Multi-physical-quantity dynamic weighting loss construction method for deep learning flow field prediction
By constructing a multi-physical quantity dynamic weighted loss method, the problems of multi-physical feature fusion and time update in deep learning flow field prediction are solved, which improves the local accuracy and temporal stability of unsteady flow fields and achieves high efficiency, stability and consistency in flow field prediction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2025-12-23
- Publication Date
- 2026-05-08
AI Technical Summary
Existing deep learning flow field prediction methods cannot effectively integrate multiple physical features in unsteady flows, and the static weighting method cannot be updated over time, resulting in high prediction errors in local complex regions and easy accumulation of errors, which affects the stability and consistency of flow field prediction.
A multi-physical quantity dynamic weighted loss construction method is adopted. By extracting physical quantity features such as vorticity, shear rate, and energy dissipation rate, and performing dimensionless processing, a fusion weighted function is constructed. The weights are dynamically adjusted by recursively updating them in the time dimension and embedded into the loss function of the deep learning model.
It improves the local accuracy and temporal stability of unsteady flow field prediction, enhances the model's predictive ability in key regions, suppresses error accumulation, and improves the overall consistency and accuracy of flow field prediction.
Smart Images
Figure CN121997801A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of fluid mechanics technology, specifically relating to a method for constructing a multi-physical quantity dynamic weighted loss for deep learning flow field prediction. Background Technology
[0002] Unsteady flows are of great significance in aerospace, marine engineering, wind energy utilization, and automotive engineering. In such flows, complex structures such as vortex shedding, shear enhancement, and small-scale dissipation enhancement continuously evolve over time. Although traditional computational fluid dynamics (CFD) methods can obtain accurate flow field information, their computational cost increases rapidly with grid size and time steps, often failing to meet engineering requirements for real-time prediction, rapid design optimization, and multi-parameter traversal.
[0003] Deep learning-based flow field prediction methods have gradually become a research hotspot due to their efficient nonlinear representation capabilities. However, existing methods typically employ a uniform and fixed error weighting approach, and the assumption of consistency across different regions of the flow field is seriously inconsistent with actual flow characteristics. In regions with intense flow structures, such as high vorticity regions, shear layers, and regions with enhanced energy dissipation, the prediction error is significantly higher than in stable regions, and the error accumulates and propagates over time along the vortex shelving structure.
[0004] Existing weighting strategies are mostly based on static spatial weighting constructed from a single physical quantity, which cannot be automatically updated as the flow field evolves, and it is also difficult to capture the combined effects of multiple physical features simultaneously. Therefore, there is an urgent need for a dynamic weighting method that can both integrate multiple physical features and adaptively update in the time dimension, in order to improve the expressive power of deep learning models in locally complex regions and improve the overall stability and physical consistency of long-term flow field predictions. Summary of the Invention
[0005] To overcome the shortcomings of existing technologies, this invention provides a method for constructing a multi-physical quantity dynamic weighted loss for deep learning flow field prediction. Based on flow field data obtained from real or numerical simulations, it extracts multiple physical quantity features such as vorticity, shear rate, and energy dissipation rate, and forms uniform-scale physical feature inputs through dimensionless processing. A local weighting function is constructed according to the fusion relationship of the multiple physical quantities, and the weighting coefficients are dynamically updated using a time-recursive approach. The resulting dynamic weights are introduced into the loss function of the deep learning model, enabling the model to focus on constraining error-sensitive regions such as vortex shedding zones and shear layers during training, thereby improving the local accuracy and long-term temporal stability of unsteady flow field prediction. This invention has a clear structure, can be used in conjunction with various deep learning flow field prediction networks, and has good versatility and engineering applicability.
[0006] The technical solution adopted by this invention to solve its technical problem is as follows: Step 1: Calculation of multiple physical quantities; Extract multiple physical quantity features from real or predicted flow field data in the training samples, including vorticity. shear rate Energy dissipation rate Pressure gradient mode and velocity gradient tensor invariants Q, R Invariants Q Used to describe the relative strength of rotation and strain in a local flow field, reflecting the intensity characteristics of the vortex structure; invariant R The third-order topological properties used to describe the velocity gradient tensor reflect the spatial organization and evolution trend of the flow structure. The physical characteristic vector is constructed as shown in equation (2):
[0007] in, x Represents spatial location coordinates, t Represents a time variable; Step 2: Dimensionless and normalization processing; The physical feature vectors are dimensionless and normalized, and then mapped to a uniform scale according to equation (2):
[0008] in For normalization operators; Indicates the first i Physical quantity in spatial position x ,time t The original value at that location, i It serves as an index for physical quantities, used to distinguish different types of physical characteristic quantities; Step 3: Construct a multi-physical quantity fusion weighting function; Based on the normalized multiple physical quantities, a fusion weighting function as shown in equation (3) is constructed:
[0009] in, For the Sigmoid function; This is the weighting function for each physical quantity in step 1; These are the upper and lower limits of the weight; Let be the action function corresponding to the i-th physical quantity, used to describe the influence of the physical quantity on the fusion weighting result; Step 4: Time-adaptive weight update; The weights are updated recursively over time according to equation (4):
[0010] in, This is a time smoothing factor; For the final dynamic weights used; For spatial fusion weights; The weights of the previous time step; Step 5: Construct a dynamic weighted loss function; During network training, dynamic weights are used for deep learning flow field prediction loss according to equation (5):
[0011] in, For network flow field prediction, For a realistic flow field; Step 6: Model training and prediction; By embedding dynamic weighted loss into the training process of convolutional networks, the prediction capability of high vorticity coupling regions is enhanced by utilizing weights, and it is used for fast prediction of temporal flow fields.
[0012] Preferably, step 1 specifically comprises: vorticity The calculation method is shown in equation (6):
[0013] In the formula, u , v The speeds are respectively at x and y Component of direction; shear rate Perform the calculation as shown in equation (7):
[0014] In the formula, and These represent the components in different directions of the velocity gradient tensor; Let be the velocity gradient vector components, where u 1= u , u 2= v ; To represent spatial coordinates; For strain rate tensor; Energy dissipation rate Perform the calculation as shown in equation (8):
[0015] In the formula, Kinematic viscosity; Pressure gradient mode Perform the calculation as shown in equation (9):
[0016] In the formula, For pressure; The velocity gradient tensor invariant is calculated according to equation (10):
[0017] In the formula i , j , k For summation indicators; Therefore, the set of multiple physical quantities is obtained as shown in equation (11):
[0018] Preferably, the kinematic viscosity .
[0019] Preferably, the normalization process in step 2 is as follows: The normalized form is shown in equation (12):
[0020] In the formula, , They are physical quantities The 1% and 99th percentile values.
[0021] Preferably, the convolutional network is a 3D U-Net or V-Net.
[0022] An electronic device includes: a processor and a memory; the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory, so that the electronic device performs the above-described method for constructing a multi-physical quantity dynamic weighted loss function.
[0023] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described method for constructing a dynamic weighted loss function for multiple physical quantities.
[0024] A chip includes a processor for calling and running a computer program from a memory, causing a device equipped with the chip to execute the above-described method for constructing a multi-physical quantity dynamic weighted loss function.
[0025] A computer program product includes a computer storage medium storing a computer program, the computer program including instructions executable by at least one processor, which, when executed by the at least one processor, implement the above-described method for constructing a multi-physical quantity dynamic weighted loss function.
[0026] The beneficial effects of this invention are as follows: (1) The present invention uses a variety of physical quantities such as vorticity, shear rate, energy dissipation rate and velocity gradient invariant to construct a spatial weighting function, which can comprehensively reflect the local complexity in unsteady flow and make the prediction model have stronger feature expression ability in key areas.
[0027] (2) The present invention introduces an adaptive weight update mechanism in the form of time recursion, which enables the weighting coefficients to be dynamically adjusted with the evolution of the flow field structure, solves the problem that the traditional static weighting method cannot be automatically updated with time changes, and improves the temporal consistency of the prediction results.
[0028] (3) The dynamic weighted loss proposed in this invention can strengthen high error regions such as vortex shedding zone and shear layer, significantly improve the prediction accuracy of the model in local complex regions, suppress the accumulation of error along the time direction, and maintain structural stability in long-term prediction.
[0029] (4) The method of the present invention has strong versatility and can be embedded in a variety of convolutional neural network structures (including 3D U-Net, V-Net and reduced-order modeling networks). It has strong adaptability to network structure and is easy to integrate and deploy. Attached Figure Description
[0030] Figure 1 Overall flowchart of the present invention; Figure 2 Schematic diagram of the multi-physical quantity fusion weighting module structure; Figure 3 The unsteady flow field prediction network structure and training framework diagram of this invention; Figure 4 A schematic diagram comparing the predicted results with the actual flow field in an embodiment of the present invention. Detailed Implementation
[0031] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0032] To overcome the limitations of existing deep learning flow field prediction methods, such as their inability to differentiate based on local flow complexity, the inability to update weighting methods over time, and the tendency for errors to accumulate over time, this invention proposes a dynamic weighting method based on the fusion of multiple physical quantities. This method constructs a local spatial weighting by fusing information such as vorticity, shear rate, energy dissipation rate, pressure gradient magnitude, and velocity gradient tensor invariants, and introduces recursive updates in the time dimension to improve the local accuracy and temporal consistency of unsteady flow field prediction.
[0033] The method of the present invention includes the following steps: This invention provides a dynamic weighted method for flow field prediction based on multiple physical quantities, comprising the following steps: Step 1: Calculation of multiple physical quantities; Extract multiple physical quantity features from real or predicted flow field data in the training samples, including vorticity. shear rate Energy dissipation rate Pressure gradient mode And the velocity gradient tensor invariants Q and R. The above physical quantities constitute the physical eigenvectors as shown in equation (2):
[0034] Step 2: Dimensionless and normalization processing; The physical feature vectors are dimensionless and normalized, and then mapped to a uniform scale according to equation (2):
[0035] in For normalization operators; Step 3: Construct a multi-physical quantity fusion weighting function; Based on the normalized multiple physical quantities, a fusion weighting function as shown in equation (3) is constructed:
[0036] in, For the Sigmoid function; The weighting function for each physical quantity; These are the upper and lower limits of the weight.
[0037] Step 4: Time-adaptive weight update; To describe the change of flow state over time, the weights are recursively updated along the time dimension according to equation (4):
[0038] in, This is the time smoothing factor.
[0039] Step 5: Construct a dynamic weighted loss function; During network training, the above dynamic weights are used for deep learning flow field prediction loss according to equation (5):
[0040] in, For network flow field prediction, This represents the actual flow field.
[0041] Step 6: Model training and prediction; By embedding dynamic weighted loss into the training process of convolutional networks (such as 3D U-Net, V-Net, etc.), the prediction capability of high vorticity coupling regions can be enhanced by the aforementioned weights, and it can be used for fast prediction of time-series flow fields.
[0042] Example: This embodiment uses OpenFOAM software as a data generation tool. By solving the incompressible Navier-Stokes equations, the continuous time series flow field of the Re=100 cylinder flow example is obtained, which is used to construct the training and testing sets of the deep learning model. 3D U-Net is used as the prediction network, and the performance difference between the traditional uniform weighted loss and the dynamic weighted loss proposed in this invention is compared.
[0043] Step 1: Generation of unsteady flow field sample set; In this embodiment, the unsteady flow field sample data around the cylinder was generated using OpenFOAM calculations. The calculation condition was set as incompressible viscous flow with Re=100, and the pimpleFoam solver was used to calculate the unsteady vortex shedding process in the cylinder wake region. The computational mesh was generated using the blockMesh tool, employing multiple structured hexahedral meshes. Locally refined regions were arranged around the cylinder to improve near-wall vortex resolution. The total mesh size was approximately 123,200, and the initial layer height and refinement ratio were set according to the default configuration of the example. The physical time step was set to... The total computation time is 200 seconds, and the velocity and pressure fields are output according to a fixed time step. The output data includes... , and This data is used to construct training samples for subsequent deep learning models. After uniform coordinate interpolation, cropping, and normalization, the calculated flow field data forms a multi-time-frame unsteady flow field dataset. This dataset is used as the sample set for training models, and is subsequently used for multi-physical quantity feature extraction and dynamic weighted model training.
[0044] Step 2: Extraction of features from multiple physical quantities; In this embodiment, in order to obtain the physical characteristic quantities used to construct the dynamic weighting function, physical quantities such as vorticity, shear rate, energy dissipation rate, pressure gradient modulus, and velocity gradient tensor invariant are calculated based on the velocity field and pressure field obtained in step S1.
[0045] Among them, vorticity The calculation method is shown in equation (6):
[0046] In the formula, u , v The speeds are respectively at x and y The directional component.
[0047] shear rate Perform the calculation as shown in equation (7):
[0048] In the formula, For the velocity gradient tensor; Let be the velocity gradient vector components, where u 1= u , u 2= v ; To represent spatial coordinates; Let be the strain rate tensor.
[0049] Energy dissipation rate Perform the calculation as shown in equation (8):
[0050] In the formula, Kinematic viscosity (taken in this embodiment) ).
[0051] Pressure gradient mode Perform the calculation as shown in equation (9):
[0052] In the formula, For pressure.
[0053] The velocity gradient tensor invariant is calculated according to equation (10):
[0054] In the formula, Q and R Topological features that reflect velocity gradients; i , j , k For summation indicators.
[0055] Based on this, we can obtain the set of multiple physical quantities as shown in equation (11):
[0056] Step 3: Dimensionless and normalized physical quantities; To avoid the scale differences between different physical quantities affecting the weighting results, this embodiment uses fractional normalization to unify each physical quantity to the same numerical range. The normalization form is shown in equation (12):
[0057] In the formula, Represents the original physical quantity; For the normalized dimensionless physical quantity; , These are the 1% and 99th percentile values for the physical quantity, respectively. Since the physical quantities involved in the weighting have different dimensions, for example, the unit of vorticity is s. - ¹, The shear rate is also s - ¹ The unit of energy dissipation rate is m² / s³, the unit of pressure gradient magnitude is Pa / m, and the velocity gradient tensor invariants Q and R have different combined dimensions. Directly participating in linear combination would lead to inconsistencies in dimensions and excessive differences in numerical scale. Therefore, this invention uses quantile normalization to map each physical quantity to the dimensionless interval [0,1], thus ensuring that all variables input to the fusion weighting function are completely consistent in dimension and order of magnitude. After normalization, both the input and output of the fusion weighting function are dimensionless, and the time recursion weights also maintain their dimensionless nature. Finally, the weights used in the loss function are completely consistent with the dimensional relationship of the classical mean square error (MSE), ensuring that the overall calculation process conforms to mathematical and physical laws. This processing method can avoid the influence of extreme values on the weighting function, while ensuring that different physical quantities have a consistent numerical scale. In this embodiment, if the CFD operating conditions change, the quantiles can be recalibrated.
[0058] Step 4: Constructing the weighted function for the fusion of multiple physical quantities; This invention introduces a sigmoid-form nonlinear mapping when constructing a multi-physical quantity fusion weighting function, which is a rewrite of the classic logistic function. This function is widely used in feature transformations in statistics, control theory, and deep learning, and has advantages such as controllable output range, smooth changes, and moderate sensitivity to input changes, making it very suitable for describing the influence of local flow field physical intensity on the weighting results. This invention first normalizes multiple physical quantities such as vorticity, shear rate, energy dissipation rate, pressure gradient magnitude, and velocity gradient invariant to achieve a consistent numerical scale. Then, a fusion term is constructed through linear combination, and this fusion term is input into the sigmoid function to obtain the initial spatial weights reflecting the complexity of the local flow.
[0059] This embodiment adopts the weighted form shown in equation (13):
[0060] In the formula, The initial weighted values after fusion; and The lower and upper weighting limits are set to 0.5 and 2.0 respectively in this embodiment, and these values can be adjusted according to actual conditions. For the Sigmoid function; These are the fusion coefficients corresponding to different physical quantities; The function is taken as a linear function in this embodiment. The above weighting form can provide differentiated weights for different spatial locations based on the characteristics of the local physical field. Compared with existing methods, this invention further adds upper and lower bound mappings to the sigmoid output, so that the final weights can reflect the changes in physical quantities without exceeding a controllable range, thus ensuring the stability of the training process.
[0061] Step 5: Dynamic weighting with time-progressive updates; In terms of time-recursive weighting, this invention adopts a structure similar to Exponential Weighted Moving Average (EWMA). EWMA was originally used in time series analysis and signal processing, characterized by its ability to respond to new inputs at the current moment while maintaining a memory of historical states. This invention borrows this mathematical idea, coupling the weights of the previous time step with the fused weights of the current time step using a fixed smoothing factor, allowing the weights to evolve naturally with the movement of structures such as vortex shears and shear layers. This approach ensures smoothness in the time dimension while reflecting the instantaneous changes in the flow field characteristics. Its mathematical structure is simple, its physical meaning is clear, and it is easy to implement and backpropagate within a deep learning framework.
[0062] The time recursion form used in this embodiment is shown in equation (14):
[0063] In the formula, For the final dynamic weights used; For spatial fusion weights; The weights of the previous time step; The time smoothing factor is set to 0.75 in this embodiment. This update method ensures that the weights maintain a certain smoothness over time and evolve gradually as the vortex sheave moves.
[0064] Step 6: Construct a neural network model for predicting unsteady flow fields; The neural network model constructed in this embodiment adopts a three-dimensional convolutional encoder-decoder structure. The model consists of multiple feature extraction and feature recovery modules, with cross-layer connections between corresponding scales to enhance information transfer between different feature layers. The feature extraction module includes three-dimensional convolution operations, normalization, and non-linear activation; the feature recovery module includes three-dimensional deconvolution, normalization, and non-linear activation. The modules are arranged hierarchically, and the overall model has a four-level downsampling structure and a four-level upsampling structure, maintaining a symmetrical relationship between the upper and lower layers. The model input is a four-dimensional array composed of a set of continuous time frames, with dimensions of: number of time frames, number of physical quantity channels, spatial height, and spatial width. Physical quantity channels include variables such as velocity components and pressure. The model output is also a four-dimensional array composed of a set of continuous time frames, in a three-dimensional array format, with dimensions of: number of time frames, number of physical quantity channels, spatial height, and spatial width. It is important to note that the number of time frames in the input and output sequences is the same, and the frame number of the output frame is sequentially shifted forward by one time step.
[0065] The form of the dynamic weighted loss is shown in Equation (15), which is an improvement on the classic mean squared error loss. The modifications include: introducing dynamic weights. This makes it sensitive to different regions; and the weights come from the coupling of multiple physical quantities, rather than traditional static weights; the multiplication method can maintain the differentiability of the loss function and is fully compatible with MSE; this method is different from Focal Loss or Weight L1 / MSE, its weights depend not only on the error magnitude, but also on the physical structure of the flow field itself, thus possessing physical interpretability.
[0066]
[0067] In the formula, Predicting the speed and pressure field for the network; This represents a real CFD flow field. The dynamic weights are obtained in step 5. The sample set is divided into a training set and a test set, with a ratio of 3:1. The optimizer uses Adam, and the initial learning rate is set to 1×10⁻⁶. -4 The learning rate is adjusted during training using an adaptive learning rate adjustment algorithm. In this embodiment, the above parameters can be adjusted according to hardware conditions and data scale.
[0068] Step 7: Prediction and Flow Field Verification; After model training is complete, the flow field at future time steps is predicted. By inputting flow field data from several consecutive time steps into the completed deep learning model at fixed time steps, the predicted flow field for the next time step can be obtained. The prediction result for a particular time step is as follows: Figure 4 As shown.
[0069] The physical quantities introduced in this invention are all derived from the basic derivations of the incompressible Navier-Stokes equations, including the definition of curl, velocity gradient tensor decomposition, energy dissipation rate expression, pressure gradient and velocity gradient tensor invariants, etc., which can characterize the local flow structure features from different perspectives (Equations 6-11). After normalization (Equation 12), the physical quantities converge into the fusion weighting function, forming a spatial weight distribution that can distinguish between the vortex core region, shear layer region, and smooth region (Equation 13). Subsequently, the time recursion formula (Equation 14) makes the weights automatically updated over time (Equation 15), so that the high weights of key regions such as high vorticity region and dissipation enhancement region can move with the flow field structure, thereby ensuring that the weight field is consistent with the actual flow field structure. Finally, this dynamic weight that changes with time and spatial distribution is incorporated into the deep learning training loss, making the model more constrained in local complex regions, improving prediction accuracy and suppressing the accumulation of errors in the time dimension.
Claims
1. A method for constructing a multi-physical quantity dynamic weighted loss for deep learning flow field prediction, characterized in that, Includes the following steps: Step 1: Calculation of multiple physical quantities; Extract multiple physical quantity features from real or predicted flow field data in the training samples, including vorticity. shear rate Energy dissipation rate Pressure gradient mode and velocity gradient tensor invariants Q, R Invariants Q Used to describe the relative strength of rotation and strain in a local flow field, reflecting the strength characteristics of vortex structures; Invariants R The third-order topological properties used to describe the velocity gradient tensor reflect the spatial organization and evolution trend of the flow structure. The physical characteristic vector is constructed as shown in equation (2): in, x Represents spatial location coordinates, t Represents a time variable; Step 2: Dimensionless and normalization processing; The physical feature vectors are dimensionless and normalized, and then mapped to a uniform scale according to equation (2): in For normalization operators; Indicates the first i Physical quantity in spatial position x ,time t The original value at that location, i It serves as an index for physical quantities, used to distinguish different types of physical characteristic quantities; Step 3: Construct a multi-physical quantity fusion weighting function; Based on the normalized multiple physical quantities, a fusion weighting function as shown in equation (3) is constructed: in, For the Sigmoid function; This is the weighting function for each physical quantity in step 1; These are the upper and lower limits of the weight; For the first i The action function corresponding to each physical quantity is used to describe the influence of that physical quantity on the fusion weighting result; Step 4: Time-adaptive weight update; The weights are updated recursively over time according to equation (4): in, This is a time smoothing factor; For the final dynamic weights used; For spatial fusion weights; The weights of the previous time step; Step 5: Construct a dynamic weighted loss function; During network training, dynamic weights are used for deep learning flow field prediction loss according to equation (5): in, For network flow field prediction, For a realistic flow field; Step 6: Model training and prediction; By embedding dynamic weighted loss into the training process of convolutional networks, the prediction capability of high vorticity coupling regions is enhanced by utilizing weights, and it is used for fast prediction of temporal flow fields.
2. The method for constructing a multi-physical quantity dynamic weighted loss for deep learning flow field prediction according to claim 1, characterized in that, Step 1 specifically involves: vorticity The calculation method is shown in equation (6): In the formula, u , v The speeds are respectively at x and y Component of direction; shear rate Perform the calculation as shown in equation (7): In the formula, and These represent the components in different directions of the velocity gradient tensor; Let be the velocity gradient vector components, where u 1= u , u 2= v ; To represent spatial coordinates; For strain rate tensor; Energy dissipation rate Perform the calculation as shown in equation (8): In the formula, Kinematic viscosity; Pressure gradient mode Perform the calculation as shown in equation (9): In the formula, For pressure; The velocity gradient tensor invariant is calculated according to equation (10): In the formula, i , j , k For summation indicators; Therefore, the set of multiple physical quantities is obtained as shown in equation (11): （11）。 3. The method for constructing a multi-physical quantity dynamic weighted loss for deep learning flow field prediction according to claim 2, characterized in that, kinematic viscosity .
4. The method for constructing a multi-physical quantity dynamic weighted loss for deep learning flow field prediction according to claim 3, characterized in that, The normalization process in step 2 is as follows: The normalized form is shown in equation (12): In the formula, , They are physical quantities The 1% and 99th percentile values.
5. The method for constructing a multi-physical quantity dynamic weighted loss for deep learning flow field prediction according to claim 1, characterized in that, The convolutional network is either 3D U-Net or V-Net.
6. An electronic device, characterized in that, include: Processor and memory; The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory to cause the electronic device to perform the method as described in any one of claims 1 to 5.
7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 5.
8. A chip, characterized in that, include: A processor for retrieving and running a computer program from memory, causing a device on which the chip is mounted to perform the method as described in any one of claims 1 to 5.
9. A computer program product, characterized in that, The computer program product includes a computer storage medium storing a computer program, the computer program including instructions executable by at least one processor, which, when executed by the at least one processor, implement the method as described in any one of claims 1 to 5.