed by processor 605 is transmitted over a wireless medium via antenna 603, which further receives data and transmits data to processor 605.

[0088] Processor 605 manages bus 601 and general processing, and also provides various functions, including timing, peripheral interface, voltage regulation, power management, and other control functions. Memory 606 can be used to store data used by processor 605 during operation.

[0089] Optionally, the processor 605 may be a central processing unit (CPU), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or a complex programmable logic device (CPLD).

[0090] This application also provides a computer-readable storage medium storing a computer program. When executed by a processor, this computer program implements the various processes of the above-described physical field reconstruction method embodiments and achieves the same technical effects. To avoid repetition, it will not be described again here. The computer-readable storage medium may be a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, etc.

[0091] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element. Furthermore, it should be noted that the scope of the methods and apparatuses in the embodiments of this application is not limited to performing functions in the order discussed, but may also include performing functions substantially simultaneously or in the reverse order, depending on the functions involved. For example, the described methods may be performed in a different order than described, and various steps may be added, omitted, or combined. Additionally, features described with reference to certain examples may be combined in other examples.

[0092] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal (which may be a mobile phone, computer, server, air conditioner, or network device, etc.) to execute the methods described in the various embodiments of this application.

[0093] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of this application.

Claims

1. A method for reconstructing a physical field, characterized in that, The method includes: Acquire observation data of the physical field on a multidimensional spatial grid, a set of observed locations, and a set of unobserved locations; the set of observed locations includes multiple observed locations, which are measured locations on the multidimensional spatial grid, and the set of unobserved locations includes multiple unobserved locations, which are unmeasured locations on the multidimensional spatial grid; Based on the observed data and the set of observed locations, the posterior prediction variance corresponding to each unobserved location in the set of unobserved locations is determined; the posterior prediction variance is used to characterize the observation weight of the unobserved location. Based on the posterior prediction variance corresponding to each unobserved location, the next observation location is determined, and the sensing platform is controlled to measure the next observation location. Update the observation data according to the measurement data corresponding to the next observation position, update the set of observed positions and the set of unobserved positions according to the next observation position, and return to the step: determine the posterior prediction variance corresponding to each unobserved position in the set of unobserved positions according to the observation data and the set of observed positions; Under the condition that the preset conditions are met, the reconstruction result corresponding to the physical field is output; Wherein, determining the posterior prediction variance corresponding to each unobserved location in the unobserved location set based on the observed data and the observed location set includes: Based on the distribution of the physical field on the multidimensional spatial grid, the data structure of the physical field, and the dimension of the multidimensional spatial grid, a Bayesian tensor completion model is constructed; the Bayesian tensor completion model includes model parameters, noise parameters, and prior distribution. Based on the observed data, the model parameters, the noise parameters, and the prior distribution, determine the posterior sample; Based on the posterior sample, determine the posterior prediction variance corresponding to each unobserved location.

2. The method according to claim 1, characterized in that, The step of determining the posterior sample based on the observed data, the model parameters, the noise parameters, and the prior distribution includes: The likelihood function is determined based on the observed data, the model parameters, and the noise parameters. Based on the likelihood function and the prior distribution, the posterior distribution is obtained; Posterior sampling is performed based on the posterior distribution to obtain posterior samples; the posterior sampling includes Markov chain Monte Carlo sampling, Gibbs sampling, Metropolis-Hastings sampling, Hamiltonian Monte Carlo sampling, importance sampling, and sequential Monte Carlo sampling.

3. The method according to claim 2, characterized in that, The likelihood function is determined based on the observed data, the model parameters, and the noise parameters, and is expressed by the following formula: in, Represents the likelihood function. This represents the observation value at grid position i. Denotes the set of observations at time T. Let N represent the observed data, and N represent the normal distribution. Indicates noise parameters, This represents the physical field value at grid position i; The posterior distribution, derived from the likelihood function and the prior distribution, is expressed by the following formula: in, Denotes the posterior distribution. Represents the likelihood function. Let d represent the prior distribution, and d represent the distribution with respect to the model parameters. Integrate the points.

4. The method according to claim 1, characterized in that, The posterior prediction variance for each unobserved location is determined based on the posterior sample, expressed by the following formula: in, Let represent the posterior prediction variance corresponding to grid position i, and M represent the number of posterior samples. This represents the physical field value of the posterior sample m at grid position i.

5. The method according to claim 1, characterized in that, The step of determining the next observation position based on the posterior prediction variance corresponding to each unobserved position includes: The unobserved location corresponding to the maximum a posteriori prediction variance is determined as the next observation location.

6. The method according to any one of claims 1-5, characterized in that, The preset conditions include any one of the following: The number of measurements of the physical field reaches a first preset threshold; The ratio between the number of observed locations and the number of grids of the physical field on the multidimensional spatial grid reaches a second preset threshold. The number of times the observed data and the set of unobserved locations are updated reaches a third preset threshold.

7. A physical field reconstruction device, characterized in that, The device includes: The acquisition module is used to acquire observation data of the physical field on a multidimensional spatial grid, a set of observed positions, and a set of unobserved positions; the set of observed positions includes multiple observed positions, which are measured positions on the multidimensional spatial grid; the set of unobserved positions includes multiple unobserved positions, which are unmeasured positions on the multidimensional spatial grid. The first determining module is used to determine the posterior prediction variance corresponding to each unobserved location in the unobserved location set based on the observation data and the observed location set; the posterior prediction variance is used to characterize the observation weight of the unobserved location. The second determining module is used to determine the next observation position based on the posterior prediction variance corresponding to each unobserved position, and control the sensing platform to measure the next observation position; The update module is used to update the observation data according to the measurement data corresponding to the next observation position, update the set of observed positions and the set of unobserved positions according to the next observation position, and return to the step: determine the posterior prediction variance corresponding to each unobserved position in the set of unobserved positions according to the observation data and the set of observed positions; The output module is used to output the reconstruction result corresponding to the physical field when the preset conditions are met; The first determining module is further configured to: Based on the distribution of the physical field on the multidimensional spatial grid, the data structure of the physical field, and the dimension of the multidimensional spatial grid, a Bayesian tensor completion model is constructed; the Bayesian tensor completion model includes model parameters, noise parameters, and prior distribution. Based on the observed data, the model parameters, the noise parameters, and the prior distribution, determine the posterior sample; Based on the posterior sample, determine the posterior prediction variance corresponding to each unobserved location.

8. An electronic device, characterized in that, include: A processor, a memory, and a program stored in the memory and executable on the processor, wherein the program, when executed by the processor, implements the steps of the method as described in any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the method as described in any one of claims 1 to 6.

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