A pinning model wake field reconstruction method based on an LSTM network

Abstract

This invention discloses a method for reconstructing the wake field of a PINN model based on an LSTM network. The method includes: numerically simulating the wake field of a pre-defined object using CFD, and obtaining a raw dataset of wake field physical quantities evolving over time for several randomly selected monitoring nodes within the computational domain; adding random noise to the wake field physical quantities in the raw dataset to obtain a preprocessed dataset; constructing a long short-term memory (LSTM) physical information neural network model; constructing a total loss function that includes data loss and physical loss corresponding to the wake field physical quantities; training the LSTM physical information neural network model based on the total loss function and the preprocessed dataset to obtain a wake field reconstruction model; and reconstructing the wake field using the PINN model based on an LSTM network according to the wake field reconstruction model. This invention solves the problem that existing methods cannot effectively utilize observation data from a very small number of sparse random observation points to achieve high-precision and robust spatiotemporal continuous reconstruction of the wake field.

Description

Technical Field

[0001] This invention relates to the field of wake field reconstruction technology, and in particular to a wake field reconstruction method for a PINN model based on an LSTM network. Background Technology

[0002] In the field of marine engineering, accurate reconstruction and analysis of the wake field around marine equipment such as marine platforms, submarine cables, and autonomous underwater vehicles (AUVs) are crucial for assessing the hydrodynamic characteristics, structural stability, and fatigue life of these equipment.

[0003] Currently, the main methods for acquiring flow field data include numerical simulation and experimental measurement. While computational fluid dynamics (CFD) simulations can provide high-resolution flow field details, the computational process is extremely time-consuming and resource-intensive, and for complex, large-scale models, it places extremely high demands on computational resources, making it difficult to meet the needs of real-time analysis and on-site assessment. In terms of experimental measurement, particle image velocimetry (PIV) is a commonly used method for flow field reconstruction, but its equipment is very expensive and limited by optical observation conditions, making it extremely unsuitable for turbid or confined underwater environments.

[0004] In recent years, with the development of deep learning technology, the emergence of Physical Information Neural Networks (PINNs) has provided a new approach for flow field reconstruction. PINNs, by introducing control physics equations into the loss function of the neural network, have demonstrated higher efficiency and reliability than purely data-driven models. However, in practical underwater engineering applications, the complex marine dynamic environment and variable underwater topography limit sensor deployment. The raw wake field information obtained by underwater sensors often exhibits high sparsity and random spatial distribution. Existing PINN models, when reconstructing flow fields, often idealistically assume that the training data is a dense and regular grid distribution. When faced with extremely sparse and randomly distributed sampling points, the reconstruction accuracy of traditional PINN models suffers a severe decline due to a lack of deep capture of the temporal evolution logic of the flow field. Therefore, how to achieve high-precision, robust, and continuous spatiotemporal reconstruction of the wake field using a very small number of sparse random observation points has become a key technical problem in the field of marine intelligent sensing. Summary of the Invention

[0005] This invention provides a method for reconstructing the wake field of a PINN model based on an LSTM network to overcome the aforementioned technical problems.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows: A method for reconstructing the wake field of a PINN model based on an LSTM network includes the following steps: S1: Use CFD to numerically simulate the wake field of a pre-set object and obtain the original dataset of the evolution of the physical quantities of the wake field over time for several monitoring nodes randomly selected in the computational domain. The original dataset includes the spatiotemporal coordinate data of each monitoring node and its corresponding wake field physical quantities; and the wake field physical quantities include the transverse velocity component, longitudinal velocity component and pressure of the wake field. S2: Add random noise to the wake field physical quantities in the original dataset to obtain a preprocessed dataset; S3: Construct a long short-term memory physical information neural network model; S4: Construct a total loss function that includes the data loss and physical loss corresponding to the physical quantities of the wake field; Based on the total loss function and the preprocessed dataset, the long short-term memory physical information neural network model is trained to obtain the wake field reconstruction model. The wake field reconstruction model based on the LSTM network is implemented to reconstruct the PINN model wake field.

[0007] Furthermore, the long short-term memory physical information neural network model constructed in S3 includes an initial state input layer, an encoding layer, an LSTM neural network layer, a coordinate input layer, a coordinate dimension-upgrading layer, a decoding layer, and a mapping output layer. The initial state input layer is used to perform smooth distance-weighted interpolation on the preprocessed dataset to obtain the initial flow field physical quantities; The encoding layer is used to encode the initial flow field physical quantities into the initial memory cell state and initial hidden state of the corresponding LSTM network; The coordinate input layer is used to input the spatiotemporal coordinate data in the preprocessed dataset to the coordinate dimension-upgrading layer; the coordinate dimension-upgrading layer is used to perform data dimension-upgrading operations on the spatiotemporal coordinate data; The LSTM neural network layer is used to obtain the abstract features of the flow field based on the output of the encoding layer and the output of the coordinate dimensionality increase layer; the decoding layer is used to perform data dimensionality reduction on the abstract features of the flow field. The mapping output layer is used to perform feature mapping operations on the fused features to output the predicted values ​​of the wake field physical quantities corresponding to each future time step; and the fused features are the features obtained by performing dimensional concatenation operations on the output of the decoding layer and the corresponding spatiotemporal coordinate data.

[0008] Furthermore, the total loss function constructed in S4, which includes the data loss and physical loss corresponding to the wake field physical quantities, is as follows:

[0009]

[0010]

[0011]

[0012] In the formula: Represents the total loss function; Indicates data loss; Indicates physical loss; Indicates the selected first term within the computational domain Location and time coordinates of each monitoring node; , , express , , The abbreviated form; This represents the transverse velocity component of the wake field; This represents the longitudinal velocity component of the wake field; This represents the pressure in the wake field; Indicates fluid density; Indicates kinematic viscosity; These represent the penalty weight coefficients for the data loss term and the physical loss term, respectively; Indicates the number of corresponding monitoring nodes; , , express , , The abbreviated form; , , Indicates correspondence , , The network prediction value; , , This represents the margin of the fluid dynamics equation and momentum equation in the spatiotemporal data of the corresponding monitoring node.

[0013] Furthermore, the method for obtaining the wake field reconstruction model in S4 is as follows: S41: Randomly divide the preprocessed dataset into training and validation sets according to a preset ratio; S42: Train the constructed long short-term memory physical information neural network model based on the training set to obtain the trained long short-term memory physical information neural network model; S43: Use the total loss function, which includes the data loss and physical loss corresponding to the physical quantities of the wake field, as the model loss function, and perform model validation on the trained long short-term memory physical information neural network model through the validation set. That is, to determine whether the output of the long short-term memory physical information neural network model after training has converged; If the output of the trained Long Short-Term Memory Physical Information Neural Network Model converges, then the trained Long Short-Term Memory Physical Information Neural Network Model is confirmed to be the wake field reconstruction model. Otherwise, the weight parameters of the trained long short-term memory physical information neural network model are adaptively adjusted based on the backpropagation method, and step S42 is repeated until the weight parameters of the trained long short-term memory physical information neural network model with converged output are confirmed to be the optimal weight parameters, and the long short-term memory physical information neural network model is reconstructed to obtain the wake field reconstruction model.

[0014] Furthermore, the formula for obtaining the abstract features of the flow field is:

[0015]

[0016]

[0017]

[0018]

[0019]

[0020] In the formula: This indicates a method used to map numerical values ​​to the range [0,1] for gating control. Activation function; Represents the hyperbolic tangent function; express Product symbol; , , , Represents the learnable weight parameters in the network; , , , Indicates the bias term; express The forget gate is used to selectively inherit the historical state of the wake field. express Input gate at all times; express Candidate states at any given moment; express Cellular state at any given moment; Indicates the output gate; express The hidden state at any given moment is the abstract feature of the flow field; express The hidden state at time -1; express Cell state at time -1; express The result of performing data dimensionality upgrade operations on spatiotemporal coordinate data at any time.

[0021] Furthermore, the IDW algorithm is used to perform smooth distance-weighted interpolation on the preprocessed dataset.

[0022] Beneficial Effects: This invention provides a wake field reconstruction method for the PINN model based on LSTM network. By adding random noise to the wake field physical quantities in the original dataset, it aims to enhance the model's reconstruction capability and robustness under real non-ideal observation conditions, ensuring that the subsequent network model can extract effective fluid physics features from uncertain information. A long short-term memory physical information neural network model is constructed. Since the LSTM neural network layer in the model fully utilizes its ability to capture and remember the evolution characteristics of the wake field over time, it effectively uses the continuity of the time dimension to fill the spatial information gaps caused by sparse data. During model training, by introducing the constructed total loss function that includes the data loss and physical loss corresponding to the wake field physical quantities, the wake field reconstruction model can successfully and faithfully reconstruct a spatiotemporally continuous wake field that is highly consistent with the computational fluid dynamics benchmark and conforms to the laws of physical evolution. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 This is a flowchart of the PINN model wake field reconstruction method based on LSTM network of the present invention; Figure 2 This is a schematic diagram of the LSTM neural network layer structure in this embodiment; Figure 3 This is a schematic diagram of the PINN model structure based on LSTM network in this embodiment; Figure 4 This is the core block diagram of the PINN model wake field construction method of the LSTM network in this embodiment; Figure 5 This is a distribution diagram of sparse random monitoring nodes in this embodiment; Figure 6 This is the initial velocity contour map of the wake field in this embodiment; Figure 7 This example shows a comparison of wake field velocity contour maps reconstructed from the model during training at 200 monitoring points. Figure 8 For training the model at 200 randomly distributed monitoring points in 3 groups in this embodiment, a velocity comparison cloud map of the reconstructed wake field is generated. Figure 9 This example shows a comparison cloud map of the wake field velocity during model reconstruction when training 100 monitoring points. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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.

[0026] This embodiment provides a method for reconstructing the wake field of a PINN model based on an LSTM network, such as... Figure 1 As shown, the specific steps include: S1: High-resolution numerical simulation of the wake field of the pre-set object around the flow is performed using CFD, and the original dataset of the wake field physical quantities evolving over time is obtained for several monitoring nodes (i.e., highly sparse and randomly distributed sensor monitoring nodes) randomly selected in the computational domain. The original dataset includes the spatiotemporal coordinate data of each monitoring node and its corresponding wake field physical quantities. The wake field physical quantities include the transverse velocity component, longitudinal velocity component, and pressure of the wake field. Specifically, in this embodiment, the physical dimensions of the computational domain of the pre-set object, i.e., the reconstructed flow field, are set to be 160cm long and 60cm wide, with a cylinder with a diameter of 20cm inside. S2: Add random noise to the wake field physical quantities in the original dataset to obtain a preprocessed dataset; This embodiment aims to enhance the model's reconstruction capability and robustness under real non-ideal observation conditions by adding random noise, ensuring that the network can extract effective fluid physics features from uncertain information; S3: Construct a long short-term memory physical information neural network model; Specifically, such as Figure 3 As shown, the constructed long short-term memory physical information neural network model includes an initial state input layer, an encoding layer, an LSTM neural network layer, a coordinate input layer, a coordinate dimension-upgrading layer, a decoding layer, and a mapping output layer. The initial state input layer is used to perform smooth distance-weighted interpolation on the preprocessed dataset based on the IDW algorithm to obtain the initial flow field physical quantities; Specifically, the long short-term memory physical information neural network model constructed in this embodiment requires the input of global physical quantities at the initial moment during the inference and reconstruction stages to activate the network and initiate the temporal evolution deduction of the flow field. However, in practical applications, the reconstruction stage often only obtains measurement data at discrete spatial points through a very small number of sensors, making it impossible to directly obtain the continuous initial physical quantity distribution at any coordinate position within the flow field. To address the aforementioned problem of missing initial data, this embodiment introduces the Inverse Distance Weighting (IDW) method. This algorithm is based on the geographical correlation law, which states that points that are spatially closer have a higher correlation in their physical properties. The core logic of the IDW algorithm is to use the inverse ratio of the distance between the target monitoring node to be estimated and each known monitoring node as a weighting coefficient, thereby achieving a smooth transition from discrete observations to a continuous flow field space. Mathematically, for any coordinate point (x, y) in the flow field computation domain, the component estimation of the flow field physical quantities at the initial moment is defined as:

[0027] In the formula: Represents the physical quantities of the flow field at the initial moment. = ; Indicates the first i The physical quantities of the wake field that evolve over time at each monitoring node, and = ; Representing the i Discrete measured values ​​of wake field physical quantities at each monitoring node; N represents the total number of monitoring nodes; Indicates the first i Normalized weighting factors corresponding to each monitoring point; weighting factors The calculation depends on the Euclidean distance between the target point and each sensor. In this embodiment, a strategy inversely proportional to the square of the distance is adopted to ensure the local smoothness of the interpolation result:

[0028] This embodiment utilizes the IDW algorithm to transform extremely low-density, randomly sampled monitoring nodes into initial lateral and longitudinal velocity component contour maps or pressure contour maps of the wake field that cover the entire computational domain. This process transforms sparse observation data into a high-density flow field physical skeleton. The generated global initial values, i.e., the initial flow field physical quantities, serve as constraints for the initial state input layer, used to encode the initial memory state into the LSTM neural network. and This not only solves the problem of missing physical quantities at the initial moment, but also provides a reliable physical benchmark for subsequent models to accurately capture the complex evolution law of wake vortex shedding.

[0029] The encoding layer is used to encode the initial flow field physical quantities into the initial memory cell state and initial hidden state of the corresponding LSTM network; The coordinate input layer is used to input the spatiotemporal coordinate data in the preprocessed dataset to the coordinate dimension-upgrading layer; the coordinate dimension-upgrading layer is used to perform data dimension-upgrading operations on the spatiotemporal coordinate data; The LSTM neural network layer is used to obtain the abstract features of the flow field based on the output of the encoding layer and the output of the coordinate dimensionality increase layer; the decoding layer is used to perform data dimensionality reduction on the abstract features of the flow field. The mapping output layer is used to perform feature mapping operations on the fused features to output the predicted values ​​of the wake field physical quantities corresponding to each future time step; and the fused features are the features obtained by performing dimensional concatenation operations on the output of the decoding layer and the corresponding spatiotemporal coordinate data.

[0030] In this embodiment, a Long Short-Term Memory (LSTM) network is introduced as the core of the reconstruction framework, such as... Figure 2 As shown, this paper aims to address the temporal gap problem inherent in traditional physical information neural networks (PINNs) when processing fluid dynamics problems. Currently, the traditional multilayer perceptron-based PINN typically treats the time variable t as merely an additional coordinate dimension alongside the spatial variable (x, y). This approach fundamentally ignores the inherent temporal evolution characteristics of fluid dynamics, namely, that the current flow field state is strictly governed by its historical evolution. Therefore, when the spatial sampling of sensor monitoring nodes is highly sparse and randomly distributed, the multilayer perceptron-based PINN struggles to deduce the complete physical evolution law from discrete spatiotemporal points. To overcome this limitation, this embodiment introduces an LSTM neural network to capture the nonlinear, long-term periodic dynamic characteristics of the fluid system. As an advanced variant of the Recurrent Neural Network (RNN), the LSTM neural network effectively solves the vanishing gradient problem common in long-sequence training of traditional RNNs by introducing a gating mechanism. The core innovation of the LSTM neural network lies in its inherent cell state and gating structure. This structure endows the network with the ability to retain key physical features and eliminate noise during long-term flow field evolution. At a given time step t, the forward propagation process of the LSTM neural network is strictly controlled by the following set of mathematical equations to obtain the abstract characteristics of the flow field, the expression of which is:

[0031]

[0032]

[0033]

[0034]

[0035]

[0036] In the formula: This indicates a method used to map numerical values ​​to the range [0,1] for gating control. Activation function; Represents the hyperbolic tangent function; express Product symbol; , , , Represents the learnable weight parameters in the network; , , , Indicates the bias term; express The forget gate is used to selectively inherit the historical state of the wake field. That is, by calculating the importance weight of historical information, the selective inheritance of the historical state of the flow field is realized. express Input gate at all times; express Candidate states at any time, input gate With candidate state Collaborative work encodes transient features from current sparse observations into cellular states. middle; express Cellular state at any given moment; Indicates output gate, output gate The generated hidden state combines long-term memory with current motivation. It contains rich spatiotemporal evolution context information; express The hidden state at any given moment is the abstract feature of the flow field; express The hidden state at time -1; express Cell state at time -1; express This is the result of performing data dimensionality upscaling on the spatiotemporal coordinate data at any given time. In this embodiment, by embedding this strict temporal logic into the PINN framework, the Long Short-Term Memory Physical Information Neural Network model, namely LSTM-PINN, can effectively utilize the continuous information of flow field evolution, thereby ensuring the reconstruction of a high-fidelity continuous flow field even under conditions of extremely sparse sensor sampling.

[0037] In this embodiment, at the front end of the model, the initial state input layer processes the physical observations at the initial or current reference time. The encoding layer maps low-dimensional physical space data to a high-dimensional feature space using a multilayer perceptron, thereby generating the initial cell states and hidden states necessary for the initialization of the LSTM neural network. Mathematically, this process deeply encodes the true physical information of the initial flow field into the basic memory of the LSTM neural network. This physical information-rich initialization strategy not only ensures high prediction accuracy at the beginning of the time step but also significantly suppresses the error accumulation phenomenon commonly seen in long-term time-series extrapolation of recurrent neural networks. The spatiotemporal coordinates of the sensor monitoring nodes to be predicted at future time steps enter the network through the coordinate input layer and undergo preliminary feature extraction (i.e., data dimensionality upscaling) through a coordinate dimensionality upscaling layer configured with convolutional layers and activation functions. Subsequently, these coordinates are input into the LSTM neural network layer and combined with the memory states initialized with physical information to perform in-depth extrapolation of the spatiotemporal evolution characteristics of the flow field. Following the LSTM neural network layer, the decoding layer is responsible for processing the high-dimensional hidden features output by the LSTM neural network layer at subsequent time steps. This involves nonlinearly compressing the high-dimensional flow field abstract features output by the LSTM neural network layer to obtain the highly abstract spatiotemporal evolution laws of the flow field. This decoding layer consists of multiple fully connected networks and acts as a nonlinear decoder, systematically compressing and reducing the high-dimensional features step by step. This dimensionality reduction process allows the model to effectively remove redundant information, improving the mapping and representation capabilities of the subsequent physical quantity mapping network layers. Finally, these decoded flow field features are concatenated with the corresponding spatiotemporal coordinate data through coordinate fusion operations and input to the corresponding physical quantity mapping output layer to obtain the predicted values ​​of the specific wake field physical quantities at the corresponding spatial location and time.

[0038] Furthermore, the input data for the Long Short-Term Memory (LSTM) physical information neural network model includes the following steps during training and inference: In training, the preprocessed dataset is reconstructed into sequence fragments. The first data vector in each sample data fragment of the preprocessed dataset is used as the initial physical constraint for the encoding layer. Subsequent data vectors are used as coordinate values ​​at different times for the same location, allowing the model to focus on learning the dynamics of flow field evolution within a local time window. In inference, the model operates in an autoregressive manner. First, the initial physical state (i.e., the initial flow field physical quantities) is input to activate the network, and the predicted physical quantities for a specified future time step are output. Then, these outputs are concatenated as new known states and iteratively input into the model's front end. Through this autoregressive loop, a continuous, long-term, and robust reconstruction of the entire complex wake field's temporal evolution process is achieved.

[0039] S4: Construct a total loss function that includes the data loss and physical loss corresponding to the physical quantities of the wake field. Its expression is:

[0040]

[0041]

[0042]

[0043] In the formula: Represents the total loss function; This represents the data loss and is used to quantify the mean square error between the network's predicted values ​​and the actual measured values ​​from N sparse sampling points. Indicates physical loss; Indicates the selected first term within the computational domain Location and time coordinates of each monitoring node; , , express , , The abbreviated form; This represents the transverse velocity component of the wake field; This represents the longitudinal velocity component of the wake field; This represents the pressure in the wake field; Indicates fluid density; Indicates kinematic viscosity; These represent the penalty weight coefficients for the data loss term and the physical loss term, respectively, used to adjust the balance between the model's fitting accuracy to the observed data and its adherence to physical laws; Indicates the number of corresponding monitoring nodes; , , express , , The abbreviated form; , , Indicates correspondence , , The network prediction value; , , It represents the margin of the fluid dynamics equation and momentum equation in the spatiotemporal data of the corresponding monitoring node. The closer its value is to 0, the more it conforms to the physical laws.

[0044] In this embodiment, the operating logic of the Physical Information Neural Network (PINN) can be summarized into three stages: forward propagation, partial derivative calculation based on automatic differentiation, and loss optimization. Its core lies in introducing fluid dynamics equations as prior constraints into the network training process, enabling the model to satisfy physical laws while fitting sparse observation data. In the forward propagation stage, the model receives the spatiotemporal coordinates of the flow field nodes to be predicted as input. Through layer-by-layer nonlinear mapping calculations of the deep neural network, it outputs the velocity components and pressure of the predicted flow field at the current coordinate point. The network uses automatic differentiation technology to accurately calculate the partial derivatives of the output physical quantities with respect to the input spatiotemporal coordinates. Unlike the traditional finite difference method, automatic differentiation can obtain analytical-level partial derivative accuracy and is independent of the computational grid. These partial derivatives are then used to construct a model based on the incompressible fluid continuity equation and NS ( The residuals of the partial differential equation of the momentum equation. Finally, in the loss optimization and parameter update stage, the network weights and bias parameters are iteratively optimized by minimizing the composite loss function, and the total loss function ( ) by data loss ( ) and physical loss ( The weighted sum of the components can be minimized during model training. The Adam optimizer continuously updates the neural network parameters, driving the model to reconstruct a high-fidelity, physically consistent continuous wake field using only a very small amount of sparse observation information. Based on the total loss function and the preprocessed dataset, the long short-term memory physical information neural network model is trained to obtain the wake field reconstruction model. Specifically, the method for obtaining the wake field reconstruction model is as follows: S41: Randomly divide the preprocessed dataset into training and validation sets according to a preset ratio; S42: Train the constructed long short-term memory physical information neural network model based on the training set to obtain the trained long short-term memory physical information neural network model; S43: Use the total loss function, which includes the data loss and physical loss corresponding to the physical quantities of the wake field, as the model loss function, and perform model validation on the trained long short-term memory physical information neural network model through the validation set. That is, to determine whether the output of the long short-term memory physical information neural network model after training has converged; If the output of the trained Long Short-Term Memory Physical Information Neural Network Model converges, then the trained Long Short-Term Memory Physical Information Neural Network Model is confirmed to be the wake field reconstruction model. Otherwise, the weight parameters of the trained long short-term memory physical information neural network model are adaptively adjusted based on the backpropagation method, and step S42 is repeated until the weight parameters of the trained long short-term memory physical information neural network model with converged output are confirmed to be the optimal weight parameters, and the long short-term memory physical information neural network model is reconstructed to obtain the wake field reconstruction model. The wake field reconstruction model based on the LSTM network is implemented to reconstruct the PINN model wake field.

[0045] This embodiment also includes the following experimental results: By comparing the high-resolution velocity contour maps reconstructed by the trained LSTM-PINN with the reconstruction results of the traditional MLP-PINN and the ground truth CFD benchmark, such as... Figure 4 As shown, its ability to reconstruct complex flow fields under extremely sparse monitoring conditions is verified, such as... Figures 5 to 9 As shown: Figure 5 This is a distribution diagram of sparse random monitoring points in this embodiment. The diagram visually illustrates the spatial distribution of random monitoring points of different densities (200 or 100 sparse monitoring points as indicated in the diagram) within the flow field computational domain. Within the entire rectangular computational domain, 1000 reconstructed points are regularly distributed; these regular nodes constitute the high-density physical framework of the flow field.

[0046] Figure 6 This is the initial velocity contour map of the wake field in this embodiment. The map shows three independent random sampling groups, row by row, with 200 random monitoring points in each group. In the first column of the image, the spatial coordinates of the random monitoring points are presented visually as a scatter plot, where the color mapping of each point directly represents the magnitude of the u-velocity component at that specific location. The second column of the image shows the global u-velocity contour map of the initial flow field, smoothly reconstructed across the entire computational domain based on the sparse monitoring point data from the left side using a smooth distance-weighted interpolation method.

[0047] Figure 7This figure presents a comparison of velocity contour maps of the reconstructed wake field during training with 200 sparse random monitoring points in this embodiment. Arranged in a matrix, the figure visually compares the velocity field reconstruction results of different neural network models with the actual calculated values ​​of fluid dynamics at four different historical moments during the flow field evolution. The color mapping of the contour map represents the magnitude of the velocity value at that spatial location. The first column shows the reconstruction results based on the LSTM and PINN fusion network architecture proposed in this embodiment. The second column shows the reconstruction results of the traditional multilayer perceptron-based physical information neural network (MLP-PINN). The third column, as a real computational fluid dynamics (CFD) calculation, clearly presents the high-resolution and complex dynamic evolution of the typical Karman vortex street shedding and wake field over time generated by flow around a cylinder.

[0048] Figure 8 This example uses a comparative contour map of the wake field velocity reconstruction during model training with 200 randomly distributed monitoring points in three groups. The map, arranged in a matrix, visually demonstrates the transient velocity field reconstruction results output by the method described in this example under three independent random measurement point distribution schemes with varying spatial locations. Each column corresponds to a specific random measurement point distribution scheme, and each row represents a different historical moment in the flow field dynamics evolution. The color mapping of the contour map represents the velocity value at that specific spatial location.

[0049] Figure 9 This is a comparison contour map of the velocity field reconstructed by the model during training with 100 sparse random monitoring points in this embodiment. The map, arranged in a matrix, visually compares the velocity field reconstruction results of different neural network models with the calculated values ​​from actual fluid dynamics at four different historical moments (Time = 0.4s, 0.8s, 1.2s, 1.4s, rows from top to bottom) during the flow field evolution. The color mapping of the contour map represents the velocity value at that spatial location. The first column shows the reconstruction results of the method used in this embodiment, the second column shows the reconstruction results of the traditional physical information neural network based on a multilayer perceptron, and the third column shows the actual computational fluid dynamics calculation results.

[0050] In summary, compared with the prior art, the beneficial effects of the method described in this embodiment are as follows: The method described in this embodiment can achieve accurate and high-fidelity reconstruction of highly complex continuous flow fields under extremely sparse random observation conditions. By combining the comparison of the transient velocity reconstruction effect of the wake field under the conditions of 200 and 100 random monitoring points, the technical advantages of the method described in this embodiment compared with the existing traditional methods can be intuitively and clearly seen.

[0051] Under extreme conditions relying solely on data from 200 sparse and randomly distributed monitoring points, the traditional MLP-PINN model suffers severe degradation or even failure in reconstruction capability due to the lack of sufficient physical boundary conditions and high-density measurement points within the flow field. Its output can only show large-scale, gentle velocity gradient changes, completely failing to capture the vortex shedding phenomenon and fine wake structure behind the cylinder. In contrast, despite extremely sparse training data, the model described in this embodiment still exhibits extremely high flow field reconstruction accuracy. This is because the LSTM neural network layer in the model fully leverages its ability to capture and memorize the wake field's evolution over time, effectively utilizing the continuity of the time dimension to fill the spatial information gaps caused by sparse data. This model successfully and faithfully reconstructs the complex spatiotemporal evolution of wake vortex shedding and downstream wake, which is highly consistent with computational fluid dynamics benchmarks.

[0052] When the number of monitoring points is drastically reduced to only 100 in the extreme sparse condition, the traditional MLP-PINN model completely loses its ability to reconstruct the dynamic evolution of the flow field, and the result degenerates into a uniform background flow field with almost no obvious gradient. However, the LSTM-PINN model proposed by the method described in this embodiment still exhibits excellent system robustness under such stringent data scarcity conditions, stably and accurately reconstructing the basic morphology of the Karman vortex street and its temporal evolution characteristics propagating downstream.

[0053] By comparing the velocity contour maps of the reconstructed wake field during training with 200 randomly distributed monitoring points in three groups, the robustness and accuracy of the LSTM-PINN model proposed in this embodiment under different spatial measurement point distribution schemes are further verified. A horizontal comparison of contour maps from different columns at the same evolution time clearly shows that regardless of the random distribution of these 200 monitoring points in the computational domain, the LSTM-PINN model proposed in this embodiment can stably and clearly reconstruct the complex alternating shedding phenomenon of the KAMAN vortex street in the cylindrical wake region. The reconstructed velocity gradient distribution, core vortex morphology, and overall wake characteristics among different random sampling groups all exhibit a high degree of consistency. This result fully demonstrates that when the number of monitoring points is only 200, the LSTM-PINN model proposed in this embodiment already possesses the ability to fully extract and reconstruct the complete physical laws of the flow field from limited and random discrete observation data. This model is insensitive to the specific spatial arrangement of the measurement points, effectively overcoming the adverse effects of the spatial randomness of sparse sensors, thereby achieving continuous, stable, and complete high-fidelity spatiotemporal flow field reconstruction.

[0054] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for reconstructing a wake flow field based on a PINN model with an LSTM network, characterized in that, Specifically, the following steps are included: S1: Use CFD to numerically simulate the wake field of a pre-set object and obtain the original dataset of the evolution of the physical quantities of the wake field over time for several monitoring nodes randomly selected in the computational domain. The original dataset includes the spatiotemporal coordinate data of each monitoring node and its corresponding wake field physical quantities; and the wake field physical quantities include the transverse velocity component, longitudinal velocity component and pressure of the wake field. S2: Add random noise to the wake field physical quantities in the original dataset to obtain a preprocessed dataset; S3: Construct a long short-term memory physical information neural network model; S4: Construct a total loss function that includes the data loss and physical loss corresponding to the physical quantities of the wake field; Based on the total loss function and the preprocessed dataset, the long short-term memory physical information neural network model is trained to obtain the wake field reconstruction model. The wake field reconstruction model based on the LSTM network is implemented to reconstruct the PINN model wake field.

2. The method for reconstructing the wake field of a PINN model based on an LSTM network according to claim 1, characterized in that, The long short-term memory physical information neural network model constructed in S3 includes an initial state input layer, an encoding layer, an LSTM neural network layer, a coordinate input layer, a coordinate dimension-upgrading layer, a decoding layer, and a mapping output layer. The initial state input layer is used to perform smooth distance-weighted interpolation on the preprocessed dataset to obtain the initial flow field physical quantities; The encoding layer is used to encode the initial flow field physical quantities into the initial memory cell state and initial hidden state of the corresponding LSTM network; The coordinate input layer is used to input the spatiotemporal coordinate data in the preprocessed dataset to the coordinate dimension-upgrading layer; the coordinate dimension-upgrading layer is used to perform data dimension-upgrading operations on the spatiotemporal coordinate data; The LSTM neural network layer is used to obtain abstract features of the flow field based on the output of the encoding layer and the output of the coordinate dimensionality increase layer; The decoding layer is used to perform data dimensionality reduction operations on the abstract features of the flow field. The mapping output layer is used to perform feature mapping operations on the fused features to output the predicted values ​​of the wake field physical quantities corresponding to each future time step; and the fused features are the features obtained by performing dimensional concatenation operations on the output of the decoding layer and the corresponding spatiotemporal coordinate data.

3. The method for reconstructing the wake field of a PINN model based on an LSTM network according to claim 1, characterized in that, The total loss function constructed in S4, which includes the data loss and physical loss corresponding to the physical quantities of the wake field, is as follows: In the formula: Represents the total loss function; Indicates data loss; Indicates physical loss; Indicates the selected first term within the computational domain Location and time coordinates of each monitoring node; , , express , , The abbreviated form; This represents the transverse velocity component of the wake field; This represents the longitudinal velocity component of the wake field; This represents the pressure in the wake field; Indicates fluid density; Indicates kinematic viscosity; These represent the penalty weight coefficients for the data loss term and the physical loss term, respectively; Indicates the number of corresponding monitoring nodes; , , express , , The abbreviated form; , , Indicates correspondence , , The network prediction value; , , This represents the margin of the fluid dynamics equation and momentum equation in the spatiotemporal data of the corresponding monitoring node.

4. The method for reconstructing the wake field of a PINN model based on an LSTM network according to claim 1, characterized in that, The method for obtaining the wake field reconstruction model in S4 is as follows: S41: Randomly divide the preprocessed dataset into training and validation sets according to a preset ratio; S42: Train the constructed long short-term memory physical information neural network model based on the training set to obtain the trained long short-term memory physical information neural network model; S43: Use the total loss function, which includes the data loss and physical loss corresponding to the physical quantities of the wake field, as the model loss function, and perform model validation on the trained long short-term memory physical information neural network model through the validation set. That is, to determine whether the output of the long short-term memory physical information neural network model after training has converged; If the output of the trained Long Short-Term Memory Physical Information Neural Network Model converges, then the trained Long Short-Term Memory Physical Information Neural Network Model is confirmed to be the wake field reconstruction model. Otherwise, the weight parameters of the trained long short-term memory physical information neural network model are adaptively adjusted based on the backpropagation method, and step S42 is repeated until the weight parameters of the trained long short-term memory physical information neural network model with converged output are confirmed to be the optimal weight parameters, and the long short-term memory physical information neural network model is reconstructed to obtain the wake field reconstruction model.

5. The method for reconstructing the wake field of a PINN model based on an LSTM network according to claim 3, characterized in that, The formula for obtaining the abstract features of the flow field is: In the formula: This indicates a method used to map numerical values ​​to the range [0,1] for gating control. Activation function; Represents the hyperbolic tangent function; express Product symbol; , , , Represents the learnable weight parameters in the network; , , , Indicates the bias term; express The forget gate is used to selectively inherit the historical state of the wake field. express Input gate at all times; express Candidate states at any given moment; express Cellular state at any given moment; Indicates the output gate; express The hidden state at any given moment is the abstract feature of the flow field; express The hidden state at time -1; express Cell state at time -1; express The result of performing data dimensionality upgrade operations on spatiotemporal coordinate data at any time.

6. The method for reconstructing the wake field of a PINN model based on an LSTM network according to claim 2, characterized in that, The method for performing smooth distance-weighted interpolation on the preprocessed dataset uses the IDW algorithm.

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