Physical field reconstruction method and storage medium

Abstract

This disclosure provides a physical field reconstruction method and storage medium. The method includes: inputting a target position set composed of the positions of multiple sensors, multiple sets of target sensor data collected by multiple sensors, and preset constraints into a target reconstruction model, and outputting target reconstruction physical quantities for the target physical field; wherein, the target model parameters and target position set of the target reconstruction model are obtained by iterative optimization operation using an initial reconstruction model, and the Kth optimization operation includes: optimizing the Kth position set of multiple sensors and the Kth set of model parameters in the Kth optimization result based on the Kth target error between the Kth optimization result obtained from the Kth optimization operation and the preset optimization result, to obtain the Kth optimization result, and the Kth optimization result includes the Kth position set and the Kth set of model parameters.

Description

Technical Field

[0001] This disclosure relates to the field of physical field reconstruction technology, and more specifically to a physical field reconstruction method and storage medium. Background Technology

[0002] High-dimensional complex flow fields include, for example, the blood flow field in the heart, the three-dimensional dynamic diffusion flow field formed in water, the atmospheric circulation field (such as wind field), and the ocean current field. For high-dimensional complex physical systems, it is often necessary to reconstruct the spatial flow field from limited local sensor information. Related methods typically utilize deep neural networks to reconstruct chaotic data from sparse measurements, and the location of sparse points or the sensor layout is crucial to the fidelity and efficiency of the field reconstruction. However, in these methods, sensor layout optimization is usually decoupled from the field reconstruction algorithms such as physical information neural networks, making it difficult for sensor layout optimization to adaptively match the updates of the field reconstruction model. Summary of the Invention

[0003] In view of the above problems, this disclosure provides a physical field reconstruction method and storage medium.

[0004] According to the first aspect of this disclosure, a physical field reconstruction method is provided, comprising: inputting a target position set consisting of the positions of multiple sensors, multiple sets of target sensor data collected by the multiple sensors, and preset constraints into a target reconstruction model, and outputting a target reconstruction physical quantity for the target physical field, wherein the target reconstruction physical quantity is used at least for state analysis of the target physical field, and the target sensor data includes physical data for the target physical field collected by the sensors at corresponding positions; wherein the target model parameters and the target position set of the target reconstruction model are obtained by iterative optimization operations using an initial reconstruction model, and the Kth optimization operation includes: optimizing the Kth position set of multiple sensors and the Kth set of model parameters in the Kth optimization result based on the Kth target error between the Kth optimization result obtained by the Kth optimization operation and the preset optimization result, to obtain the Kth optimization result, wherein the Kth optimization result includes the Kth position set and the Kth set of model parameters, and K is a positive integer.

[0005] According to embodiments of this disclosure, the Kth optimization result further includes the Kth group of reconstructed physical quantities; the Kth optimization operation further includes: updating the encoder and decoder of the initial reconstruction model according to the Kth group of model parameters to obtain the Kth updated encoder and the Kth updated decoder; predicting sensor data collected by multiple sensors at the positions indicated by the Kth position set to obtain the Kth group of predicted sensor data corresponding to the Kth optimization operation; performing feature extraction and stitching operations on the Kth group of predicted sensor data and the K position set to obtain multiple stitched feature vectors; using the Kth updated encoder to perform a fusion operation on the multiple stitched feature vectors to obtain a fused feature vector; and using the Kth updated decoder to decode the fused feature vector to obtain the Kth group of reconstructed physical quantities.

[0006] According to embodiments of this disclosure, the fusion operation of multiple stitched feature vectors using the Kth updated encoder to obtain a fused feature vector includes: using the Kth updated encoder, determining the attention weights of each of the multiple stitched feature vectors based on the sensor association relationships represented by the multiple stitched feature vectors, wherein the sensor association relationships include positional associations and physical quantity data associations between sensors; and performing weighted fusion of the multiple stitched feature vectors based on the attention weights to obtain a fused feature vector.

[0007] According to embodiments of this disclosure, predicting sensor data collected by multiple sensors at locations indicated by a Kth location set to obtain the Kth set of predicted sensor data corresponding to the Kth optimization operation includes: acquiring the (K-1)th set of predicted sensor data corresponding to the (K-1)th location set obtained from the (K-1)th optimization operation; determining at least one first location from the (K-1)th location set whose spatial distance to each location in the Kth location set is less than a first distance threshold; determining at least one target sensor data corresponding to the at least one first location from the (K-1)th set of predicted sensor data; and performing interpolation calculation on the at least one target sensor data to obtain the Kth set of predicted sensor data.

[0008] According to embodiments of this disclosure, based on the target error between the (K-1)th optimization result obtained from the (K-1)th optimization operation and the preset optimization result, the (K-1)th position set of multiple sensors and the (K-1)th group of model parameters in the (K-1)th optimization result are optimized to obtain the Kth optimization result. This includes: determining the direction to be adjusted and the displacement to be adjusted corresponding to the (K-1)th position set based on the target error; adjusting the (K-1)th position set based on the direction to be adjusted, the displacement to be adjusted, and the preset sensor position boundary constraints to obtain the Kth position set, wherein the sensor position boundary constraints are used to constrain each position in the Kth position set to be within the preset sensor installation position range; determining the amount to be corrected corresponding to the (K-1)th group of model parameters based on the target error; and adjusting the (K-1)th group of model parameters based on the amount to be corrected to obtain the Kth group of model parameters.

[0009] According to embodiments of this disclosure, adjusting the (K-1)th set of locations based on the direction to be adjusted, the displacement to be adjusted, and a preset sensor position boundary constraint includes: determining the boundary of the sensor installation position range; adjusting the direction to be adjusted to the second direction when at least one second location in the (K-1)th set is less than a second distance threshold and the direction to be adjusted includes a first direction, wherein the first direction is the direction closer to the boundary and the second direction is the opposite direction of the first direction; and adjusting the (K-1)th set of locations based on the second direction and the displacement to be adjusted.

[0010] According to embodiments of this disclosure, the preset optimization result includes: a predetermined reconstructed physical quantity, the physical equation of the target physical field that the preset reconstructed physical quantity needs to satisfy, and the initial condition value and boundary condition value that the target physical field needs to satisfy; the Kth optimization operation further includes: determining the difference between the Kth group of reconstructed physical quantities and the predetermined reconstructed physical quantity to obtain a first error; determining the deviation value of the Kth group of reconstructed physical quantities from the physical equation to obtain a second error; determining the deviation value of the Kth group of reconstructed physical quantities from the initial condition value and boundary condition value to obtain a third error; and performing a weighted summation of the first error, the second error, and the third error to obtain the Kth target error corresponding to the Kth optimization operation.

[0011] According to embodiments of this disclosure, the physical field includes at least one of the following: a temperature field, a fluid flow field, a pressure field, and a concentration field. The state analysis includes one of the following: physical quantity distribution analysis, and physical quantity correlation analysis between multiple physical fields.

[0012] A second aspect of this disclosure also provides a computer-readable storage medium having a computer program or instructions stored thereon, which, when executed by a processor, implement the steps of the above-described method. Attached Figure Description

[0013] The foregoing contents, as well as other objects, features, and advantages of this disclosure, will become clearer from the following description of embodiments with reference to the accompanying drawings, in which:

[0014] Figure 1 A flowchart illustrating a physical field reconstruction method according to an embodiment of the present disclosure is shown schematically.

[0015] Figure 2 A schematic diagram of a physical field reconstruction method according to an embodiment of the present disclosure is shown.

[0016] Figure 3 A schematic diagram illustrating the framework of an initial reconstruction model according to an embodiment of the present disclosure is shown.

[0017] Figure 4(a) schematically illustrates a comparison of sensor position optimization results according to an embodiment of the present disclosure;

[0018] Figure 4(b) schematically illustrates the clustering results of sensor position optimization according to an embodiment of the present disclosure. Detailed Implementation

[0019] The embodiments of the present disclosure will now be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the disclosure. In the following detailed description, numerous specific details are set forth to provide a thorough understanding of the embodiments of the present disclosure for ease of explanation. However, it will be apparent that one or more embodiments may be practiced without these specific details. Furthermore, descriptions of well-known structures and techniques are omitted in the following description to avoid unnecessarily obscuring the concepts of the present disclosure.

[0020] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit this disclosure. The terms “comprising,” “including,” etc., as used herein indicate the presence of features, steps, operations, and / or components, but do not exclude the presence or addition of one or more other features, steps, operations, or components.

[0021] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted in a manner consistent with the context of this specification, and not in an idealized or overly rigid way.

[0022] When using expressions such as "at least one of A, B and C", they should generally be interpreted in accordance with the meaning that is commonly understood by those skilled in the art (e.g., "a system having at least one of A, B and C" should include, but is not limited to, a system having A alone, a system having B alone, a system having C alone, a system having A and B, a system having A and C, a system having B and C, and / or a system having A, B and C, etc.).

[0023] On the one hand, related methods are usually based on linear theory for physical field reconstruction, such as linear stochastic estimation methods based on Galerkin transform, Gappy orthogonal decomposition, and Kalman filtering. However, these methods are difficult to use to reconstruct the global field from a finite number of sensors for complex physical systems.

[0024] On the other hand, related methods often reconstruct chaotic data from sparse measurements using deep neural networks. Methods for recovering high-resolution fields from low-resolution data using deep neural networks originate from super-resolution and primarily utilize convolutional neural networks. However, the experimental measurements and numerical simulations in these methods typically rely on unstructured grids or random sensor layouts, while the training data for convolutional neural networks is structured and uniformly arranged. This makes the aforementioned unstructured grids generally incompatible with convolutional neural network methods.

[0025] Furthermore, for neural network-based simulation methods such as solving incompressible flows using two different mathematical formulations of the Navier-Stokes equations, indirectly calculating velocity and pressure fields by measuring temperature fields through tomographic background-guided schlieren imaging, and accurately calculating ideal vascular flow using physical information neural networks without any simulation data, as well as linear theory-based tools and super-resolution methods, the location of sparse points or sensor layout is crucial to the fidelity and efficiency of field reconstruction. Related methods for determining sensor layout typically include: optimization strategies within a deep neural network-based turbulent flow data assimilation framework, selecting sensor locations by evaluating the residuals of the governing equations, and generating various sensor configurations for two-dimensional stenotic hemodynamic problems. However, these optimization methods are often decoupled from field reconstruction algorithms such as physical information neural networks, making it difficult for sensor layout optimization to adaptively match the updates of the reconstruction model. Moreover, the optimization algorithms combined with physical information neural network methods are largely empirical, relying primarily on experimental trial and error in engineering research, domain experience, and qualitative rule summaries for design and parameter tuning.

[0026] In view of this, embodiments of the present disclosure provide a physical field reconstruction method, which inputs a target position set consisting of the positions of multiple sensors, multiple sets of target sensor data collected by multiple sensors, and preset constraints into a target reconstruction model, and outputs a target reconstruction physical quantity for the target physical field. The target reconstruction physical quantity is used at least for state analysis of the target physical field. The target sensor data includes physical data for the target physical field collected by sensors at corresponding positions. The target model parameters and target position set of the target reconstruction model are obtained by iterative optimization of the initial reconstruction model. The Kth optimization operation includes: optimizing the Kth position set of multiple sensors and the Kth set of model parameters in the Kth optimization result based on the Kth target error between the Kth optimization result obtained from the Kth optimization operation and the preset optimization result, to obtain the Kth optimization result. The Kth optimization result includes the Kth position set and the Kth set of model parameters, where K is a positive integer.

[0027] Figure 1 A flowchart illustrating a physical field reconstruction method according to an embodiment of the present disclosure is shown schematically.

[0028] Figure 2 A schematic diagram of a physical field reconstruction method according to an embodiment of the present disclosure is shown.

[0029] like Figure 1 As shown, the physical field reconstruction method of this embodiment includes operations S110 to S120.

[0030] In operation S110, the target model parameters and target location set of the target reconstruction model are obtained by iterative optimization using the initial reconstruction model.

[0031] According to embodiments of this disclosure, the target model parameters and target location set of the target reconstruction model are obtained by iterative optimization of the initial reconstruction model.

[0032] The Kth optimization operation includes: based on the K-1th target error between the K-1th optimization result obtained from the K-1th optimization operation and the preset optimization result, optimizing the K-1th location set and the K-1th set of model parameters of multiple sensors in the K-1th optimization result to obtain the Kth optimization result. The Kth optimization result includes the Kth location set and the Kth set of model parameters, where K is a positive integer.

[0033] In operation S120, the target position set consisting of the positions of multiple sensors, multiple sets of target sensor data collected by multiple sensors, and preset constraints are input into the target reconstruction model, and the target reconstruction physical quantity for the target physical field is output.

[0034] For example, the target physical field may include a temperature field, a fluid flow field, etc., and the type of target physical field may be expanded according to actual needs.

[0035] A limited number of sensors can be deployed in the target physical field. For example, sensor A can be deployed at position (x1, y1), sensor B at position (x2, y2), and sensor C at position (x3, y3). The sensors can be used to collect local physical quantities at their respective locations (i.e., physical data specific to the target physical field). For instance, sensor A can collect the temperature at position (x1, y1), while sensor B can collect the temperature at position (x2, y2), and sensor C can collect the temperature at position (x3, y3). The type of sensor can be determined based on actual needs, and may include temperature sensors, pressure sensors, etc.

[0036] Due to the limitations of the physical characteristics and spatial structure of the target physical field, it is difficult to deploy sensors at every location in the entire target physical field. For example, if sensors are deployed throughout the entire pipeline, a large number of sensors will occupy the flow channel space and disturb the fluid flow. Moreover, deploying a large number of sensors will increase hardware and deployment costs. Therefore, usually only a limited number of sensors are deployed (the number of sensors can be set according to actual needs and is not limited here). Based on the local physical quantities collected by the limited number of sensors, the physical quantities of the entire target physical field are reconstructed to obtain the target reconstructed physical quantities.

[0037] For example, for a temperature field, the target reconstructed physical quantity may include the temperature value and temperature rise value of the entire temperature field; for a fluid flow field, the target reconstructed physical quantity may include the flow velocity, flow rate, and flow direction of the entire fluid flow field.

[0038] For example, the target location set, multiple sets of target sensor data collected by multiple sensors, and preset constraints can be simultaneously input into the target reconstruction model to output the target reconstruction physical quantity using the target reconstruction model.

[0039] For example, the target location set may include the locations of multiple sensors that have been deployed in the target physical field. For instance, if sensors A to C have been deployed in the target physical field, the target location set may include (x1, y1), (x2, y2), and (x3, y3).

[0040] Target sensor data can include local physical quantities of the target physical field collected by the sensor. For example, for a fluid flow field, the target sensor data collected by sensor A can include the flow velocity of the fluid at position (x1, y1), and the target sensor data collected by sensor B can include the flow velocity of the fluid at position (x2, y2), etc.

[0041] Preset constraints can be determined based on the physical laws of the target physical field. For example, preset constraints may include the Navier-Stokes equations (NS equations) for incompressible fluids, used to constrain the target reconstructed physical quantities output by the fluid flow field to satisfy the spatial variation laws of water velocity and pressure; preset constraints may also include a water velocity of 0 m / s at the wall, used to limit the target reconstructed physical quantities to satisfy the boundary constraints of the pipe. Preset constraints can be adaptively adjusted according to the type of target physical field.

[0042] For example, an initial reconstruction model can be pre-trained to determine the final model parameters and the locations where multiple sensors should be deployed in the target physical field, resulting in a set of target model parameters and target locations. The process of training the initial reconstruction model may include iterative optimization operations using the initial reconstruction model.

[0043] For example, a training sample set can be input into the initial reconstruction model (SOPINN). The training sample set may include: a set of training locations, training sensor data collected by multiple sensors for the training physics field, and preset constraints for the training physics field. The actual reconstructed physical quantities for the training physics field can be used as label data for model training. The training physics field may include a pre-constructed ideal physics field. For example, if the target physics field includes the actual water supply pipeline flow field of a factory, the training physics field may include a pre-constructed simulated flow field used to simulate the aforementioned water supply pipeline flow field.

[0044] For example, the optimization result of each optimization operation may include at least: a set of locations composed of the individual positions of multiple sensors obtained in this optimization operation, and the model parameters of the initial reconstruction model. The set of locations and model parameters obtained in this optimization operation can be optimized to obtain the set of locations and model parameters corresponding to the next optimization operation.

[0045] For the Kth optimization operation, we can first determine the K-1th optimization result obtained from the (K-1)th optimization operation. For example, we can determine the K-1th location set and the K-1th set of model parameters obtained from the K-1th optimization operation. We can also determine the difference between the reconstructed physical quantity obtained from the K-1th optimization operation and the actual reconstructed physical quantity. The larger the difference, the larger the K-1th target error between the K-1th optimization result and the preset optimization result. This indicates that the location set and model parameters obtained from this optimization operation are not reasonable enough and need further optimization. For example, we need to further adjust the positions of multiple sensors and / or further adjust the model parameters.

[0046] For example, the iteration operation can be stopped when a preset number of iterations (which can be set according to actual needs) is reached, and the target model parameters and target position set are output. Alternatively, the iteration operation can be stopped when the target error is less than a preset threshold (which can be set according to actual needs).

[0047] According to embodiments of this disclosure, by performing iterative optimization operations using an initial reconstruction model, each optimization operation optimizes both the location set and model parameters. The sensor positions are dynamically adjusted after each optimization iteration. By using the sensor positions as trainable parameters of the model, the sparse sensor layout method is integrated into the physical information neural network, solving the problem in related methods where the sensor optimization method and the physical information neural network are decoupled from field reconstruction algorithms, resulting in limited reconstruction accuracy and efficiency due to the inability to adaptively match the parameter updates of the reconstruction model. Furthermore, by optimizing the location set of multiple sensors and model parameters in the optimization result based on the target error between the optimization result obtained from the optimization operation and the preset optimization result, the sensor positions can be optimized through backpropagation to achieve field reconstruction. Backpropagation optimization improves the solution performance of the subsequent decoder, thereby enhancing the model's ability to explore the spatial domain and the sensor localization effect.

[0048] like Figure 2 As shown, data preprocessing can be performed first, and then the preprocessed training sample set can be input into the initial reconstruction model. Data preprocessing can include dataset preparation, discrete point removal, and balancing and normalization.

[0049] For example, sparse sensor data and corresponding high-precision field data under multiple operating conditions can be collected. Sparse sensor data includes parameters such as velocity, pressure, and temperature. For unsteady-state problems, this data is stored in time-step segments to obtain a training sample set. Statistical filtering (such as 3D filtering) can be used. Criteria, etc., can be set according to actual needs to remove outliers, and missing data can be filled in using KNN interpolation to remove discrete points. Gaussian filtering (e.g., kernel size can be 3×3) can be applied to sensor data to smooth noise and normalize it to the [-1,1] interval, and scale standardization of spatial coordinates can be performed to avoid interference from dimensional differences in training.

[0050] According to embodiments of this disclosure, the Kth optimization result also includes the Kth group of reconstructed physical quantities.

[0051] For example, the Kth group of reconstructed physical quantities may include: global physical quantities for the training physical field predicted by the initial reconstruction model based on the Kth location set and the Kth group of model parameters.

[0052] According to embodiments of this disclosure, the Kth optimization operation further includes: updating the encoder and decoder of the initial reconstruction model according to the Kth set of model parameters to obtain the Kth updated encoder and the Kth updated decoder; predicting sensor data collected by multiple sensors at the positions indicated by the Kth location set to obtain the Kth set of predicted sensor data corresponding to the Kth optimization operation; performing feature extraction and stitching operations on the Kth set of predicted sensor data and the Kth location set to obtain multiple stitched feature vectors; using the Kth updated encoder to perform a fusion operation on the multiple stitched feature vectors to obtain a fused feature vector; and using the Kth updated decoder to decode the fused feature vector to obtain the Kth set of reconstructed physical quantities.

[0053] For example, each set of model parameters may include a set of all trainable parameters for the encoder and decoder of the initial reconstructed model obtained from each optimization operation, such as updated parameters for the encoder (e.g., convolutional kernel weights, biases, etc.) and updated parameters for the decoder (e.g., deconvolutional kernel weights, normalization parameters, etc.).

[0054] Updating the encoder and decoder of the initial reconstructed model based on the Kth group of model parameters can include replacing the encoder parameters with the updated encoder parameters from the Kth group of model parameters, and replacing the decoder parameters with the updated decoder parameters from the Kth group of model parameters.

[0055] For example, after adjusting the position of the sensor, it is necessary to determine the sensor data that the sensor can collect at the new position. For instance, in the Kth optimization operation, the position of sensor A is adjusted from (x1, y1) to (x1, y2). Therefore, it is necessary to determine the sensor data collected by sensor A at (x1, y2) so as to output the Kth set of reconstructed physical quantities corresponding to the Kth optimization operation using the optimized positions of each sensor, the sensor data that the sensor can collect at the new position, and the preset constraints. The preset constraints of the input initial reconstruction model and the preset constraints of the input target reconstruction model can be the same.

[0056] Since sensor location optimization is performed through the training process of the initial reconstruction model, rather than by actually deploying sensors at the corresponding locations in the training physical field, it is difficult to obtain the actual sensor data collected by the sensors at the new locations. Therefore, it is possible to predict the sensor data collected by multiple sensors at the locations indicated by the Kth location set. For example, differentiable interpolation can be used to predict the Kth set of predicted sensor data. Differentiable interpolation methods include, for example, bilinear or trilinear interpolation based on neighborhood information.

[0057] Figure 3A schematic diagram of the framework of an initial reconstruction model according to an embodiment of the present disclosure is shown.

[0058] like Figure 3 As shown, the framework of the initial reconstruction model may include a sensor value interpolator.

[0059] Such as 2 and Figure 3 As shown, the sensor value interpolator can be used to: interpolate the set of locations (such as...) in each optimization operation. Figure 3 In ) is optimized, and in each optimization operation, the sensor data collected by multiple sensors at the locations indicated by the location set (e.g.) is predicted. Figure 3 Vs in the equation are used to obtain the predicted sensor data corresponding to the optimization operation.

[0060] The sensor value interpolator can also be used to perform feature extraction and concatenation operations on predicted sensor data and location sets to obtain multiple concatenated feature vectors. For example, in the Kth optimization operation, the sensor value interpolator can perform feature extraction and concatenation operations on the Kth set of predicted sensor data and K location sets to obtain multiple concatenated feature vectors, which can be used as input tensors for the encoder.

[0061] For example, features can be extracted from the predicted sensor data and the location set separately to obtain the predicted sensor data feature vector and multiple location feature vectors. The predicted sensor data feature vector and multiple location feature vectors from the same sensor can be concatenated to form a concatenated feature vector.

[0062] By performing feature extraction and stitching operations on the Kth group of predicted sensor data and the K sets of locations, the initial reconstruction model can learn the correlation between sensor data and spatial location.

[0063] The sensor value interpolator can be used to recalculate the physical quantities corresponding to the optimized sensor positions, and the calculation results can be seamlessly integrated into the network optimization process.

[0064] like Figure 3 As shown, the framework of the initial reconstruction model can also include a sensor data encoder. (See Figures 2 and 3). Figure 3 As shown, the sensor data encoder can receive the sensor's position and values ​​as input (e.g., a concatenated feature vector as input) and process them through a fully connected layer (such as linear layer 1) to match the input dimension required for subsequent attention blocks. The sensor data encoder may include a multi-head self-attention layer and a feedforward layer, wherein the multi-head self-attention layer keeps the output dimension consistent with the input and introduces residual connections around it to fully preserve sensor information.

[0065] The sensor data encoder can map the feature vectors into a compressed latent space matrix. The training quality of the latent space matrix directly affects the quality of the compressed representation, which in turn affects the optimization of the subsequent decoder.

[0066] For example, the sensor data encoder can be updated based on the Kth set of model parameters to obtain the Kth updated encoder. The Kth updated encoder can then be used to perform a fusion operation on multiple spliced ​​feature vectors based on an attention mechanism to obtain a fused feature vector.

[0067] like Figure 3 As shown, the framework of the initial reconstruction model may also include a decoder.

[0068] like Figure 2 and Figure 3 As shown, the decoder can utilize multi-head cross-attention, allowing residual points to selectively focus on specific dependencies in the compact representation of the input sensor during the decoding process. Compared to a relevance-based physical information neural network, this approach can capture more relevant and useful information. The keys and values ​​for cross-attention can be provided by the encoder output, and the spatial vector encoded from the residual point positions can serve as a query array. Similar to the encoder, the decoder can employ residual connections around the cross-attention layer; the decoder's cross-attention layer is followed by three feedforward layers to learn the PDE solution for the residual points. Through the decoder, appropriate sensor data can be selected for specific residual points, assisting their physical information neural network solution process.

[0069] For example, the decoder can be updated based on the Kth set of model parameters to obtain the Kth updated encoder. The Kth updated decoder can then be used to decode the fused feature vector to obtain the Kth set of reconstructed physical quantities.

[0070] According to embodiments of this disclosure, the fusion operation of multiple stitched feature vectors using the Kth updated encoder to obtain a fused feature vector includes: using the Kth updated encoder, determining the attention weights of each of the multiple stitched feature vectors based on the sensor association relationships represented by the multiple stitched feature vectors, wherein the sensor association relationships include positional associations and physical quantity data associations between sensors; and performing weighted fusion of the multiple stitched feature vectors based on the attention weights to obtain a fused feature vector.

[0071] For example, location correlation includes the spatial relative relationship between sensors, such as the spatial distance, orientation, and whether they are in the same flow channel between the elbow sensor and the inlet sensor. Physical quantity data correlation can characterize the inherent correlation between the physical quantity values ​​collected by multiple sensors, such as the higher the inlet flow velocity, the greater the pressure at the elbow, and the gradient correlation between the temperature of the wall sensor and the temperature of the center sensor.

[0072] Since the spliced ​​feature vector is obtained by splicing the predicted sensor data and the location set, it carries the correlation information between the sensors. Therefore, the sensor data encoder can directly extract the sensor correlation from multiple spliced ​​feature vectors.

[0073] Sensor data encoders can utilize multi-head self-attention layers to determine the attention weights of multiple stitched feature vectors through operations such as QKV mapping, attention score calculation, and softmax normalization. The attention weights can range from 0 to 1. For example, sensors that are more important for global physical field reconstruction can be assigned higher weights to their corresponding stitched feature vectors; for instance, the attention weight of a pipe bend sensor can be higher than that of a mid-section sensor.

[0074] For example, the multiple concatenated feature vectors can be weighted and summed according to their respective attention weights to obtain a fused feature vector.

[0075] By weighting and summing multiple spliced ​​feature vectors according to attention weights, features with higher weights can dominate after fusion, while features with lower weights only serve as auxiliary features. This approach preserves local information from all sensors while highlighting core features at key locations.

[0076] According to embodiments of this disclosure, predicting sensor data collected by multiple sensors at locations indicated by a Kth location set to obtain the Kth set of predicted sensor data corresponding to the Kth optimization operation includes: acquiring the (K-1)th set of predicted sensor data corresponding to the (K-1)th location set obtained from the (K-1)th optimization operation; determining at least one first location from the (K-1)th location set whose spatial distance to each location in the Kth location set is less than a first distance threshold; determining at least one target sensor data corresponding to the at least one first location from the (K-1)th set of predicted sensor data; and performing interpolation calculation on the at least one target sensor data to obtain the Kth set of predicted sensor data.

[0077] For example, differentiable interpolation can be used to predict sensor data collected by multiple sensors at a location indicated by the Kth location set.

[0078] For example, the differentiable interpolation method needs to calculate the physical quantity of the new location based on the neighborhood data of the existing location. The neighborhood data may include existing locations that are spatially close enough to the new location to be interpolated and their corresponding sensor data. For example, the locations around the new location that are spatially close enough can be determined from the (K-1)th location set as existing sensor locations, and the corresponding sensor data can be determined from the (K-1)th set of predicted sensor data.

[0079] For example, the location set and predicted sensor data obtained from each optimization operation can be cached. The (K-1)th set of predicted sensor data corresponding to the (K-1)th location set can be retrieved from historical data storage.

[0080] For example, the first distance threshold can be set according to actual needs and is not limited here. If the spatial distance is less than the first distance threshold, it means that the spatial distance between the two sensor positions is close enough.

[0081] Since the Kth position set is obtained by directly optimizing the (K-1)th position set, it is closest to the Kth position set compared to the position sets obtained by other optimization operations. Therefore, the first position can be determined directly from the (K-1)th position set, avoiding the problem of high computational cost and low efficiency caused by determining the first position from all optimization results obtained from all historical optimization operations.

[0082] The spatial distance between each position in the Kth position set and each position in the (K-1)th position set can be calculated to determine at least one first position. For example, spatial distances can be calculated using planar rectangular coordinates, spatial rectangular coordinates, etc. The method for calculating spatial distances can be set according to actual needs.

[0083] After determining at least one first position, the target sensor data corresponding to each first position can be directly read from the (K-1)th group of predicted sensor data to obtain at least one target sensor data.

[0084] Interpolation can be performed using interpolation algorithms, such as bilinear differentiable interpolation and trilinear differentiable interpolation. For example, bilinear differentiable interpolation can be used for two-dimensional physical fields such as planar flow fields and surface temperature fields, while trilinear differentiable interpolation can be used for three-dimensional physical fields such as three-dimensional flow channels and battery pack temperature fields.

[0085] Differentiable interpolation can be used to accurately determine the physical quantities corresponding to any optimized sensor position.

[0086] According to embodiments of this disclosure, based on the target error between the (K-1)th optimization result obtained from the (K-1)th optimization operation and the preset optimization result, the (K-1)th position set of multiple sensors and the (K-1)th group of model parameters in the (K-1)th optimization result are optimized to obtain the Kth optimization result. This includes: determining the direction to be adjusted and the displacement to be adjusted corresponding to the (K-1)th position set based on the target error; adjusting the (K-1)th position set based on the direction to be adjusted, the displacement to be adjusted, and the preset sensor position boundary constraints to obtain the Kth position set, wherein the sensor position boundary constraints are used to constrain each position in the Kth position set to be within the preset sensor installation position range; determining the amount to be corrected corresponding to the (K-1)th group of model parameters based on the target error; and adjusting the (K-1)th group of model parameters based on the amount to be corrected to obtain the Kth group of model parameters.

[0087] For example, if the target error at a certain location is large, it indicates that the features of that area at that location have not been effectively captured. Therefore, the sensor can be moved towards the location with the large target error. The displacement to be adjusted can be positively correlated with the magnitude of the target error; that is, the larger the target error, the larger the displacement to be adjusted.

[0088] like Figure 2 As shown, when optimizing the sensor position, in addition to optimizing through position backpropagation, the position must also be adjusted based on boundary constraints.

[0089] For example, to ensure numerical stability during position updates, sensor position boundary constraints can be applied to the direction and displacement to be adjusted. For instance, position boundary constraints can restrict the sensor to be installed only within the inner wall of the pipe, preventing it from extending beyond that area.

[0090] For example, the target error can be calculated using the backpropagation algorithm to determine the gradient (i.e., the quantity to be corrected) of each model parameter. For instance, the larger the target error, the larger the absolute value of the quantity to be corrected. The K-1 group of model parameters can be adjusted according to the correction direction and magnitude represented by the quantity to be corrected to obtain the K-th group of model parameters.

[0091] According to embodiments of this disclosure, adjusting the (K-1)th set of locations based on the direction to be adjusted, the displacement to be adjusted, and a preset sensor position boundary constraint includes: determining the boundary of the sensor installation position range; adjusting the direction to be adjusted to the second direction when at least one second location in the (K-1)th set is less than a second distance threshold and the direction to be adjusted includes a first direction, wherein the first direction is the direction closer to the boundary and the second direction is the opposite direction of the first direction; and adjusting the (K-1)th set of locations based on the second direction and the displacement to be adjusted.

[0092] For example, the boundary of the sensor installation location range may include the geometric boundary coordinates of the sensor installation area. For instance, in a pipe flow field, the sensor can only be installed on the inner wall of the pipe, so the boundary of the sensor installation location range may include the coordinate range of the inner wall of the pipe.

[0093] The second position can include the sensor positions that need to be adjusted in the (K-1)th position set. If the distance to the boundary is less than the second distance threshold, and the direction to be adjusted includes the first direction, it means that the second position is already close to the boundary, and moving along the direction of movement will bring it even closer to the boundary, resulting in a higher probability that the second position will exceed the boundary after optimization. The second distance threshold can be set according to actual needs and is not limited here.

[0094] When the sensor that needs to be adjusted is very close to the installation boundary, and the original direction of movement is close to the boundary, the direction of movement can be reversed to adjust the direction to be adjusted to a second direction, thus avoiding crossing the boundary or being too close to the boundary.

[0095] For example, if the current position of a sensor is 0.05m away from the inner wall of a pipe (less than the second distance threshold of 0.1m), the original direction to be adjusted is to move towards the inner wall (first direction). At this time, the direction can be adjusted to move away from the inner wall (second direction). The second direction can be set according to actual needs. For example, it can be the direction obtained by rotating the first direction by 180 degrees, or it can be another direction away from the boundary selected according to the actual installation space.

[0096] When a sensor approaches the boundary of the computational domain, the gradient sign of its update direction vector can be reversed, preventing the sensor from going out of bounds while maintaining differentiability.

[0097] For example, the optimization objective of the initial optimization model may include learning sensor locations, network weights, and biases by solving an optimization problem. The objective function of the initial optimization model may include a sensor data-driven term, an interior physical information term, and an initial / boundary condition term. The weights of the sensor data-driven term, the interior physical information term, and the initial / boundary condition term can be determined separately. For example, the weights of the sensor data-driven term, the interior physical information term, and the initial / boundary condition term can be set to 2, 0.2, and 2, respectively (the values ​​of the weights can be adjusted according to actual needs and are not limited here). By penalizing the residuals of the PDE at a set of collocations inside the network and penalizing the associated boundary / initial condition residuals at a set of collocations on the boundary, the physical information can be encoded into SOPINN. Training can use the Adam optimizer with a fixed learning rate of 0.001.

[0098] According to embodiments of this disclosure, the preset optimization results include: a predetermined reconstructed physical quantity, the physical equation of the target physical field that the preset reconstructed physical quantity needs to satisfy, and the initial condition values ​​and boundary condition values ​​that the target physical field needs to satisfy.

[0099] For example, the predetermined reconstructed physical quantities may include the actual reconstructed physical quantities for the training physical field. The physical equations may include PDE equations, etc. Initial condition values ​​include, for example, that the initial flow velocity in the pipe is 0 m / s when the flow field starts, and boundary condition values ​​include, for example, that the flow velocity at the wall is 0 when there is no slippage on the pipe wall, etc.

[0100] For example, the target error can characterize the difference between the (K-1)th optimization result and the preset optimization result. Figure 3 As shown, the target error can be calculated using formula (1).

[0101]

[0102] Where Loss is the target error, Loss data For the first error, Loss pde For the second error, Loss BC / IC This is the third error.

[0103] According to an embodiment of this disclosure, the Kth optimization operation further includes: determining the difference between the Kth group of reconstructed physical quantities and the predetermined reconstructed physical quantities to obtain a first error; determining the deviation of the Kth group of reconstructed physical quantities from the physical equation to obtain a second error; determining the deviation of the Kth group of reconstructed physical quantities from the initial condition value and the boundary condition value to obtain a third error; and performing a weighted summation of the first error, the second error, and the third error to obtain the Kth target error corresponding to the Kth optimization operation.

[0104] For example, the difference between the Kth group of reconstructed physical quantities and the predetermined reconstructed physical quantities may include mean square error, mean absolute error, etc. The smaller the first error, the closer the value of the Kth group of reconstructed physical quantities is to the true value, and the better the data fitting effect.

[0105] The second error can characterize whether the reconstructed physical quantities conform to the core governing equations of the physical field, thereby reflecting whether the K-group reconstructed physical quantities conform to physical laws. For example, a large second error indicates that the K-group reconstructed physical quantities violate objective physical laws and are impossible to occur in reality (such as the reconstructed flow velocity values ​​not satisfying mass conservation, momentum conservation, etc.).

[0106] The third error can characterize whether the reconstructed physical quantities of the Kth group satisfy the engineering constraints of the physical field. For example, the reconstructed flow velocity on the pipe wall must be 0, otherwise it has no engineering significance. For example, the deviation (such as mean square error) between the value of the reconstructed physical quantity of the Kth group at the pipe boundary and the preset boundary condition value can be calculated. The smaller the deviation, the more the reconstructed physical quantity of the Kth group satisfies the engineering constraints.

[0107] The weights of the first error, the second error, and the third error can be set according to actual needs, and the first error, the second error, and the third error can be weighted and summed based on the weights.

[0108] By determining the first, second, and third errors, and then performing a weighted summation of these errors, we obtain the Kth target error corresponding to the Kth optimization operation. This allows for a comprehensive evaluation of the Kth group of reconstructed physical quantities from multiple dimensions. This ensures that the reconstructed physical quantities are not only numerically close to the true values, but also logically sound and feasible in engineering applications. Furthermore, it allows for precise identification of specific problems in the reconstruction (such as a large first error), enabling targeted optimization in the next optimization operation.

[0109] According to embodiments of this disclosure, the target physical field includes at least one of the following: a temperature field, a fluid flow field, a pressure field, and a concentration field.

[0110] For example, a temperature field can include the temperature values ​​at all locations within a space or object, and their distribution and variation patterns over time or space. Temperature fields can include, for example, the temperature field of a power battery pack, such as the temperature distribution at various locations within the battery cells, liquid cooling plates, and casing; and the temperature field of an industrial kiln, such as the temperature distribution within the furnace chamber, furnace walls, and workpieces of a ceramic kiln.

[0111] For example, a fluid flow field can include the velocity, direction, flow regime (such as laminar flow, turbulent flow, etc.) and distribution patterns of a liquid or gas at all locations within a flow channel. Fluid flow fields can include, for example, the flow velocity of water or air in HVAC ducts, and the airflow field in a wind tunnel test section.

[0112] For example, the concentration field can include the spatial distribution, diffusion, and reaction characteristics of the concentration of a target component within a mixed medium system. The concentration field may include, for example, the concentration distribution of reactants or products within a chemical synthesis reactor.

[0113] For example, a pressure field may include the fluid pressure at all locations within a certain space and its distribution patterns. A pressure field may also include, for example, the crude oil pressure distribution within an oil and gas pipeline.

[0114] like Figure 2As shown, the physical field reconstruction method of this disclosure embodiment can be applied to various scenarios according to actual needs, such as fluid baseline design, environmental monitoring, energy system optimization, etc.

[0115] According to embodiments of this disclosure, state analysis includes one of the following: physical quantity distribution analysis, physical quantity correlation analysis between multiple physics fields.

[0116] For example, physical quantity distribution analysis may include analyzing the distribution characteristics and variation patterns of physical quantities across a single physical field in the spatial or temporal dimensions. For instance, for the temperature distribution data of a battery pack, the temperature gradient distribution can be analyzed.

[0117] Correlation analysis of physical quantities between multiple physical fields includes analyzing the inherent correlation, causal relationship, and interaction mechanism between physical quantities of two or more coupled physical fields. For example, for pipeline global velocity distribution data and global pressure distribution data, the correlation characteristics between pressure leakage points and flow velocity can be analyzed.

[0118] like Figure 2 As shown, the target reconstruction model can be verified and applied, such as Allen-Cahn verification, Doran number cavity flow testing, and cylinder flow reconstruction.

[0119] Figure 4(a) schematically illustrates a comparison of sensor position optimization results according to an embodiment of the present disclosure.

[0120] Figure 4(b) schematically illustrates the clustering results of sensor position optimization according to an embodiment of the present disclosure.

[0121] Based on the lid-driven cavity flow (LDC) problem, the performance of the models OSSOPINN (Fixed) with fixed sensor positions, OSSOPINN (Moving) with dynamic sensor positions, and the related physical information neural network Vanilla PINN are compared. OSSOPINN (Fixed) optimizes model parameters only based on fixed sensor positions and the model is not used to optimize sensor positions. OSSOPINN (Moving) includes the target reconstruction model of the present disclosure embodiment. The related physical information neural network usually does not have actual sensor data and relies only on PDE constraints (Navier-Stokes equations) and conditional constraints to reconstruct the flow field.

[0122] Model performance can be evaluated using the L2 norm error. At a specific Reynolds number, conduct multiple experiments using different numbers of sensors (e.g., experiments using 2, 4, and 6 sensors respectively), setting the maximum number of iterations and the number of residual points in the PDE loss term.

[0123] As shown in 4(a), the target reconstruction model obtained using the present invention has the lowest error (median close to 0) and minimal fluctuation (narrower box), indicating that the target reconstruction model of the present invention can significantly improve the field reconstruction capability of the network and reduce the mean and standard deviation of the error.

[0124] In Figure 4(b), red represents the initial sensor positions, and black represents the optimized sensor positions. Figure 4(b) shows that the initial sensor positions are distributed arbitrarily and do not focus on key areas of the flow field. Clustering results obtained through 40 repeated experiments indicate that the sensors are concentrated in high-gradient regions (such as the boundary layer and near the vortex core).

[0125] This disclosure also provides a computer-readable storage medium, which may be included in the device / apparatus / system described in the above embodiments; or it may exist independently and not assembled into the device / apparatus / system. The computer-readable storage medium carries one or more programs that, when executed, implement the method according to the embodiments of this disclosure.

[0126] According to embodiments of this disclosure, the computer-readable storage medium may be a non-volatile computer-readable storage medium, such as including, but not limited to: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this disclosure, the computer-readable storage medium may be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. For example, according to embodiments of this disclosure, the computer-readable storage medium may include ROM 902 and / or RAM and / or one or more memories other than ROM and RAM.

[0127] Those skilled in the art will understand that the features described in the various embodiments of this disclosure can be combined and / or combined in various ways, even if such combinations or combinations are not explicitly described in this disclosure. In particular, the features described in the various embodiments of this disclosure can be combined and / or combined in various ways without departing from the spirit and teachings of this disclosure. All such combinations and / or combinations fall within the scope of this disclosure.

[0128] The embodiments of this disclosure have been described above. However, these embodiments are for illustrative purposes only and are not intended to limit the scope of this disclosure. Although various embodiments have been described above, this does not mean that the measures in the various embodiments cannot be used advantageously in combination. Various substitutions and modifications can be made by those skilled in the art without departing from the scope of this disclosure, and all such substitutions and modifications should fall within the scope of this disclosure.

Claims

1. A method of physical field reconstruction, characterized by, The method includes: The target location set consisting of the positions of multiple sensors, multiple sets of target sensor data collected by the multiple sensors, and preset constraints are input into the target reconstruction model, and the target reconstruction physical quantity for the target physical field is output. The target reconstruction physical quantity is used at least for state analysis of the target physical field. The target sensor data includes physical data for the target physical field collected by the sensors at corresponding positions. The target model parameters of the target reconstruction model and the target location set are obtained by iterative optimization of the initial reconstruction model. The Kth optimization operation includes: Based on the K-1 target error between the K-1th optimization result obtained from the K-1th optimization operation and the preset optimization result, the K-1th location set and the K-1th set of model parameters of the multiple sensors in the K-1th optimization result are optimized to obtain the Kth optimization result. The Kth optimization result includes the Kth location set and the Kth set of model parameters, where K is a positive integer.

2. The method of claim 1, wherein, The Kth optimization result also includes the Kth group of reconstructed physical quantities; The Kth optimization operation also includes: The encoder and decoder of the initial reconstruction model are updated according to the Kth group of model parameters to obtain the Kth updated encoder and the Kth updated decoder. Predict the sensor data collected by the multiple sensors at the positions indicated by the Kth position set to obtain the Kth set of predicted sensor data corresponding to the Kth optimization operation; Feature extraction and concatenation operations are performed on the Kth group of predicted sensor data and the K location sets to obtain multiple concatenated feature vectors; The Kth updated encoder is used to perform a fusion operation on the multiple concatenated feature vectors to obtain a fused feature vector. The Kth updated decoder is used to decode the fused feature vector to obtain the Kth group of reconstructed physical quantities.

3. The method of claim 2, wherein, The step of fusing the multiple concatenated feature vectors using the Kth updated encoder to obtain the fused feature vector includes: Using the Kth updated encoder, the attention weights of each of the multiple stitched feature vectors are determined based on the sensor association relationships represented by the multiple stitched feature vectors, wherein the sensor association relationships include positional associations and physical quantity data associations between sensors; The multiple concatenated feature vectors are weighted and fused according to the attention weights to obtain the fused feature vector.

4. The method of claim 2, wherein, The process of predicting sensor data collected by the multiple sensors at the location indicated by the Kth location set to obtain the Kth set of predicted sensor data corresponding to the Kth optimization operation includes: Obtain the (K-1)th set of predicted sensor data corresponding to the (K-1)th location set obtained from the (K-1)th optimization operation; Determine at least one first location from the (K-1)th location set whose spatial distance to each location in the Kth location set is less than a first distance threshold; Determine at least one target sensor data corresponding to the at least one first location from the (K-1)th group of predicted sensor data; Interpolation calculations are performed on the at least one target sensor data to obtain the Kth group of predicted sensor data.

5. The method of claim 1, wherein, The step of optimizing the K-1th location set and the K-1th set of model parameters of the plurality of sensors in the K-1th optimization result based on the target error between the K-1th optimization result obtained from the K-1th optimization operation and the preset optimization result, to obtain the Kth optimization result, includes: Based on the target error, determine the direction and displacement to be adjusted corresponding to the (K-1)th position set; The (K-1)th set of positions is adjusted according to the direction to be adjusted, the displacement to be adjusted, and the preset sensor position boundary constraints to obtain the Kth set of positions. The sensor position boundary constraints are used to constrain each position in the Kth set of positions to be within the preset sensor installation position range. Based on the target error, determine the amount to be corrected corresponding to the (K-1)th group of model parameters; The model parameters of the (K-1)th group are adjusted according to the amount to be corrected to obtain the model parameters of the Kth group.

6. The method of claim 5, wherein, The adjustment of the (K-1)th position set based on the direction to be adjusted, the displacement to be adjusted, and the preset sensor position boundary constraints includes: Determine the boundaries of the sensor installation location range; If at least one second location in the (K-1)th location set is less than a second distance threshold from the boundary, and the direction to be adjusted includes a first direction, the direction to be adjusted is changed to a second direction, wherein the first direction is the direction closer to the boundary, and the second direction is the opposite direction of the first direction; The (K-1)th position set is adjusted according to the second direction and the displacement to be adjusted.

7. The method of claim 2, wherein, The preset optimization results include: the preset reconstructed physical quantity, the physical equation of the target physical field that the preset reconstructed physical quantity needs to satisfy, and the initial condition value and boundary condition value that the target physical field needs to satisfy. The Kth optimization operation also includes: The difference between the Kth group of reconstructed physical quantities and the predetermined reconstructed physical quantities is determined to obtain the first error; The deviation of the Kth group of reconstructed physical quantities from the physical equation is determined to obtain the second error; The deviation of the Kth group of reconstructed physical quantities from the initial condition values ​​and boundary condition values ​​is determined to obtain the third error; The first error, the second error, and the third error are weighted and summed to obtain the Kth target error corresponding to the Kth optimization operation.

8. The method of claim 1, wherein, The target physical field includes at least one of the following: temperature field, fluid flow field, pressure field, and concentration field.

9. The method of claim 1, wherein, The state analysis includes one of the following: physical quantity distribution analysis, physical quantity correlation analysis between multiple physical fields.

10. A computer readable storage medium having stored thereon a computer program or instructions, characterized in that, When the computer program or instructions are executed by a processor, they implement the steps of the method according to any one of claims 1 to 7.

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