A termite nest detection bayesian inversion method based on integrated physical information neural network and MCMC sampling

Abstract

The application discloses a termite nest detection Bayesian inversion method based on integrated physical information neural network and MCMC sampling, and belongs to the field of underground medium inversion and uncertainty quantification. The application is parallel pre-trained through M randomly initialized physical information neural networks, extracts point-by-point mean and variance of parameter field output on a discrete space grid, and constructs an informationized diagonal Gaussian prior of the physical parameter field space; the parameter field itself is taken as a Markov chain Monte Carlo sampling object, a joint potential energy function containing an informationized prior term, a data likelihood term and a partial differential equation constraint term is constructed to carry out sampling, and when the grid scale is higher than a threshold or the acceptance rate is lower than a lower limit, the Hamilton Monte Carlo method is adaptively switched. The application realizes strict Bayesian inversion and uncertainty quantification, reduces the sampling dimension by one to two orders of magnitude, and is suitable for termite nest detection of ground penetrating radar or resistivity tomography.

Description

Technical Field

[0001] This invention relates to the field of underground medium inversion and uncertainty quantification technology, specifically a Bayesian inversion method for termite nest detection based on integrated physical information neural network and MCMC sampling. Background Technology

[0002] Ground-penetrating radar (GPR) and resistivity tomography (RTT) are currently the mainstream methods for non-destructive detection of termite nests. They work by emitting electromagnetic waves or injecting current into the underground medium, collecting reflected or transmitted signals from the surface or structural surfaces, and then retrieving the physical parameter distribution of the underground medium. However, termite nests are characterized by their strong concealment, irregular distribution, and blurred boundaries. Furthermore, the acquisition of field observation data is limited by the space and cost of measuring point deployment, often resulting in sparse observation data with a low signal-to-noise ratio. Under these conditions, accurately retrieving the physical parameter field of the underground medium from limited observation data is essentially an ill-conditioned nonlinear inversion problem with severe ambiguity.

[0003] Traditional inversion methods typically employ regularization strategies or iterative optimization algorithms to solve the aforementioned inversion problem. These methods only output point estimates of the parameters, failing to quantify the reliability of the inversion results, and are sensitive to initial value selection, easily getting trapped in local optima under strongly nonlinear scenarios. In recent years, Physical Information Neural Networks (PINs) have provided an end-to-end solution paradigm for the inversion problem by embedding partial differential equations into neural network loss functions, alleviating to some extent the dependence of purely data-driven methods on labeled samples. However, existing PIN inversion methods still fall under the category of deterministic inversion, making it difficult to provide information on the uncertainties in the inversion results.

[0004] To quantify the uncertainty of inversion, existing research has incorporated Bayesian inference into the framework of physical information neural networks. One approach is to introduce Dropout random deactivation into the neural network to approximate the uncertainty, but this method lacks rigorous Bayesian probabilistic meaning, resulting in insufficient reliability of the inference results. Another approach is to use a Bayesian physical information neural network combined with variational inference to approximate the true posterior distribution through variational distribution. However, variational inference is essentially a biased approximation of the true posterior, and its accuracy is limited under complex posterior geometries. Other research has used a Bayesian physical information neural network combined with the Hamiltonian Monte Carlo method for posterior sampling. While this can obtain a relatively accurate posterior distribution, this method uses all the weight parameters of the neural network as the sampling object. Since the dimensionality of network weights is usually much higher than the discrete dimensionality of the physical parameter field, and neural networks exhibit parameter non-discrimination, a large number of weight combinations can correspond to the same physical parameter field, leading to extremely low sampling efficiency and high computational cost in the weight space, making it difficult to meet practical engineering needs. Furthermore, the aforementioned Bayesian physical information neural network methods all apply prior distributions to the network weights, but the weights themselves do not have physical meaning and are difficult to effectively encode prior information about the structure of the physical parameter field to be inverted. Under the condition of sparse observation data, they cannot give full play to the prior guidance role. Summary of the Invention

[0005] The purpose of this invention is to provide a Bayesian inversion method for termite nest detection based on integrated physical information neural network and MCMC sampling, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a Bayesian inversion method based on integrated physical information neural networks and Markov chain Monte Carlo sampling, comprising the following steps: acquiring observation data and defining partial differential equations describing the physical process; constructing M randomly initialized physical information neural networks, where M is an integer greater than or equal to 3; pre-training the M physical information neural networks until convergence to obtain M sets of physical parameter field estimates; constructing a discrete spatial grid in the inversion domain, and extracting the physical parameter field outputs of the M physical information neural networks at each grid point to obtain a parameter sample matrix; Based on the parameter sample matrix, the statistical characteristics of the physical parameter field values ​​are calculated at each grid point to construct an information-based prior distribution in the physical parameter field space. Based on Bayes' theorem, a joint potential function is constructed, which includes the prior constraint term corresponding to the information-based prior distribution, the likelihood term corresponding to the observed data, and the physical constraint term corresponding to the partial differential equation. Using the physical parameter field as the sampling object, Markov chain Monte Carlo sampling is performed according to the joint potential function to obtain the posterior sample set of the physical parameter field. Based on the posterior sample set, the posterior statistic is calculated, and the inversion result and uncertainty quantification index are output.

[0007] Furthermore, each of the physical information neural networks takes spatial coordinates as input and physical parameter field values ​​as output. The structures of the physical information neural networks are the same, but the initial weights are different.

[0008] Furthermore, the M physical information neural networks are pre-trained until convergence, specifically including: for each physical information neural network, pre-training is performed using a loss function that includes a fitting term for the observed data and a residual term for the partial differential equation, wherein the loss function is:

[0009] in, For observation data, For the orthogonal operator, For partial differential equation operators, For source terms, Indicates the first A physical information neural network; pre-trained using the Adam optimizer or the L-BFGS optimizer.

[0010] Furthermore, based on the statistical characteristics of the physical parameter field values ​​calculated at each grid point using the parameter sample matrix, an information-based prior distribution in the physical parameter field space is constructed. Specifically, this includes: at each grid point... Above, calculate the physical parameter field output of the M physical information neural network. mean With variance :

[0011] Construct a diagonal Gaussian prior distribution in the physical parameter field space:

[0012] in, For discretized parameter field vectors, The total number of grid points; the variance of the prior distribution. The magnitude of the value reflects the constraint strength at the corresponding grid point location.

[0013] Furthermore, based on the statistical characteristics of the physical parameter field values ​​calculated at each grid point according to the parameter sample matrix, an information-based prior distribution in the physical parameter field space is constructed. This also includes: assigning confidence weights to each network based on the inversion accuracy or loss function convergence value of each physical information neural network on the validation set, wherein the sum of the weights is 1; and calculating the weighted mean and weighted variance at each grid point as the statistical characteristics.

[0014] Furthermore, the joint potential energy function is specifically as follows:

[0015] Wherein, the first term is the prior constraint term corresponding to the aforementioned information prior distribution, the second term is the likelihood term corresponding to the observed data, and the third term is the physical constraint term corresponding to the aforementioned partial differential equation. These are the physical constraint weighting coefficients. The number of observation data points, For the first The noise standard deviation of the observation data.

[0016] Furthermore, Markov chain Monte Carlo sampling is performed using physical parameter fields as the sampling object. Specifically, this includes: using the mean vector of the information prior distribution as the initial state of the Markov chain; sampling candidate physical parameter fields from the proposal distribution, which is a diagonal Gaussian distribution with the current state as the mean, and whose covariance matrix is ​​determined by the product of the square of the global step size scaling factor and the diagonal matrix formed by the point-by-point variance vector of the information prior distribution; using a large step size for exploration at grid points with large variance and a small step size for fine-tuning at grid points with small variance; calculating the joint potential function value of the candidate physical parameter fields, and deciding whether to accept the candidate physical parameter fields based on the acceptance probability.

[0017] in, The joint potential function is defined as follows: after a certain number of preheating steps, posterior samples of the physical parameter field are collected.

[0018] Furthermore, the Markov chain Monte Carlo sampling also includes a Hamiltonian Monte Carlo adaptive switching step: when the size of the discrete space grid exceeds a preset threshold, or when the sampling acceptance rate during the preheating stage is lower than a preset lower limit, the sampling is automatically switched to the Hamiltonian Monte Carlo method. In the Hamiltonian Monte Carlo method, an auxiliary momentum variable is introduced to construct the Hamiltonian, and numerical integration is performed through a leapfrog integrator to update the physical parameter field and the auxiliary momentum variable. The gradient of the joint potential function is calculated using the adjoint state method. After the leapfrog integration is completed, the acceptance of the new physical parameter field is determined according to the Hamiltonian Monte Carlo acceptance probability.

[0019] Furthermore, the preset threshold is a grid point count greater than 10,000, and the preset lower limit is an average acceptance rate of less than 15% for a preset number of consecutive steps during the preheating phase.

[0020] Furthermore, based on the posterior sample set, posterior statistics are calculated, and the inversion results and uncertainty quantification indicators are output. Specifically, this includes: calculating the posterior mean at each grid point as the optimal estimate for inversion and outputting a map of the mean values ​​of the physical parameters; calculating the posterior standard deviation at each grid point and outputting a point-by-point uncertainty map; calculating the confidence interval at each grid point and outputting a confidence interval map; and evaluating the inversion accuracy through relative error, structural similarity index, and confidence interval coverage.

[0021] Furthermore, the method is applied to termite nest detection using ground-penetrating radar or resistivity tomography, wherein the observation data is ground-penetrating radar B-scan echo data or resistivity tomography observation data, and the physical parameter field is the dielectric constant or resistivity spatial distribution of the underground medium.

[0022] Compared with the prior art, the beneficial effects of the present invention are: 1. This invention directly constructs the prior distribution in the physical parameter field space. The mean and variance of the prior directly correspond to the parameter estimates and uncertainties at each spatial location, with clear physical meaning. At the same time, through parallel pre-training of M randomly initialized physical information neural networks, multiple sets of parameter field estimates are extracted at each spatial grid point and point-by-point statistical features are calculated. The information-based prior constructed in this way can objectively reflect the differences in the strength of constraints at different spatial locations. Even in scenarios with sparse observation data or low signal-to-noise ratio, it can still effectively guide the subsequent acceptance to converge to a physically reasonable parameter field region, overcoming the problems of fuzzy physical meaning and non-discrimination caused by applying priors in the weight space of existing Bayesian physical information neural networks. 2. This invention uses the discretized parameter field itself as the sampling object of Markov chain Monte Carlo, rather than the neural network weights. The sampling dimension is reduced from the number of network weights to the number of discrete grid points in the physical parameter field, which can reduce the dimension by one to two orders of magnitude in practical applications. This significantly alleviates the computational pressure caused by high-dimensional space sampling, allowing the standard Markov chain Monte Carlo method to work efficiently in medium-sized inversion problems without incurring the high gradient calculation overhead of the Hamiltonian Monte Carlo method throughout.

[0023] 3. This invention adopts a hybrid sampling architecture that primarily uses standard Markov chain Monte Carlo and adaptively switches to Hamiltonian Monte Carlo. It maintains the simplicity of implementation in small- to medium-scale inversion tasks. When the grid size exceeds a preset threshold or the sampling acceptance rate drops significantly, it automatically switches to the Hamiltonian Monte Carlo method. It uses the potential gradient calculated by the adjoint state method to guide sampling, overcoming the bottleneck of low efficiency of random walks, and taking into account both the versatility and computational efficiency of the method.

[0024] 4. This invention constructs a three-in-one joint potential function comprising an information-based prior term, a data likelihood term, and a partial differential equation constraint term, deeply integrating prior information, observational data, and physical laws within the same Bayesian framework. Specifically, the information-based prior term is determined by the integrated statistical results of multiple physical information neural networks; the data likelihood term characterizes the degree of fit to the observational data; and the physical constraint term ensures that the inversion result satisfies the physical laws described by the partial differential equation. These three terms synergistically constrain the posterior distribution, effectively suppressing the ambiguity of ill-conditioned inversions.

[0025] 5. In the Markov chain Monte Carlo sampling process, this invention automatically adjusts the step size of each dimension of the suggested distribution by utilizing the pointwise variance of the prior distribution. In regions with high uncertainty, a large step size is used to explore and accelerate mixing, while in regions with low uncertainty, a small step size is used for fine-grained search to improve the acceptance rate, thus achieving spatial adaptive optimization of sampling efficiency.

[0026] 6. The parameter field mean plot, point-by-point standard deviation uncertainty plot, and confidence interval plot output by this invention can intuitively reflect the reliability of the inversion results, providing a quantitative risk assessment basis for engineering decisions. In termite nest detection scenarios, it can clearly distinguish between the core area of ​​the nest and the area with ambiguous boundaries, effectively guiding the formulation of subsequent treatment plans.

[0027] 7. The integration mechanism of multiple physical information neural networks suppresses the bias of the pre-training results of a single network through statistical averaging. The pointwise variance objectively reflects the uncertainty of the inversion result at that location, fundamentally improving the robustness of the whole method under conditions of low signal-to-noise ratio and scarce observation data. Attached Figure Description

[0028] Figure 1 This is a comparison chart of the inversion performance of different uncertainty quantification methods provided in an embodiment of the present invention. Subplot (a) corresponds to the inference result of PINN combined with the Dropout method, subplot (b) corresponds to the inference result of Bayesian PINN combined with the variational inference method, subplot (c) corresponds to the inference result of Bayesian PINN combined with the Hamiltonian Monte Carlo method, and subplot (d) is a bar chart comparing the inference results of the three methods for the reaction rate parameter. Figure 2 A flowchart illustrating the overall workflow of a Bayesian inversion method based on integrated physical information neural network and Markov chain Monte Carlo sampling, provided for embodiments of the present invention; Figure 3 A schematic diagram of an integrated PINN information prior construction process provided in an embodiment of the present invention; Detailed Implementation The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] The method in this embodiment is executed by a terminal, which can be a mobile phone, computer, PDA, laptop or desktop computer, etc. Of course, it can also be other devices with similar functions, and this embodiment does not limit them.

[0030] This invention provides a Bayesian inversion method and system based on integrated physical information neural networks and Markov chain Monte Carlo sampling. This method constructs an informational prior of the physical parameter field on a spatial grid through parallel pre-training of M randomly initialized PINNs. The parameter field itself is used as the MCMC sampling object, and adaptively switches to HMC to achieve rigorous Bayesian inversion and uncertainty quantification. Its overall workflow is as follows: Figure 2 As shown, the integrated PINN prior construction process is as follows: Figure 3 As shown.

[0031] Example 1 This embodiment provides a Bayesian inversion method based on an integrated physical information neural network and Markov chain Monte Carlo sampling, using a termite nest detection scenario as an example. A comparison of the inversion performance of different uncertainty quantification methods is provided. Figure 1 As shown, the overall workflow of this method is as follows: Figure 2 As shown, the integrated PINN prior construction process is as follows: Figure 3 As shown.

[0032] This embodiment includes the following steps: Step 1: Observational data acquisition and problem definition.

[0033] Acquire noisy observation data In the termite nest detection scenario, the observation data refers to B-scan echo data of suspected termite nest areas collected by ground-penetrating radar in common-offset or multi-offset modes, or resistivity tomography observation data. Define the partial differential equations describing the physical processes:

[0034] in For physical fields, For the physical parameter field to be inverted, For partial differential equation operators, The source term. In the termite nest detection scenario, the physical parameter field... This represents the spatial distribution of the dielectric constant or resistivity of the underground medium. The observation data were normalized and the noise standard deviation was calculated. Calibration.

[0035] Step 2: Construct and randomly initialize M PINN models.

[0036] Build the basic PINN architecture, using spatial coordinates As input, physical parameter field values For output. Set the integration scale. M is an integer greater than or equal to 3. Different random seeds are used for initialization. Independent PINNs with identical structures but different initial weights: The loss function for each network includes a term for fitting the observed data and a term for the residuals of the partial differential equation:

[0037] in For the orthogonal operator, Indicates the first Each network takes spatial coordinates as input and outputs the parameter field estimates for the corresponding locations.

[0038] Step 3: Integrate PINN parallel pre-training and parameter field extraction.

[0039] right Each independent PINN is pre-trained in parallel until convergence using either the Adam optimizer or the L-BFGS optimizer. Due to different initial parameters, each network explores different local regions of the parameter field space, resulting in... Estimation of different sets of parameter fields.

[0040] In the inversion domain Constructing Discrete Spatial Grids Extract at each grid point The parameter field output of the network: ,get The parameter sample matrix.

[0041] Step 4: Constructing the prior information of the parameter field space.

[0042] For each grid point On Statistical analysis was performed on each sample, and the point-by-point mean and variance were calculated:

[0043] Constructing an information-based diagonal Gaussian prior in the parameter field space:

[0044] in This is the discretized parameter field vector. Mean The best estimate of the ensemble, variance Reflecting point-by-point cognitive uncertainty: regions with strong constraints Small, weakly constrained areas Large. The above prior construction process is as follows: Figure 3 As shown, the point-by-point outputs of M PINNs are statistically aggregated into a prior distribution of the parameter field, and the variance directly reflects the strength of the constraint at each spatial location.

[0045] Step 5: Construct the joint potential function and posterior distribution.

[0046] Based on Bayes' theorem:

[0047] Assuming the observed noise is independently distributed by a Gaussian distribution, construct the likelihood function:

[0048] Define the potential energy function (negative logarithmic posterior):

[0049] in These are the constraint weighting coefficients for the partial differential equation. For a given parameter field Time through forward modeling operator The predicted physical field obtained by solving the partial differential equation, i.e. The first term is the integrated prior term, the second term is the data likelihood term, and the third term is the partial differential equation constraint term.

[0050] Step 6: Markov chain Monte Carlo sampling and Hamiltonian Monte Carlo adaptive switching.

[0051] The standard Markov chain Monte Carlo method (Metropolis-Hastings) is used by default to analyze the parameter fields. Perform sampling: With integrated prior means Initial state Candidate parameter fields are sampled from an adaptive proposal distribution. The proposal distribution is based on the current state. A diagonal Gaussian distribution with mean:

[0052] It is recommended that the step size be scaled point by point by the prior variance, and that a large step size be used for exploration in regions with high uncertainty, and a small step size be used for fine search in regions with low uncertainty.

[0053] Whether to accept a candidate state is determined by the acceptance probability:

[0054] through After preheating, collect posterior samples .

[0055] Hamilton Monte Carlo adaptive switching is automatically triggered in the following scenarios: (1) Mesh size Exceeding the preset threshold ; or (2) the average acceptance rate is less than 15% for 50 consecutive steps during the preheating phase.

[0056] Hamilton Monte Carlo method introduces momentum Construct the Hamiltonian: After switching to Hamilton Monte Carlo, a burn-in phase is also required. Set the number of burn-in steps. During the warm-up phase, all generated samples are excluded from the posterior sample set to ensure the chain converges to a stationary distribution. The warm-up phase also serves to adaptively adjust sampling hyperparameters: dynamically adjusting the step size of the leapfrog integrator based on the real-time acceptance rate. (If the acceptance rate is below 60%, decrease the step size; if it is above 90%, increase the step size), and a diagonal quality matrix can be introduced. The identity matrix is ​​replaced to improve the mixing effect. After preheating, the step size and quality matrix parameters are fixed, and the formal sampling phase begins.

[0057] Execute via frog jump integrator For each step of the numerical integration, the momentum and position variables of the leapfrog integrator are updated sequentially as follows: First, perform a half-step update on the momentum variable:

[0058] Then, perform a full-step update on the position variable:

[0059] Finally, the momentum variable is updated again in half a step:

[0060] in Here are the step size parameters for the frog jump integrator. For the joint potential function with respect to the parameter field The gradient. Preferably, the step size of the frog-jump integrator. The range of values ​​is to The specific value is adaptively determined based on the standard deviation scale of the target distribution to ensure that the acceptance rate of Hamiltonian Monte Carlo sampling remains between 60% and 90%. Potential gradient The sensitivity of the observed residuals to the parameter field is calculated using the adjoint state method, avoiding the computational instability of directly numerically differentiating the partial differential equations. After integration, the following formula determines whether to accept the new state:

[0061] If the new state is accepted, then Use this as the current state; otherwise, retain the original state. .

[0062] During the aforementioned warm-up phase, updates to the current state are used solely to drive Markov chain mixing and do not record any samples; after the warm-up is complete, the new state accepted in each subsequent iteration... All were preserved as valid posterior samples.

[0063] Step 7: Inversion results and uncertainty quantification output.

[0064] In this step, the following is used Each posterior sample refers to a valid sample collected after preheating is completed, excluding any samples generated during the preheating phase; based on posterior samples Calculate the posterior statistic:

[0065] The output includes three types of inversion results: a parameter field mean plot, reflecting the spatial distribution of medium parameters; an uncertainty plot, i.e., the point-by-point standard deviation distribution, indicating the inversion confidence of each spatial location; and a confidence interval plot, corresponding to the 95% confidence interval, providing quantitative risk assessment for engineering decisions.

[0066] Through relative error The Structural Similarity Index (SSIM) and Confidence Interval Coverage (CIC) are used to assess inversion accuracy. Among these, relative error... according to Calculation: SSIM is calculated according to the standard structural similarity index definition; CIC is defined as the proportion of actual covered posterior sample points falling within the 95% confidence interval. If accuracy is insufficient, the integration scale can be adjusted retrospectively. Grid density Alternatively, the sampling hyperparameters can be re-inverted.

[0067] An optional embodiment differs from Embodiment 1 in that when the size of the discrete spatial grid exceeds a preset threshold, the Hamiltonian Monte Carlo method is directly used for sampling, without going through the standard Markov chain Monte Carlo stage.

[0068] Specifically, in step six, when At this time, the warm-up and sampling process of the standard Markov chain Monte Carlo method is skipped, and the Hamiltonian Monte Carlo sampler is directly initialized. This is done by integrating prior means. Initial state Auxiliary momentum variables are sampled from the standard normal distribution. Similarly, perform Hamilton Monte Carlo warm-up, discarding the previous steps. The sampling process iterates through the samples, and during the warm-up period, the frog-jump step size or quality matrix is ​​adaptively adjusted based on the acceptance rate to optimize sampling efficiency. After warm-up, the sampling is performed using a frog-jump integrator. Numerical integration updates the physical field parameters and auxiliary momentum variables. This is performed via a leapfrog integrator. The physical parameters and auxiliary momentum variables are updated through numerical integration, and the potential energy gradient is calculated using the adjoint state method. After integration, the Hamiltonian Monte Carlo acceptance probability is used to determine whether to accept the new state. This process is repeated until a sufficient number of posterior samples are collected.

[0069] The other steps in this embodiment are the same as in Embodiment 1, and will not be repeated here.

[0070] An optional embodiment differs from Embodiment 1 in that, after the M PINN parallel pre-training is completed, the parameters at each grid point are... We perform weighted statistics on each sample to construct an improved information-based prior.

[0071] Specifically, based on the inversion accuracy or loss function convergence value of each PINN on the validation set, a confidence weight is assigned to each network. ,satisfy The point-by-point mean and variance are calculated using the following formula:

[0072] The network with high inversion accuracy is given a larger weight, while the network with low inversion accuracy is given a smaller weight, so that the prior distribution is more concentrated in the parameter estimation region with high confidence.

[0073] The other steps in this embodiment are the same as in Embodiment 1, and will not be repeated here.

[0074] An optional embodiment differs from Embodiment 1 in that, when pre-training the M physical information neural networks, a two-parameter coupling loss term is added to the loss function.

[0075] Specifically, when the physical parameter field to be inverted contains two correlated parameters, a coupling loss term is introduced into the loss function. This is used to constrain the physical relationship between two parameters, using the dielectric constant. and conductivity For example, the coupling loss term is constructed based on the electromagnetic wave equation:

[0076] The total loss function is:

[0077] in These are the coupling loss weighting coefficients.

[0078] The other steps in this embodiment are the same as in Embodiment 1, and will not be repeated here.

[0079] An optional embodiment differs from Embodiment 1 in that the number of preheating steps in the standard Markov chain Monte Carlo method in step six is ​​increased. and posterior sample size The adjustments are made dynamically based on the convergence diagnosis results of the actual problem.

[0080] Specifically, during Markov chain Monte Carlo sampling, the potential scale reduction factor of the currently collected samples is calculated at preset intervals. ,when When the sample size falls below a preset threshold, the chain is considered converged, and the preheating phase is terminated. The preset threshold is 1.1. In the posterior sample collection phase, the effective sample size is calculated after collecting a preset number of new samples. Sampling is terminated when the effective sample size meets the preset accuracy requirement.

[0081] The other steps in this embodiment are the same as in Embodiment 1, and will not be repeated here.

[0082] An optional embodiment differs from Embodiment 1 in that the confidence interval in step seven uses the highest posterior density interval.

[0083] Specifically, for the posterior sample at each grid point, the kernel density estimation method is used to estimate the posterior probability density curve. At a given confidence level, the region with the highest probability density is identified as the highest posterior density interval. The sharpness of convergence is judged by the ratio of the width of the highest posterior density interval to the posterior mean: if the width is less than 10% of the posterior mean, it is considered sharp convergence, and the inversion result has high reliability; if the width is greater than 20% of the posterior mean, it is considered to have high uncertainty.

[0084] The other steps in this embodiment are the same as in Embodiment 1, and will not be repeated here.

[0085] An optional embodiment differs from Embodiment 1 in that the spatial grid in step three adopts a non-uniform grid division strategy.

[0086] Specifically, in the inversion domain, the grid is refined in areas where the parameter field changes drastically, while a sparse grid is used in areas where the parameter field changes gradually. The non-uniform grid is divided based on: the spatial distribution of the parameter field gradients output by each PINN pre-training; or the spatial coverage density distribution of the observation data; or key areas of interest indicated by prior geological or engineering information. Under the non-uniform grid, the prior statistics of each grid point are calculated separately according to the actual grid location.

[0087] The other steps in this embodiment are the same as in Embodiment 1, and will not be repeated here.

[0088] Those skilled in the art will recognize that the modules and method steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0089] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the devices, equipment, and modules described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0090] In addition, the functional modules in the various embodiments of the present invention can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0091] If the aforementioned functions are implemented as software functional modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program instructions, such as USB flash drives, portable hard drives, read-only storage servers, random access storage servers, magnetic disks, or optical disks.

[0092] Furthermore, it should be noted that the combination of the various technical features in this case is not limited to the combination methods described in the claims of this case or the combination methods described in the specific embodiments. All technical features described in this case can be freely combined or combined in any way, unless they contradict each other.

[0093] It should be noted that the above examples are merely specific embodiments of the present invention, and the present invention is obviously not limited to the above embodiments, with many similar variations. All modifications that can be directly derived or conceived by those skilled in the art from the content disclosed in this invention should fall within the protection scope of this invention.

[0094] The above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., 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 Bayesian inversion method for termite nest detection based on integrated physical information neural network and MCMC sampling, characterized in that, Includes the following steps: Acquire observational data and define partial differential equations describing the physical processes; Construct M randomly initialized physical information neural networks, where M is an integer greater than or equal to 3; M physical information neural networks are pre-trained until convergence to obtain M sets of physical parameter field estimates; A discrete spatial grid is constructed in the inversion domain, and the physical parameter field outputs of M physical information neural networks are extracted at each grid point to obtain the parameter sample matrix. Based on the parameter sample matrix, the statistical characteristics of the physical parameter field values ​​are calculated at each grid point, and an information-based prior distribution on the physical parameter field space is constructed. Based on Bayes' theorem, a joint potential energy function is constructed, which includes the prior constraint term corresponding to the information prior distribution, the likelihood term corresponding to the observation data, and the physical constraint term corresponding to the partial differential equation. Using the physical parameter field as the sampling object, Markov chain Monte Carlo sampling is performed according to the joint potential energy function to obtain the posterior sample set of the physical parameter field. The posterior statistic is calculated based on the posterior sample set, and the inversion results and uncertainty quantification index are output.

2. The Bayesian inversion method for termite nest detection based on integrated physical information neural network and MCMC sampling as described in claim 1, characterized in that, Each of the physical information neural networks takes spatial coordinates as input and physical parameter field values ​​as output. The structures of the physical information neural networks are the same, but the initial weights are different.

3. The Bayesian inversion method for termite nest detection based on integrated physical information neural network and MCMC sampling as described in claim 1, characterized in that, Pre-training each of the M physical information neural networks until convergence is performed, specifically including: For each of the physical information neural networks, pre-training is performed using a loss function that includes a fitting term for the observed data and a residual term for the partial differential equation. The loss function is: in, For observation data, For the orthogonal operator, For partial differential equation operators, For source terms, Indicates the first A physical information neural network; The pre-training is performed using either the Adam optimizer or the L-BFGS optimizer.

4. The Bayesian inversion method for termite nest detection based on integrated physical information neural network and MCMC sampling as described in claim 1, characterized in that, The step of calculating the statistical characteristics of the physical parameter field values ​​at each grid point based on the parameter sample matrix, and constructing an information-based prior distribution in the physical parameter field space, specifically includes: At each grid point Above, calculate the physical parameter field output of the M physical information neural network. mean With variance : Construct a diagonal Gaussian prior distribution in the physical parameter field space: in, For discretized parameter field vectors, The total number of grid points; the variance of the prior distribution. The magnitude of the value reflects the constraint strength at the corresponding grid point location.

5. The Bayesian inversion method for termite nest detection based on integrated physical information neural network and MCMC sampling as described in claim 4, characterized in that, The step of calculating the statistical characteristics of the physical parameter field values ​​at each grid point based on the parameter sample matrix, and constructing an information-based prior distribution in the physical parameter field space, further includes: Based on the inversion accuracy or loss function convergence value of each physical information neural network on the validation set, a confidence weight is assigned to each network, and the sum of the weights is 1. The weighted mean and weighted variance are calculated at each grid point as the statistical features.

6. The Bayesian inversion method for termite nest detection based on integrated physical information neural network and MCMC sampling as described in claim 1, characterized in that, The joint potential energy function is specifically: Wherein, the first term is the prior constraint term corresponding to the aforementioned information prior distribution, the second term is the likelihood term corresponding to the observed data, and the third term is the physical constraint term corresponding to the aforementioned partial differential equation. These are the physical constraint weighting coefficients. The number of observation data points, For the first The noise standard deviation of the observation data.

7. The Bayesian inversion method for termite nest detection based on integrated physical information neural network and MCMC sampling as described in claim 1, characterized in that, The Markov chain Monte Carlo sampling, which uses physical parameter fields as sampling objects, specifically includes: The mean vector of the aforementioned information prior distribution is used as the initial state of the Markov chain; Candidate physical parameter fields are sampled from the proposed distribution, which is a diagonal Gaussian distribution with the current state as the mean. Its covariance matrix is ​​determined by the product of the square of the global step size scaling factor and the diagonal matrix formed by the pointwise variance vector of the information prior distribution. Each element in the pointwise variance vector corresponds to the prior variance at each grid point in the discrete space grid. Large step sizes are used for exploration at grid points with large variances, and small step sizes are used for fine-grained search at grid points with small variances. Calculate the joint potential function value of the candidate physical parameter fields, and decide whether to accept the candidate physical parameter fields based on the acceptance probability: in, Let be the joint potential energy function; After the preheating steps, posterior samples of the physical parameter field are collected.

8. The Bayesian inversion method for termite nest detection based on integrated physical information neural network and MCMC sampling as described in claim 1, characterized in that, The Markov chain Monte Carlo sampling also includes a Hamiltonian Monte Carlo adaptive switching step: When the size of the discrete spatial grid exceeds a preset threshold, or when the sampling acceptance rate during the preheating stage is lower than a preset lower limit, the sampling will be automatically switched to the Hamilton Monte Carlo method. In the Hamiltonian Monte Carlo method, an auxiliary momentum variable is introduced to construct the Hamiltonian. Numerical integration is performed through a frog-leap integrator to update the physical parameter field and the auxiliary momentum variable. The gradient of the joint potential energy function is calculated using the adjoint state method. After the frog-leap integral is completed, the Hamiltonian Monte Carlo acceptance probability determines whether to accept the new physical parameter field.

9. The Bayesian inversion method for termite nest detection based on integrated physical information neural network and MCMC sampling as described in claim 8, characterized in that, The preset threshold is when the number of grid points is greater than 10,000, and the preset lower limit is when the average acceptance rate of a preset number of consecutive steps in the preheating stage is less than 15%.

10. The Bayesian inversion method for termite nest detection based on integrated physical information neural network and MCMC sampling as described in claim 1, characterized in that, The step of calculating the posterior statistic based on the posterior sample set and outputting the inversion result and uncertainty quantification index specifically includes: Calculate the posterior mean at each grid point as the optimal estimate for inversion, and output the mean value map of physical parameters. Calculate the posterior standard deviation at each grid point and output a point-by-point uncertainty plot; Calculate the confidence intervals at each grid point and output the confidence interval plot; The accuracy of the inversion is assessed by relative error, structural similarity index, and confidence interval coverage.

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