A novel deep U-Net-LSTM framework for time-sequenced hydrodynamics prediction of the SUBOFF AFF-8

ABSTRACT The computational fluid dynamics (CFD) simulation method is commonly used for large-scale computational engineering problems. However, it usually leads to higher computational costs. The deep learning method has gained significant attention in recent years. However, the traditional methods fail to achieve high-precision pixel-level predictions. They are difficult to predict more detailed, multi-scale features of complex engineering. This study proposes a novel deep U-shaped network-long short term memory (U-Net-LSTM) framework for the rapid time-sequenced hydrodynamic prediction of the SUBOFF. First, a novel framework composed of a deep U-shaped network, two LSTM layers, and a skip connection part is proposed for time-sequenced hydrodynamics prediction. Second, the CFD simulation results of the SUBOFF AFF-8 are validated by referring to published experimental data. Finally, three types of AFF-8 motions are investigated to demonstrate the advantages of the proposed framework in detail. The results demonstrate that the predicted outputs agree well with the CFD simulation results, show good stability and ability to predict additional future results. Compared with the traditional hybrid convolutional neural network-LSTM (CNN-LSTM) framework, the mean square error and mean absolute error are reduced by almost one order of magnitude and two orders of magnitude, respectively, showing that the proposed framework is highly competitive. The GPU cost utilized for running the deep U-Net-LSTM is only 0.33 s for each result, making it possible to achieve real-time prediction. In addition, the computation costs are reduced by six orders of magnitude compared with those in the CFD method.


Introduction
With the development of computer technology, the computational fluid dynamics (CFD) method is widely used for simulating the hydrodynamics of underwater mechanisms (Bhushan et al., 2013), and it is indispensable in many engineering applications (Liu et al., 2021;Gao et al., 2016).
Multiple numerical studies on the hydrodynamics of underwater mechanisms have been performed. A CFD model was established based on RANS equations, combined with the realizable k-turbulence and Euler multiphase flow to study the hydrodynamic performances of an underwater submarine navigating in density-stratified fluid models (Liu et al., 2020). The results showed that the forward speed and submerged depth significantly affected the hydrodynamic performances of the submarine. For analysing the hydrodynamic performance of DARPA SUBOFF, specific towing experiments and CFD simulations were carried out . It was found that the simulation results were in good agreement CONTACT Hui Li li_hui@whu.edu.cn;Hong Chen chenhong22001@163.com with the towing experiment results. Currently, the CFD method could obtain the high-precision hydrodynamic performance of the underwater mechanism. However, the calculation of large-scale computing projects is still computationally expensive. It may take hours or even days, requiring high-performance parallel computing hardware. Therefore, a rapid and accurate hydrodynamic performance method is needed. Recently, the deep learning (DL) method has gained significant attention in multiple fields. It provides a datadriven method to solve computational engineering problems (Reichstein et al., 2019). Various DL techniques have been applied to computational engineering problems. The machine learning method of ANFIS combined with CFD data to predict the macroscopic parameters such as gas velocity in the multiphase reactor . The results showed a substantial reduction in the time required for making calculations and obviated the need for complex CFD simulation. Optimization of the first blade of a new test rig was pursued using a hybrid model comprising the genetic algorithm, artificial neural networks, and the design of experiments. The CFD verification results demonstrated that the coupled behavior of the blade and aerodynamic performance improved by 5.7% (Ghalandari et al., 2019). Convolutional neural network (CNN) has been proven to learn invariant high-level features when the data has a strong spatial correlation (Zhang & Yin, 2021), drawing attention to applying DL techniques to fluid dynamics. Hui et al. (2020) proposed a CNN framework and applied it to predict the invisible pressure distribution of airfoils. The results demonstrated that it could achieve predicting the pressure coefficient in seconds, with a less than 2% mean square error. Long short term memory (LSTM) is a special kind of recurrent neural network (RNN), and LSTM and its variants are characterized by sequence prediction, in which the historical information can be stored and learned . LSTM can learn long-term dependence information and avoid the gradient explosion and disappear during the training period. Unlike other traditional machine learning algorithms, LSTM is an effective model to automatically learn the features from sequence data. Zhao et al. (2020) proposed a bidirectional recurrent neural network (bi-RNN) model with LSTM. They applied it to the prediction of the in-cylinder flow field. The results demonstrated that it could accurately predict the interactions of in-cylinder flow fields. The deep convolutional generative adversarial network (DCGAN) was also developed and applied to predict spatio-temporal flow distributions for any given new inputs (Cheng et al., 2020), in which CNN extracted complex features. It achieved a reasonable accuracy and could provide a reliable prediction for nonlinear fluid flows. However, the prediction results are still some significantly different from the real flow field.
In order to capture the relationship between spatial and temporal, Donahue et al. (2015) proposed a hybrid CNN-LSTM framework. CNN is utilized to extract features that are then utilized as inputs in the LSTM model and LSTM is utilized to learn time-sequenced information (Barzegar et al., 2021). Several studies have found that a hybrid CNN-LSTM model is better than independent CNN and LSTM models (Kim & Cho, 2019). Bogaerts et al. (2020) proposed a graph CNN-LSTM neural network that simultaneously extracted the spatial features of traffic, using graph convolution and its temporal features through LSTM cells to make short-term and long-term predictions. The result showed that the predicted model could maintain its performance over different time-horizons from 5 min to up to 4 h with multistep predictions. To overcome the lacking delineation of foreground (FG) regions due to missing temporal information, Akilan et al. (2020) proposed a 3D CNN with LSTM. The results showed that the proposed model achieved competitive performance in terms of figure of merit evaluated against prior and state-of-the-art methods. An architecture named LSTM multi-modal UNet was proposed for brain tumor segmentation in multimodal magnetic resonance images (Xu et al., 2019). Experiments results on BRATS-2015 showed that this method outperformed the state-of-the-art biomedical segmentation approaches. The above literature showed that the CNN and LSTM framework hybrid has been utilized in multiple fields. However, few researches studied the time-sequenced hydrodynamic prediction of underwater mechanisms. The flow field of SUBOFF has many complex multi-scale features, and needs high-precision pixel-level predictions, which is more challenging than time domain problems in other fields. Therefore, it is of great significance to study the rapid hydrodynamic prediction of underwater mechanisms.
Considering these current difficulties and constraints, this study proposes a novel deep U-shaped network-LSTM (U-Net-LSTM) framework for complex timesequenced hydrodynamics prediction of underwater mechanisms. The main contributions and innovations of this paper are summarized as follows: A novel deep U-Net-LSTM methods framework is proposed, which composing of a deep U-shaped network, two LSTM layers, and a skip connection part. The proposed framework provides a new data driven method for rapid, high-precision pixel-level and time-sequenced hydrodynamics prediction of complex multi-scale underwater mechanisms.
This paper is organized as follows. Section 2 introduces and describes the components of the proposed deep U-Net-LSTM framework. Section 3 presents validation of the CFD simulation results of the SUBOFF AFF-8. Section 4 demonstrates the hydrodynamic prediction of the SUBOFF AFF-8 with three motions to show the detailed advantages of the proposed deep U-Net-LSTM framework. Finally, Section 5 concludes the paper.

Deep U-Net-LSTM framework
CNN requires fewer trainable parameters while providing flexibility in learning complex geometric contours. Owing to its strong non-linear mapping capacity , CNN and its variants can directly extract microscopic information from images. However, due to the loss of information caused by the pooling of CNN, the feature contours of the predicted images obtained from the traditional CNN-LSTM framework are fuzzy. This shortcoming makes it difficult to achieve high-precision pixel-level predictions and fails to predict more detailed, complex multi-scale features of complex engineering.
This paper proposes a novel deep U-Net-LSTM framework to predict complex time-sequenced hydrodynamics features. Figure 1 demonstrates the structure of the proposed deep U-Net-LSTM framework. It is designed by combining a deep U-shaped network (Zhang et al., 2019), two LSTM layers and a skip connection part. The proposed framework composes of an encoding part, a LSTM part, a decoding part and a skip connection part. The encoding part is utilized to extract complex features, the LSTM layer is utilized to learn time information and the decoding part recovers the vector output of the LSTM layer at the same size as the input shape. The skip connection part could send more high-level semantics to the decoding part and overcome as much lost information as possible (caused by pooling). A total of 38 layers are designed: 25 convolutional layers, 5 max pool layers, 1 Global Average Pool (GAP) layer, 2 LSTM layers and 5 upsampling layers.
The encoding part consists of two 3 × 3 convolutions and a ReLU activation function, and it performs a 2 × 2 max pooling. The number of feature channels double after the max pooling. Each layer of the decoding part consists of two 3 × 3 convolutions, a 2 × 2 upsampling layer and ReLU activation functions.
The input layer of the encoding part accepts timesequenced images as inputs and extracts complex features to the LSTM part. Unlike the traditional CNN-LSTM framework that uses the reshape function, the GAP layer could reduce the dimensions of input images and avoid overfitting in the framework. After the last layer of the decoding part, the output shape is revealed (none, n, 512).
The LSTM part has two LSTM layers that are connected in series to possess these extracted sequential vectors from the encoding part. Each LSTM layer has 512 hidden layers. The return sequences of the first LSTM layer are set to true and constructed to possess these extracted sequential vectors from the encoding part. Then, the output sequential vectors with the shape (none, n, 512) will be sent to the second LSTM layer. The return sequences of the second LSTM layer are set to false, meaning that only the last predicted vectors of the LSTM layer are outputs. Such as the conv10 layer and conv16 layer in the symmetry position with the same size feature map (32,64,256). The time series features output by the conv10 layer are feature-fused and then sent to the conv16 layer. After the channels concatenate, the shape will change (none, 32, 64, 512). Finally, the decoding part recovers the vectors of the same size as the input by upsampling.

Training and predictive processes
The framework for the hydrodynamic prediction is instantiated with the SUBOFF AFF-8 (Groves et al., 1989). This study predicts future hydrodynamic results using the first two time-sequenced data. Considering that this is a pixel-level regression issue, the mean square error (MSE) between the ground truth t+1 and the predicted result * t+1 is utilized as the loss function. The mean absolute error (MAE) and peak signal-tonoise ratio (PSNR) are also utilized to further evaluate the performance of the predicted results. The calculation formulas are given as follows: where n, t+1 , * t+1 , and MAX 2 i stand for the number of samples, the ground truth, the predicted result, and the biggest pixels in the two images, respectively. In the case of 8-bit samples, MAX 2 i = 225. Figure 2 shows the detailed workflow of the proposed deep U-Net-LSTM framework. This Workflow mainly includes data preparation, training, and validation. The learning procedures are summarized as follows: (a) The CFD simulation method is utilized to obtain the dynamic time-sequenced hydrodynamic results of the SUBOFF AFF-8. Each result can be regarded as a color image with a size of 1,024 × 512 × 3. Subsequently, three time-sequenced results are grouped as a unit, and all the sequential units compose the dataset. (b) The dataset is then split into the training and validation sets. The data from the first and second results of each sequential unit constitute the input sequence. The data from the third results constitute the target used to validate the output results.
The training set will be utilized for training the deep U-Net-LSTM framework to optimize the deep U-Net-LSTM's weights by forward and backward propagations. The weights are updated with every input in training set to minimize the MSE between the target result and output. (c) The loss of prediction results in the validation set will evaluate the performance of the proposed deep U-Net-LSTM framework. The training will only end when a suitable lower bias (MSE) is obtained; otherwise, the prediction model will be retrained. When the training is complete, the framework can predict additional future results. 3. Validation of the CFD simulation results for the SUBOFF AFF-8

Numerical model of the SUBOFF AFF-8
To obtain the target dataset, the DARPA SUBOFF AFF-8 is applied for the validation of the CFD simulation. The total length (L) of the SUBOFF AFF-8 is 4.356 m, with a maximum diameter (D) of 0.508 m. The computational domain and boundary conditions for the AFF-8 are shown in Figure 3(a). In this paper, the dimension of the computational domain is designed with reference to the recommendations of Amiri et al. (2019). The overset mesh technique could simplify the construction of the computational grids with complex geometries and allows for relative motion between the embedded grids. To improve accuracy and save on computational time, the computational domain was discretised using multi-block/overset structured grids, Figure 3. Computational domain and overset grid system for the SUBOFF AFF-8. and the size of the component mesh was much smaller than that of the background mesh. Figure 3(b) illustrates the overset grid system, including component mesh, the background mesh and the boundary layer of the AFF-8, with a total of 8.6 million grid points.

Validation of the CFD simulation results
The SUBOFF AFF-8 provides a large amount of experimental data available from the DARPA SUBOFF project. Liu and Huang (1998) summarized all collected data (Groves et al., 1989;Crook, 1990) that serve as the final database for future submarine flow research. It is already widely used as a benchmark for experimental validations. Ahn et al. (2020) used the SUBOFF-8 experimental data for a resistance test in a large cavitation tunnel (Ahn et al., 2020), and Efremov and Milanov (2019) used the experimental data for the investigation of hydrodynamic forces and moments of SUBOFF-8. Figure 4(a) and 4(b) show the resistance test installation. The experimental data are also widely used as the database for CFD validations and other submarine-related flow field analyses Sezen et al., 2018).
To validate the CFD simulation results, the resistance of the SUBOFF AFF-8 at different velocities was computed by the commercial software Fluent 19.1 CFD solver (ANSYS Inc., USA) using the k-turbulence model and a coupled algorithm. The computational environments used are Intel R Xeon R Gold 6230R CPU at 2.1 GHz × 52 cores (256 G RAM). Table 1 shows the relative differences between the numerical and experimental results (Liu & Huang, 1998) for the AFF-8. The CFD simulation results are very close to the experimental results. The maximum difference is 2.34%, and the minimum difference is 0.19%. Therefore, this study's numerical model is effective and reasonable.

Hydrodynamic prediction of the AFF-8 using the proposed framework
To demonstrate the performance of the hydrodynamic prediction by the proposed deep U-Net-LSTM  framework, three different motions of the SUBOFF AFF-8 were studied. One uniform acceleration motion was studied in detail to show the advantages of the proposed deep U-Net-LSTM framework. The uniform deceleration motion and sinusoidal motion were also discussed as concrete applications of the proposed deep U-Net-LSTM framework.

Generation of training and validation set
The numerical model validated in Section 3 is used for the dynamic fluid field analyses to obtain the target dataset. The inlet velocity of the boundary condition is 0.1 m/s, and the timestep size is 0.01 s. The user-defined function (UDF) and the overset mesh function are utilized to define the velocity of the component grid. The motion of the AFF-8 used in this section can be expressed as follows: where v and n stand for the velocity of the AFF-8 (unit: m/s), the number of timesteps, respectively. As the AFF-8 increases in velocity from 0.514 to 1.604 m/s, 110 hydrodynamics results are collected at different timesteps.
To fully demonstrate the framework's capability, two typical hydrodynamic datasets are collected for each motion (Maziar et al., 2020). Figure 5(a) shows the first typical dataset (the velocity set) that illustrates the velocity distribution around the AFF-8 in the X-Z crosssection at different timesteps. Note that the contours vary obviously over time, and the velocity distribution has multi-scale characteristics, especially around the forebody and sail of the AFF-8. Figure 5(b) shows the second typical dataset (the pressure set) that illustrates the threedimensional pressure distribution of the AFF-8. The characteristics of the pressure distribution also demonstrate significant change. Multiple complex features are concentrated on the forebody and sail of the AFF-8, bringing the greatest challenges to the prediction work.

Setting the parameters
This study utilizes the Adam optimization algorithm (Kingma & Ba, 2014) to adjust the weight matrices. The total epochs are set to 300, and the initial learning rate is 0.001. To reach optimality, the 'ReduceLROn-Plateau' function is also used. The 'patience number' of the 'ReduceLROnPlateau' function is set to 10. If there is no improvement after 10 epochs, the learning rate will be reduced by two times. To overcome the problem that the training process is difficult to converge (Joshi et al., 2019), the RGB values of all images are scaled to the range (0, 1) by multiplying by 1/255. The environments used are GPU at NVIDIA GTX2080Ti (11 G RAM) and Python 3.6. The number of trainable parameters is 12,848,339. The memory footprint (GPU) during training is 9.87 G and the file size of the framework is 0.14 G.

Algorithm validation
The scope of the verification timestep depends on the percentage of the validation set. Therefore, to study the influence of the scope of the validation timesteps on the prediction performance of the proposed framework, the percentage of the training set will be determined from six option values (5%, 10%, 15%, 20%, 30% and 40%). For example, when the validation set percentage is 5%, the validation timestep range is 105-110. When the validation set percentage is 40%, the validation timestep range is 68-110. A 40% validation set has more timestep results in the future than has a 5% validation set.
As is shown in Figure 6, with the percentage of the validation set increases, the contour feathers of the predicted results of both the velocity and pressure distribution become fuzzier. This is especially true in some small features of the forebody and sail of the AFF-8. Table 2 summarizes the MSE of different percentages of the validation set. As the percentage of the validation set increases, the MSE of the validation set increases significantly. When the validation set is 30%, it is still close to the CFD simulation result and only demonstrates slight differences in the forebody and sail of the submarine. These results indicate that the proposed framework has good stability and ability to predict future timestep results. To further study the performance of the proposed framework, the dataset is fixed as 85% and 15% for training and validation, respectively.
As the pixel value at each point corresponds to the hydrodynamic value one-to-one, the pixel values of the predicted image can be indirectly converted to a velocity or pressure value using the Python program. As is shown in Figure 7, the comparison of velocity and pressure distribution obtained from the six test points are demonstrated at timestep 94 when the percentage of the validation set is 15%. Most test points demonstrate a good  To demonstrate the proposed deep U-Net-LSTM framework's advantages, the performance of the proposed framework is compared in detail with the traditional CNN-LSTM framework. Figure 8(a) presents the comparison of the velocity set obtained from the predicted results between the traditional CNN-LSTM and proposed deep U-Net-LSTM frameworks at timestep 94, 102 and 110. Clearly, the traditional CNN-LSTM framework failed to predict complicated features, whereas the proposed deep U-Net-LSTM framework could predict the velocity distribution for some micro-scale features. The proposed deep U-Net-LSTM framework predicts the large-scale features and predicts the small-scale features around the submarine's forebody and sail with a high agreement to those from the CFD simulation results.
Figure 8(b) shows the performance of the proposed framework in the pressure set. It is clearly better than the performance of the traditional CNN-LSTM framework. The differences obtained from the predicted results between the CFD simulation and the proposed framework are quite small, indicating that the proposed deep U-Net-LSTM framework can obtain more reasonable and accurate solutions for complex hydrodynamic results than can the traditional CNN-LSTM framework.
The convergence history of the traditional CNN-LSTM framework and the proposed deep U-Net-LSTM framework is shown in Figure 9. Both the MSE and MAE decrease as the epoch increases. When the convergence curve is stable, both the MSE and MAE are reduced by at least one order of magnitude and two orders of magnitude, respectively. In addition, the performance comparison of the predicted results at three different timesteps between the traditional CNN-LSTM and proposed deep U-Net-LSTM frameworks are summarized in Table 3.  The training time and predicted time of each result are also slightly reduced. The proposed deep U-Net-LSTM framework has an MSE of 2.0 × 10 −4 at the last timestep of the pressure validation set. This is still an order of magnitude lower than that of the traditional CNN-LSTM framework at the first validation timestep. A prediction framework with a smaller MSE ensures more accurate hydrodynamic prediction results. Figure 10 shows the PSNR (defined in equation 3) distribution of the validation set. It ranged from 16.86 to 31.52 of the traditional CNN-LSTM framework and 37.19-40.09 of the proposed framework. The mean PSNR demonstrated significant improvement from 20.94 to 39.14, proving that the performance of the proposed framework has higher accuracy and is more stable than that of the traditional CNN-LSTM framework.
An ablation study is carried out to explore the influence of the LSTM and the skip connection parts on the prediction ability. CNN is chosen as the baseline model. Based on the baseline model, the LSTM part (CNN-LSTM), the skip connection part (U-Net), and two parts together (U-Net-LSTM) will be added separately.   These algorithms also stand for the most popular DL algorithms, commonly found in the literature. Ablation results are shown in Table 4. When the LSTM part is Training 9.0e-05 3.7e-05 3.1e-03 1.5e-03 Validation 2.1e-04 1.4e-04 4.5e-03 2.9e-03 added, the mean MSE and MAE on the two validation datasets are reduced by 9.7% and 8.1%, respectively, which verifies the effectiveness of LSTM part. When the skip connection part is added, the mean MSE and MAE on two validation datasets performance are reduced by almost one order of magnitude and two orders of magnitude, respectively, which verifies the significant effectiveness of the skip connection part. It can be found that both the skip connection part and LSTM part positively affect prediction accuracy. When both parts are added, the proposed framework achieves the best performance in term of the two evaluation criteria based on two validation datasets, showing that the proposed model is highly competitive.

Hydrodynamic prediction of uniform deceleration motion
The uniform deceleration motion of the AFF-8 is discussed as one concrete application of the proposed framework, and it can be expressed as follows: v = 1.809 − 0.01 × n, 1 ≤ n ≤ 110 (5) Figure 11. Comparison of the velocity and pressure distribution of the uniform deceleration motion obtained by the CFD simulation and the prediction by the proposed deep U-Net-LSTM framework. where v and n stand for the velocity of the AFF-8 (unit: m/s), the number of timesteps, respectively. The comparison of fluid results between the CFD simulation and the prediction by the proposed deep U-Net-LSTM framework in uniform deceleration motion is shown in Figure 11. The results demonstrate that the proposed deep U-Net-LSTM framework performs very well. The MSE and MAE distributions of the validation set are further illustrated in Figure 12. The MSE and MAE of the two validation sets increase steadily as the validation timestep increases. The MSE ranges from 5.4 × 10 −5 to 1.4 × 10 −4 , and the MAE ranges from 1.9 × 10 −4 to 4.0 × 10 −4 , indicating that both demonstrate a better performance than those in the uniform acceleration prediction.

Hydrodynamic prediction of sinusoidal motion
The sinusoidal motion of the AFF-8 is discussed as another concrete application of the proposed framework. The velocity of this motion is more intense than that of the other two motions and can be expressed as follows: v = sin(2.854 × 0.01 × n) + 0.514, 1 ≤ n ≤ 110 where v and n stand for the velocity of the AFF-8 (unit: m/s), the number of timesteps, respectively.
The comparison of fluid results between the CFD simulation and the prediction by the proposed deep U-Net-LSTM framework in sinusoidal motion is shown in Figure 13. The proposed framework demonstrates good performances under this motion. As is illustrated in Figure 14, the values range from 8.1 × 10 −5 to 3.7 × 10 −4 for MSE and 2.8 × 10 −3 to 4.8 × 10 −3 for MAE. These results confirm that the proposed deep U-Net-LSTM framework is a powerful framework for time-sequenced hydrodynamics prediction.

Performance assessment
Comparison of the running time and the loss of three motions are summarized in Table 5. It is worth mentioning that the GPU cost for running the proposed framework for one time-step is only 0.33 s, which makes it possible to achieve real-time predictions. Although  In summary, the proposed deep U-Net-LSTM framework successfully captures complex hydrodynamic features and provides high-resolution future hydrodynamic results. It can be applied to predict the complex timesequenced hydrodynamic prediction of underwater mechanisms and provides an efficient artificial intelligence framework to solve complex computational science and multi-scale engineering problems.

Conclusions
To solve the lead-time prediction problems of complex multi-scale features of SUBOFF AFF-8, a novel deep U-Net-LSTM framework has been proposed for rapid hydrodynamic prediction. This framework composed of a deep U-shaped network, two LSTM layers, and a skip connection part. The CFD simulation results of the SUB-OFF AFF-8 were validated by referring to the published experimental data. The velocity and pressure sets of the AFF-8 were collected to define three types of motions, and the impact of the validation set percentage on the prediction performance was studied based on the uniform acceleration motion. The proposed framework was validated by comparing the CFD method and the traditional CNN-LSTM framework. An ablation study was used to identify the effects of the LSTM and skip connecting parts on the prediction performance of the proposed framework, and the competitiveness of the proposed framework was verified. The uniform deceleration and sinusoidal regular motions were also discussed as concrete applications of the proposed framework.
The predicted results were very close to the CFD simulation results, indicating that the proposed framework had good stability and the ability to predict the results of additional future timesteps. Compared with the traditional CNN-LSTM framework, the mean PSNR was significantly improved from 20.94 to 39.14, and the MSE and MAE were reduced by at least one order of magnitude and two orders of magnitude, respectively. The GPU cost for running the proposed deep U-Net-LSTM framework was only 0.33 s for each result, making it possible to achieve real-time prediction. The computation cost was reduced by six orders of magnitude compared with that in the CFD method.
A novel deep U-Net-LSTM framework for timesequenced hydrodynamic predictions was presented and proven successful in this paper. This framework is also genetic, meaning that other time-sequenced results can replace the dataset to study various time-sequenced prediction problems, such as structural engineering, fluid mechanics and heat conduction. In addition, many factors will affect the prediction accuracy, such as the geometry model, motion velocity, timestep and number of CFD simulation results. In future work, more robust framework will be developed to predict more complex and more types of motions simultaneously.

Disclosure statement
No potential conflict of interest was reported by the author(s).