Virtual reality display method and system based on reduced-order model and deep learning

Abstract

The invention provides a virtual reality display method and system based on a reduced-order model and deep learning, and relates to the field of virtual reality, and the method comprises the steps: obtaining the physical characteristics and environment information of a simulation object; performing fluid dynamic simulation on the simulation object based on the physical characteristics and the environmental information of the simulation object to obtain flow field data of the simulation object; performing order reduction processing on the flow field data of the simulation object based on an intrinsic orthogonal decomposition method, and extracting a target spatial pattern and a target time coefficient of the simulation object; a TCN-LSTM-KAN model and a physical field prediction model are established and trained; predicting a future time coefficient according to the time coefficient of the simulation object through a TCN-LSTM-KAN model; predicting a physical field of the future time according to the future time coefficient and the target space mode of the simulation object; according to the physical field of the future time, the virtual model of the target simulation object is established in the virtual reality environment, virtual reality display is performed, and the method has the advantage of improving the sense of reality of the virtual reality scene.

Description

Technical Field

[0001] The present invention relates to the field of virtual reality, and in particular to a virtual reality display method and system based on a reduced-order model and deep learning. Background Art

[0002] Virtual reality (VR) technology has been widely used in many fields such as entertainment, healthcare, architecture and chemical engineering. It provides a highly immersive interactive environment where users can experience various scenarios, thereby replacing the real environment with virtual scenes to improve learning, decision-making and work efficiency.

[0003] At present, in the field of industrial production, existing applications of virtual reality simulation only model and animate physical objects, without considering the state changes of real physical properties under the coupling of multiple physical fields such as electricity, magnetism, heat, force, and fluid; in the field of safety and emergency response, existing application software only provides virtual scenes and prompts, and lacks research on the basic theory of disaster development, disaster numerical simulation and high-risk toxicity models; although multi-physics field coupling numerical simulation technology is often used in these fields to capture the changes in the physical properties of objects, such as finite element analysis and computational fluid dynamics; numerical simulation usually requires a lot of computing resources and time, which hinders the improvement of the efficiency of realistic dynamic scene modeling in VR and makes it difficult to meet the requirements of realism and real-time performance.

[0004] Therefore, it is necessary to provide a virtual reality display method and system based on reduced-order models and deep learning to improve the realism of virtual reality scenes. Summary of the Invention

[0005] The present invention provides a virtual reality display method based on a reduced-order model and deep learning, comprising: acquiring physical characteristics and environmental information of a simulation object; performing fluid dynamics simulation on the simulation object based on the physical characteristics and environmental information of the simulation object to acquire flow field data of the simulation object; performing order reduction processing on the flow field data of the simulation object based on an intrinsic orthogonal decomposition method to extract a target spatial pattern and a target time coefficient of the simulation object; establishing and training a TCN-LSTM-KAN model and a physical field prediction model; predicting a future time coefficient based on the time coefficient of the simulation object through the TCN-LSTM-KAN model; predicting a physical field at a future time based on the future time coefficient and the target spatial pattern of the simulation object; and establishing a virtual model of the target simulation object in a virtual reality environment based on the physical field at a future time to perform virtual reality display.

[0006] Furthermore, the flow field data of the simulation object is reduced in order based on the intrinsic orthogonal decomposition method to extract the target spatial mode and target time coefficient of the simulation object, including: reducing the flow field data of the simulation object based on the intrinsic orthogonal decomposition method to obtain the reduced-order flow field data of the simulation object; determining the spatial mode and time coefficient of the simulation object based on the reduced-order flow field data of the simulation object; determining the target mode based on the energy contribution of each mode; and extracting the target spatial mode and target time coefficient of the simulation object from the spatial mode and time coefficient of the simulation object according to the target mode.

[0007] Furthermore, based on the energy contribution of each mode, a target mode is determined, including: determining multiple mode combinations, wherein the mode combination includes at least one mode; for each mode combination, calculating the truncated energy ratio of the mode combination according to the energy contribution of each mode included in the mode combination; and determining the target mode combination according to the truncated energy ratio of each mode combination, wherein the mode included in the target mode combination is used as the target mode.

[0008] Furthermore, according to the cutoff energy ratio of each modal combination, a target modal combination is determined, including: taking a modal combination with a cutoff energy ratio greater than a cutoff energy ratio threshold as a candidate modal combination; and taking a candidate modal combination with a minimum cutoff energy ratio as the target modal combination.

[0009] Furthermore, the TCN-LSTM-KAN model includes a TCN layer, an LSTM layer and a KAN layer; the TCN layer is used to extract key fluid features from the time coefficient of the simulation object; the LSTM layer is used to generate time-step prediction results based on the key fluid features extracted by the TCN layer; and the KAN layer is used to generate future time coefficients based on the time-step prediction results output by the LSTM layer.

[0010] Furthermore, the physical field at future time is predicted based on the future time coefficient and the target spatial pattern of the simulation object, including: updating the time coefficient sequence based on the future time coefficient; and predicting the physical field at future time based on the updated time coefficient sequence and the target spatial pattern of the simulation object.

[0011] Furthermore, according to the physical field at the future time, a virtual model of the target simulation object is established in the virtual reality environment, and virtual reality display is performed, including: according to the physical field at the future time, a virtual model of the target simulation object is established in the virtual reality environment; and virtual reality display is performed using data mapping technology and rendering optimization technology.

[0012] Furthermore, the cutoff energy ratio of the modal combination is calculated based on the following formula:

[0013]

[0014] Where E is the cutoff energy ratio of the mode combination, λ j is the energy contribution of the jth mode, N is the total number of modes included in the modal combination, and M is the total number of modes.

[0015] Furthermore, the physical characteristics of the simulation object include at least density, viscosity, compressibility and expansibility; the environmental information of the simulation object includes at least temperature, pressure and flow rate; and the flow field data of the simulation object includes at least velocity field, pressure field and density field.

[0016] The present invention provides a virtual reality display system based on a reduced-order model and deep learning, which applies the above-mentioned virtual reality display method based on the reduced-order model and deep learning, including: an information acquisition module, used to obtain physical characteristics and environmental information of a simulation object; an object simulation module, used to perform fluid dynamics simulation on the simulation object based on the physical characteristics and environmental information of the simulation object, and obtain flow field data of the simulation object; a feature extraction module, used to perform order reduction processing on the flow field data of the simulation object based on the proper orthogonal decomposition method, and extract the target spatial pattern and target time coefficient of the simulation object; a feature prediction module, used to establish and train a TCN-LSTM-KAN model and a physical field prediction model, and predict the future time coefficient based on the time coefficient of the simulation object through the TCN-LSTM-KAN model, and predict the physical field in the future time based on the future time coefficient and the target spatial pattern of the simulation object; and an object display module, used to establish a virtual model of the target simulation object in a virtual reality environment based on the physical field in the future time, and perform virtual reality display.

[0017] Compared with the existing technology, the virtual reality display method and system based on reduced-order model and deep learning provided by the present invention have at least the following beneficial effects:

[0018] By combining order reduction algorithms and deep learning techniques, the complex dynamic characteristics of physical systems can be captured more effectively. The reduced-order model can simplify the complexity of the system, while deep learning can explore and utilize the potential patterns in large amounts of data. The combination of the two can produce more accurate prediction results. By reducing the order, the dimension of the system is reduced, and the computational complexity is reduced. Deep learning improves computing efficiency by optimizing the algorithm, thereby reducing the overall computing cost. The demand for high-quality data is reduced, which helps to accurately predict the physical state in extreme environments (such as deep-sea environments, high-radiation environments, polar environments, etc.) where data is scarce or difficult to obtain. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] This specification will be further described in the form of exemplary embodiments, which will be described in detail with reference to the accompanying drawings. These embodiments are not limiting, and in these embodiments, like numbers represent like structures, wherein:

[0020] Figure 1 is a flowchart of a virtual reality display method based on a reduced-order model and deep learning according to some embodiments of this specification;

[0021] Figure 2 is a velocity distribution diagram in a flow field at t1 = 2 seconds and t2 = 3.02 seconds according to some embodiments of this specification;

[0022] Figure 3 is a schematic diagram of energy sorting according to some embodiments of this specification;

[0023] Figure 4 is a schematic diagram of the structure of the TCN-LSTM-KAN model according to some embodiments of this specification;

[0024] Figure 5 This is a comparison chart of the actual and predicted effects of the sixth-order modal flow field reconstruction under 1-second, 3-second, and 5-second time coefficient predictions based on the TCN-LSTM-KAN model shown in some embodiments of this specification;

[0025] Figure 6 is a schematic diagram of the main POD mode distribution in the flow field according to some embodiments of this specification;

[0026] Figure 7 is R shown in some embodiments of this specification 2 Schematic diagram of values;

[0027] Figure 8a is a schematic diagram of the first-order modal prediction results of the TCN-LSTM-KAN model shown in some embodiments of this specification;

[0028] Figure 8b is a schematic diagram of the second-order modal prediction results of the TCN-LSTM-KAN model according to some embodiments of this specification;

[0029] Figure 8c is a schematic diagram of the third-order modal prediction results of the TCN-LSTM-KAN model according to some embodiments of this specification;

[0030] Figure 8d is a schematic diagram of the fourth-order modal prediction results of the TCN-LSTM-KAN model according to some embodiments of this specification;

[0031] Figure 8e is a schematic diagram of the fifth-order modal prediction results of the TCN-LSTM-KAN model according to some embodiments of this specification;

[0032] Figure 8fis a schematic diagram of the sixth-order modal prediction results of the TCN-LSTM-KAN model described in some embodiments of this specification;

[0033] Figure 9 This is a module diagram of a virtual reality display system based on reduced-order model and deep learning according to some embodiments of this specification. DETAILED DESCRIPTION

[0034] To more clearly illustrate the technical solutions of the embodiments of this specification, the following briefly describes the drawings required for describing the embodiments. Obviously, the drawings described below are merely examples or embodiments of this specification. Those skilled in the art can apply this specification to other similar scenarios based on these drawings without inventive effort. Unless otherwise apparent from the context or otherwise noted, the same reference numerals in the figures represent the same structure or operation.

[0035] Figure 1 is a flowchart of a virtual reality display method based on a reduced-order model and deep learning according to some embodiments of this specification, such as Figure 1 As shown, the virtual reality display method based on reduced-order model and deep learning may include the following steps.

[0036] Step 110: Acquire physical characteristics and environmental information of the simulation object.

[0037] Specifically, physical characteristics refer to the properties of a simulated object related to its material nature and structure. These properties determine the object's behavior under various physical influences. For example, the physical characteristics of a simulated object include at least density, viscosity, compressibility, and expansibility.

[0038] The various physical conditions of the external environment in which the simulation object is located, which will affect the behavior and performance of the simulation object. For example, the environmental information of the simulation object includes at least temperature, pressure and flow rate.

[0039] Experimental testing tools can be used to obtain information about the physical characteristics and environment of the simulated object. These tools include, but are not limited to, sensors used to measure various physical quantities, such as temperature, pressure, velocity, and acceleration, which are important components of the simulated object's attribute data; measuring instruments such as multimeters, oscilloscopes, and spectrometers, used to accurately measure electrical and optical parameters; and experimental equipment used to test the performance of the simulated object under specific conditions.

[0040] Step 120 : Based on the physical characteristics and environmental information of the simulation object, perform fluid dynamics simulation on the simulation object to obtain flow field data of the simulation object.

[0041] Specifically, the flow field data of the simulation object includes at least a velocity field, a pressure field, and a density field.

[0042] Fluid dynamics simulation is a computer-generated technique for simulating fluid flow, heat transfer, and related physical phenomena. It uses fundamental equations of fluid mechanics (such as the Navier-Stokes equations) and numerical calculation methods to determine the motion and behavior of fluids under varying conditions.

[0043] Based on the physical characteristics and environmental information of the simulation object, fluid dynamics simulation of the simulation object may include the following steps:

[0044] Build a geometric model: Based on the actual shape and size of the object being simulated, a corresponding geometric model is created in the computer. For example, if you want to simulate the effect of a car's shape on air flow, you need to build a 3D geometric model of the car.

[0045] Meshing: Divide the geometric model into many small units (grids). The quality and density of the mesh affect the simulation accuracy and computational efficiency. Generally speaking, areas with drastic flow field changes (such as the front and rear of a car) require a denser mesh.

[0046] Set boundary conditions: Based on the environment and simulation requirements, set boundary conditions such as inlet velocity, outlet pressure, and wall conditions. For example, when simulating a car, the inlet can be set to a certain air velocity, and the wall can be set to a no-slip condition (i.e., the relative velocity between the fluid and the wall is zero).

[0047] Select a solver: Choose an appropriate solver based on the simulation problem and the properties of the fluid. Common solvers include those based on the finite volume method and the finite element method. The solver discretizes and solves the fluid dynamics equations, obtaining physical quantities such as velocity, pressure, and temperature at each grid point in the flow field.

[0048] Perform simulation calculations: Run the solver to perform simulation calculations. During the calculation process, the solver will iteratively solve the fluid dynamics equations according to the initial conditions and boundary conditions until convergence conditions are reached.

[0049] Obtain flow field data: After the simulation calculation is completed, the required flow field data, such as velocity field, pressure field, density field, etc., are extracted from the solution results. This data can be displayed in the form of charts, animations, etc. to intuitively reflect the flow state of the fluid.

[0050] Taking a two-dimensional cylinder simulating von Karman vortex as an example, a fluid dynamics simulation is performed on the simulation object to obtain the flow field data of the simulation object: the simulation domain is divided into 199 grids along the x direction and 449 grids along the y direction, the Noble number is 100, the Strouhal number is 0.16, the time interval is 0.02 seconds, and 150 data snapshots are taken at different time points to capture the key flow simulation data around the two-dimensional cylinder; to ensure the accuracy of the simulation results, a high-density grid division strategy is adopted to divide the entire calculation domain into 89,351 computing nodes. In addition, the time evolution of fluid dynamics is studied in detail, especially at two key time points t1 = 2 seconds and t2 = 3.02 seconds. The velocity distribution diagram in the flow field is presented at these two time points through the virtualization method, as shown in the figure below. Figure 2 shown.

[0051] Step 130 : performing order reduction processing on the flow field data of the simulation object based on the proper orthogonal decomposition method to extract the target spatial pattern and target time coefficient of the simulation object.

[0052] In some embodiments, step 130 specifically includes:

[0053] Performing order reduction processing on the flow field data of the simulation object based on the proper orthogonal decomposition method to obtain the reduced-order flow field data of the simulation object;

[0054] Determine the spatial pattern and time coefficient of the simulation object based on the reduced-order flow field data of the simulation object;

[0055] Based on the energy contribution of each mode, the target mode is determined, where the mode refers to a series of orthogonal spatial structural features obtained by performing intrinsic orthogonal decomposition on the flow field data. These modes are mathematical representations of different flow structures in the flow field. Each mode corresponds to a specific flow feature in the flow field, and different modes occupy different proportions of energy in the flow field. The mode with a larger energy contribution represents the main flow feature in the flow field, while the mode with a smaller energy contribution corresponds to the secondary or local flow feature in the flow field.

[0056] According to the target mode, the target spatial pattern and the target time coefficient of the simulation object are extracted from the spatial pattern and the time coefficient of the simulation object.

[0057] Specifically, the eigenorthogonal decomposition method is a data-driven order reduction method that decomposes the flow field data into a set of orthogonal spatial patterns and temporal coefficients by performing eigenvalue decomposition on the covariance matrix of the flow field data. These spatial patterns represent the main flow structures in the flow field, while the temporal coefficients describe how these flow structures change over time.

[0058] Assume that the flow field data of the simulation object can be represented as a matrix X, where each column represents a snapshot of the flow field at a moment in time. The goal of POD is to find a set of orthogonal basis vectors Φ = [φ1, φ2, …, φr] (spatial patterns) such that the projection of the flow field data onto these basis vectors preserves the original data information to the greatest extent possible.

[0059] The flow field data of the simulation object is reduced in order based on the proper orthogonal decomposition method. Obtaining the reduced-order flow field data of the simulation object may include the following steps:

[0060] Data preprocessing:

[0061] Perform centralization on the original flow field data, that is, subtract the average value of the flow field data to make the mean value of the data zero. This can eliminate the DC component in the data and highlight the dynamic changes of the data;

[0062] Perform singular value decomposition on the flow field data matrix U,

[0063]

[0064] Among them, U i (x,t)∈R M×N represents the i-th snapshot of the flow field, The data matrix representing the flow field, N represents the total number of columns of a single snapshot in the data matrix, and U is decomposed into three different matrices:

[0065] [B,S,V]=svd(U)

[0066] That is, the matrix U(x,t)=BSV T , where B∈R M×M , S∈R M×N ,V∈R N×N ;

[0067] The set B consists of the vector UU T The data is composed of orthogonal eigenvectors, including , which are the pattern construction matrix of the data. These eigenvectors represent the main spatial patterns in the flow field, and each eigenvector corresponds to a specific flow field structure. For example, in the simulation of fluid flow, these patterns may correspond to different vortex structures, boundary layer characteristics, etc.

[0068] The matrix S is a diagonal matrix. The singular values ​​of all solutions are arranged in descending order. The elements on its diagonal are singular values ​​and are arranged in descending order. Larger singular values ​​contain the main energy and information of the data, while smaller singular values ​​correspond to components that contribute less to the data.

[0069] The vector V represents the spatial pattern obtained by decomposition, which is related to time information. The column vector of V describes the change of each spatial pattern over time, that is, the weight or activation degree of different patterns at different times;

[0070] Calculate the covariance matrix: Calculate the covariance matrix based on the centered flow field data matrix X. The covariance matrix describes the correlation between different locations in the flow field data.

[0071] Eigenvalue decomposition: Perform eigenvalue decomposition on the covariance matrix C to obtain the eigenvalue λ i and the corresponding eigenvector φ i The size of the eigenvalue reflects the amount of information contained in the corresponding eigenvector (spatial pattern):

[0072] Cφ i =λ i φ i .

[0073] Using the eigenvector φ ij and the mean-decreased snapshot x' j Extract features of the main spatial structure:

[0074] ψ i =∑ j φ ij x′ j .

[0075] Among them, ψ i is the i-th main spatial structure feature, which represents the main flow pattern related to the i-th eigenvector in the flow field data. It is also the orthogonal basis vector obtained by the intrinsic orthogonal decomposition method. They can retain the information in the flow field data to the greatest extent. ij is the component of the ith eigenvector (spatial mode) in the jth snapshot. By calculating multiple ψ i , multiple main spatial structure features in flow field data can be extracted.

[0076] Calculate the time coefficient a from the spatial pattern i (t):

[0077] a i (t)=ψ i x(t)

[0078] Where x(t) is the snapshot at time t in the original flow field data.

[0079] Obtain reduced-order flow field data: Project the original flow field data X onto the selected spatial mode φ to obtain the time coefficient matrix A. The reduced-order flow field data can be expressed as X r =φA, where X rIt is an approximate representation of the original flow field data X, and its dimension is much lower than the original data.

[0080] In some embodiments, determining a target modality based on the energy contribution of each modality includes:

[0081] determining a plurality of modal combinations, wherein the modal combination includes at least one modality;

[0082] For each mode combination, the cutoff energy ratio of the mode combination is calculated according to the energy contribution of each mode included in the mode combination;

[0083] A target mode combination is determined according to the cutoff energy ratio of each mode combination, wherein the modes included in the target mode combination are used as target modes.

[0084] In some embodiments, determining a target modal combination according to the cutoff energy ratio of each modal combination includes:

[0085] The mode combination whose cutoff energy ratio is greater than the cutoff energy ratio threshold is taken as a candidate mode combination;

[0086] The candidate mode combination with the smallest truncated energy ratio is selected as the target mode combination.

[0087] In some embodiments, the cutoff energy ratio of the modal combination is calculated based on the following formula:

[0088]

[0089] Where E is the cutoff energy ratio of the mode combination, λ j is the energy contribution of the jth mode, N is the total number of modes included in the modal combination, and M is the total number of modes.

[0090] Specifically, data processing and data analysis software can be used to perform POD calculations on the simulation object to obtain reduced-order flow field data. As an example only, mathematical calculation and data analysis software MATLAB can be used, or a calculation and data analysis library in Python and a specialized POD implementation library can be used.

[0091] In some embodiments, decomposing and extracting the time coefficient and spatial pattern corresponding to the simulation object includes:

[0092] Taking the two-dimensional cylinder simulating von Karman vortex as an example, ANSYS software can be used to establish a calculation domain with a length of 5 meters and a width of 1.5 meters. In this domain, a cylinder with a center coordinate of (0.5m, 0.5m) is placed. Its radius is set to 0.1 meters. The fluid passes through the entire flow field from left to right at a constant speed of 1 meter per second. Its density is set to 1 kilogram per cubic meter to simulate the fluid behavior under standard conditions.

[0093] A detailed evaluation of the energy contribution of each mode is an important step in streamlining the reduced-order data set. Through energy analysis, it can be found that the energy contribution rate of the first ten modes is significantly higher. By retaining these ten key modes, the dynamic characteristics of the original flow field can be approximated with minimal information loss. Based on the simplified data level, the energy of the data set under different modes is compared, and the mode that can best restore the real flow field is selected. Figure 3 The energy ranking shown in the figure shows that the first six order energies are obviously sufficient to approximately restore the flow field. Therefore, the time coefficient data of these six modes are selected as the training data set.

[0094] For example, suppose the original flow field data is decomposed into multiple orthogonal modes, each mode corresponds to an eigenvalue, and the size of the eigenvalue reflects the amount of energy contained in the mode.

[0095] 1. Calculate the energy ratio I(N) under each retained mode number

[0096] When N=1, assuming I(1)=0.3, this means that when the first mode is retained, the retained energy accounts for 30% of the total energy of the original system.

[0097] When N=2, I(2)=0.55, that is, when the first two modes are retained, the retained energy accounts for 55% of the total energy of the original system.

[0098] When N=3, I(3)=0.7, and when the first three modes are retained, the retained energy accounts for 70% of the total energy of the original system.

[0099] When N=4, I(4)=0.8, and when the first four modes are retained, the retained energy accounts for 80% of the total energy of the original system.

[0100] When N=5, I(5)=0.85, and when the first five modes are retained, the retained energy accounts for 85% of the total energy of the original system.

[0101] 2. Set the preset threshold value Y

[0102] Assume that the preset threshold Υ=0.75, that is, the mode set to be retained must contain at least 75% of the total energy of the original system.

[0103] 3. Find the N value that meets the conditions

[0104] For N=1, I(1)=0.3<0.75, which does not meet the condition of I(N)≥Y, and is discarded.

[0105] For N=2, I(2)=0.55<0.75, which does not meet the conditions and is discarded.

[0106] For N=3, I(3)=0.7<0.75, which does not meet the conditions and is discarded.

[0107] For N = 4, I(4) = 0.8 ≥ 0.75, which satisfies the condition.

[0108] For N = 5, I(5) = 0.85 ≥ 0.75, which also satisfies the condition.

[0109] 4. Determine the optimal N value

[0110] Among the N values (N = 4 and N = 5) that satisfy I(N) ≥ Υ, find the N value that makes I(N) the smallest. Since I(4) = 0.8 < I(5) = 0.85, the finally determined number of retained modes N = 4, and the first 4 modes are used as the target modes.

[0111] Step 140, establish and train the TCN-LSTM-KAN model and the physical field prediction model.

[0112] Specifically, the TCN-LSTM-KAN model includes a TCN layer, an LSTM layer, and a TCN layer;

[0113] The TCN layer is used to extract the key fluid features from the time coefficients of the simulation object;

[0114] The LSTM layer is used to generate the prediction results for each time step based on the key fluid features extracted by the TCN layer;

[0115] The KAN layer is used to generate the future time coefficients based on the prediction results for each time step output by the LSTM layer.

[0116] Step 150, predict the future time coefficients according to the time coefficients of the simulation object through the TCN-LSTM-KAN model.

[0117] Specifically, the TCN (Temporal Convolutional Network) layer captures the temporal dependencies and complex patterns in the fluid time coefficient sequence data and is used to extract the key fluid features; as Figure 4 shown, according to each time step X t-n , the data is processed to generate the hidden state information h and the cell state c, and then propagated along the time axis through multiple LSTM (Long Short-Term Memory) layers (intuitively represented by five right arrows), gradually accumulating the physical correlation and temporal dependency of the sequence, and deeply transmitting it into the network; the KAN (Kolmogorov-Arnold Network) layer introduces an auxiliary non-linear transformation to enhance the model's ability to refine the fluid time features and optimize the prediction results.

[0118] Taking a two-dimensional cylinder simulating von Karman vortices as an example, the batch size of the TCN-LSTM-KAN model was set to 10. To facilitate processing multidimensional data, an additional dimension L was introduced with a value of 3. The input layer consisted of 50 neurons, responsible for receiving raw data features, and the hidden layer was expanded to 200 neurons, enhancing the model's nonlinear representation ability and capacity. The output layer consisted of 100 neurons. In addition, a task-specific parameter, grid size, was defined with a value of 300 to determine the size of the grid search. The model underwent 500 iterations, and the learning rate of the Adam optimizer was set to 5e-4. The input data was normalized to a uniform scale. In the output layer, the tanh function was selected as the activation function, ensuring that the function can generate outputs in the range of -1 to 1. The ReLU function was uniformly used as the activation function throughout the convolutional layer design.

[0119] Step 160 , predicting the physical field at the future time based on the future time coefficient and the target spatial pattern of the simulation object.

[0120] In some embodiments, step 160 specifically includes:

[0121] Based on the future time coefficients, update the time coefficient sequence;

[0122] The physical field at future times is predicted based on the updated time coefficient sequence and the target spatial pattern of the simulation object.

[0123] Specifically, within the Proper Orthogonal Decomposition (POD) space-time field modeling framework with a fixed modal number N, the first N-order spatial orthogonal basis function matrices and corresponding time coefficient sequences are extracted from historical observation data to construct a low-dimensional subspace describing the system's spatiotemporal characteristics. A long short-term memory network is then used to perform mode-by-mode prediction of the time coefficients of each mode for the next T time steps, generating a predicted time coefficient matrix containing future time series information. Subsequently, while maintaining the POD spatial basis function matrix unchanged, the space-time field is reconstructed in the low-dimensional subspace through matrix multiplication, ensuring the synchronous updating of the spatial modal structure and the temporal evolution law. Finally, a visual interface simultaneously displays the spatiotemporal distribution of the actual observed field and the predicted field, dynamically presenting the spatiotemporal pattern evolution trajectory from the current observation moment to the future prediction moment, and intuitively comparing the differences in the spatial distribution of the actual observed data and the predicted data, thus completing the technical closed loop from time series prediction to spatiotemporal reconstruction.

[0124] Taking the two-dimensional cylinder simulating von Karman vortex as an example, we provide a more specific perspective on the prediction results. We select three different time points and compare the actual and predicted situations at these time points using the TCN-LSTM-KAN network under the sixth-order model. Figure 5, the TCN-LSTM-KAN model accurately predicted the data features or states at the 1-second, 3-second, and 5-second time points; ultimately, after being reduced to the first six modes, the original flow field was advanced twenty time steps to a duration of 6.44 seconds.

[0125] Step 170: Based on the physical field at the future time, a virtual model of the target simulation object is established in the virtual reality environment and displayed in virtual reality.

[0126] In some embodiments, step 170 specifically includes:

[0127] According to the physical field in the future time, a virtual model of the target simulation object is established in the virtual reality environment;

[0128] Data mapping technology and rendering optimization technology are used to perform virtual reality display, which can describe complex on-site phenomena intuitively and realistically, ensuring that the flow field phenomena in the virtual reality environment are highly consistent with the reduced-order simulation results.

[0129] Figure 6 It is based on the main POD modal distribution in the flow field shown in some embodiments of this specification. Taking the two-dimensional cylinder simulating the von Karman vortex as an example, through fluid dynamics simulation, after POD reduction, based on the simplified data level, the first six orders of energy are sufficient to approximately restore the flow field. Figure 7 The network R shown in some embodiments of this specification 2 Values ​​(left: TCN-LSTM-KAN right: TCN-LSTM), taking the two-dimensional cylinder simulating von Karman vortex as an example, as shown in Figure 7 As shown in Figure 2, the TCN-LSTM-KAN model exhibits significant stability during training. 2 The value rises rapidly from the initial stage to close to 1 and remains at this high level throughout the subsequent training process, with only slight fluctuations, but the overall performance is very stable. This shows that the model fits the data well and the predicted results are very close to the actual values, thus demonstrating its strong predictive ability. In contrast, the TCN-LSTM model shown in the right figure also shows R 2 Rapid growth in value.

[0130] Figures 8a to 8f The sixth-order modal prediction results of the TCN-LSTM-KAN model are shown, where the red line represents the predicted value and the blue line represents the actual value. Taking the two-dimensional cylinder simulating von Karman vortex as an example, Figures 8a to 8f It can be seen that the prediction performance of the TCN-LSTM-KAN model under 6 different modalities is close to the actual value.

[0131] Figure 9is a module diagram of a virtual reality display system based on a reduced-order model and deep learning according to some embodiments of this specification, such as Figure 9 As shown, the virtual reality display system based on the reduced-order model and deep learning may include an information acquisition module, an object simulation module, a feature extraction module, a feature prediction module and an object display module.

[0132] An information acquisition module is used to obtain the physical characteristics and environmental information of the simulation object;

[0133] The object simulation module is used to perform fluid dynamics simulation on the simulation object based on the physical characteristics and environmental information of the simulation object and obtain the flow field data of the simulation object;

[0134] A feature extraction module is used to perform order reduction processing on the flow field data of the simulation object based on the intrinsic orthogonal decomposition method to extract the target spatial pattern and target time coefficient of the simulation object;

[0135] The feature prediction module is used to establish and train the TCN-LSTM-KAN model and the physical field prediction model. The TCN-LSTM-KAN model predicts the future time coefficient based on the time coefficient of the simulation object, and predicts the physical field in the future time based on the future time coefficient and the target spatial pattern of the simulation object.

[0136] The object display module is used to establish a virtual model of the target simulation object in the virtual reality environment according to the physical field in the future time, and perform virtual reality display.

[0137] The virtual reality display system based on reduced-order model and deep learning can be used to execute the virtual reality display method based on reduced-order model and deep learning, which will not be described in detail here.

[0138] Finally, it should be understood that the embodiments described in this specification are intended only to illustrate the principles of the embodiments of this specification. Other variations may also fall within the scope of this specification. Therefore, by way of example and not limitation, alternative configurations of the embodiments of this specification may be considered consistent with the teachings of this specification. Accordingly, the embodiments of this specification are not limited to the embodiments explicitly described and illustrated in this specification.

Claims

1. A virtual reality display method based on reduced-order model and deep learning, characterized in that: include: Obtain physical characteristics and environmental information of the simulation object; Based on the physical characteristics and environmental information of the simulation object, fluid dynamics simulation is performed on the simulation object to obtain the flow field data of the simulation object; Based on the intrinsic orthogonal decomposition method, the flow field data of the simulation object is reduced to extract the target spatial pattern and target time coefficient of the simulation object; Establish and train the TCN-LSTM-KAN model and physical field prediction model; Predict the future time coefficient based on the time coefficient of the simulation object through the TCN-LSTM-KAN model; Predict the physical field at future time based on the future time coefficient and the target spatial pattern of the simulation object; According to the physical field in the future, a virtual model of the target simulation object is established in the virtual reality environment for virtual reality display.

2. The virtual reality display method based on reduced-order model and deep learning according to claim 1, characterized in that: Based on the intrinsic orthogonal decomposition method, the flow field data of the simulation object is reduced to extract the target spatial pattern and target time coefficient of the simulation object, including: Performing order reduction processing on the flow field data of the simulation object based on the proper orthogonal decomposition method to obtain the reduced-order flow field data of the simulation object; Determine the spatial pattern and time coefficient of the simulation object based on the reduced-order flow field data of the simulation object; Determine the target mode based on the energy contribution of each mode; According to the target mode, the target spatial pattern and the target time coefficient of the simulation object are extracted from the spatial pattern and the time coefficient of the simulation object.

3. The virtual reality display method based on reduced-order model and deep learning according to claim 2, characterized in that: Based on the energy contribution of each mode, the target mode is determined, including: determining a plurality of modal combinations, wherein the modal combination includes at least one modality; For each mode combination, the cutoff energy ratio of the mode combination is calculated according to the energy contribution of each mode included in the mode combination; A target mode combination is determined according to the cutoff energy ratio of each mode combination, wherein the modes included in the target mode combination are used as target modes.

4. The virtual reality display method based on reduced-order model and deep learning according to claim 3, characterized in that: According to the cutoff energy ratio of each modal combination, the target modal combination is determined, including: The mode combination whose cutoff energy ratio is greater than the cutoff energy ratio threshold is taken as a candidate mode combination; The candidate mode combination with the smallest truncated energy ratio is selected as the target mode combination.

5. The virtual reality display method based on reduced-order model and deep learning according to claim 2, characterized in that: The TCN-LSTM-KAN model includes a TCN layer, an LSTM layer and a KAN layer; The TCN layer is used to extract key fluid features from the time coefficient of the simulation object; The LSTM layer is used to generate time-step prediction results based on the key features of the fluid extracted by the TCN layer; The KAN layer is used to generate future time coefficients based on the time-step prediction results output by the LSTM layer.

6. The virtual reality display method based on reduced-order model and deep learning according to claim 2, characterized in that: Predict the physical field at future times based on the future time coefficients and the target spatial pattern of the simulation object, including: Based on the future time coefficients, update the time coefficient sequence; The physical field at future times is predicted based on the updated time coefficient sequence and the target spatial pattern of the simulation object.

7. The virtual reality display method based on reduced-order model and deep learning according to claim 1, characterized in that: According to the physical field in the future, a virtual model of the target simulation object is established in the virtual reality environment and virtual reality display is performed, including: According to the physical field in the future time, a virtual model of the target simulation object is established in the virtual reality environment; Use data mapping technology and rendering optimization technology to perform virtual reality display.

8. The virtual reality display method based on reduced-order model and deep learning according to claim 3, characterized in that: The cutoff energy ratio of the mode combination is calculated based on the following formula: Where E is the cutoff energy ratio of the mode combination, λ j is the energy contribution of the jth mode, N is the total number of modes included in the modal combination, and M is the total number of modes.

9. The virtual reality display method based on reduced-order model and deep learning according to any one of claims 1 to 8, characterized in that: The physical characteristics of the simulation object include at least density, viscosity, compressibility and expansibility; The environmental information of the simulation object includes at least temperature, pressure and flow rate; The flow field data of the simulation object at least includes velocity field, pressure field and density field.

10. A virtual reality display system based on reduced-order model and deep learning, characterized in that: The virtual reality display method based on reduced-order model and deep learning according to any one of claims 1 to 9 comprises: An information acquisition module is used to obtain the physical characteristics and environmental information of the simulation object; The object simulation module is used to perform fluid dynamics simulation on the simulation object based on the physical characteristics and environmental information of the simulation object and obtain the flow field data of the simulation object; A feature extraction module is used to perform order reduction processing on the flow field data of the simulation object based on the intrinsic orthogonal decomposition method to extract the target spatial pattern and target time coefficient of the simulation object; The feature prediction module is used to establish and train the TCN-LSTM-KAN model and the physical field prediction model. The TCN-LSTM-KAN model predicts the future time coefficient based on the time coefficient of the simulation object, and predicts the physical field in the future time based on the future time coefficient and the target spatial pattern of the simulation object. The object display module is used to establish a virtual model of the target simulation object in the virtual reality environment according to the physical field in the future time, and perform virtual reality display.

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