# Internal Flow Prediction in Arbitrary Shaped Channel Using Stream-Wise Bidirectional LSTM
## 1 Introduction  
Engineering advancements in computational fluid dynamics (CFD) have facilitated the comprehension of flow and object-flow interactions. However, even if the pre-processing for numerical simulation, such as mesh generation, the differentiation of governing equations, boundary condition setting, and solver algorithms, is implemented in advance, the high computational cost of calculating the flow and post-processing the results has become an issue. This poses a significant problem for fluid mechanics engineers who need to conduct numerous experiments under diverse conditions. Hence, neural network (NN) models have emerged as a viable alternative to address the aforementioned issues, particularly in cases where a substantial amount of data has been generated through CFD simulation. NN models [1, 2] are trained by adopting the supervised learning strategy, which uses a dataset of paired inputs and the corresponding target obtained through numerous CFD processes. Specifically, various NN structures are designed according to the data type, such as a fully connected (FC) NN for a sampled point set [3], a graph neural network (GNN) for an unstructured grid [4, 5], or a convolutional neural network (CNN) [6] for a structured grid [7]. Among these approaches, the CNN-based framework has a well-structured usage environment, demonstrating particular strength in constructing deep NNs [8, 9]. Hence,it is widely used for the interpolation of other types of data in a structured grid [10; 11] or when using domain transformation [12]. For instance, [PERSON] et al. [13] introduced AeroCNN-2, in which the drag and lift coefficients are predicted based on the shape of the airfoil. [PERSON] et al. [14] proposed VGG-like networks [15] that can forecast drag forces for arbitrary shapes. [PERSON] et al. [16] presented Shock-Net, which detects shocks in flow and is three times faster than traditional non-deep-learning methods. [PERSON] et al. [17] proposed Vortex-Net, which identifies vortices in shorter execution times with performance similar to that of the instantaneous vorticity deviation (IVD) method [18]. [PERSON] et al. [19] introduced a composite CNN-RNN architecture to estimate the viscosity from flow sequences. [PERSON] et al. [20] designed Metric-Net to select a key time step for simulations. Moreover, accelerating flow generation using DL methods has also become a mainstream research area. In certain instances, researchers have focused on replacing the spatial information processing of the fluid solver with CNNs. For example, [PERSON] et al. [21] proposed FluidNet, which accelerates the Eulerian fluid simulation by utilizing a CNN to solve a sparse linear system instead of the Euler equation. [PERSON] et al. [22] presented a CNN-based Poisson solver that employs a hierarchical structure to efficiently represent large sparse matrices. In addition, researchers have examined the combination of recurrent neural networks (RNNs) to learn temporal information from sequential data. [PERSON] et al. [23] proposed a long short-term memory (LSTM)-CNN solver to predict the pressure field during the simulation, which is 100 times faster than a regular pressure solver. [PERSON] et al. [24] proposed U-Net-LSTM, which combines U-Net and LSTM to learn the unsteady flow around a submarine, and they showed results with a higher resolution than those of other CNN-LSTM-based data-driven simulators. However, the problem of a model yielding critical errors upon encountering boundary conditions not previously included in the training dataset [25; 26] has not been addressed yet. As a result, research has actively focused on obtaining flow fields through the encoder-decoder (ED) structure to predict steady-state or averaged flows for various shapes and conditions. [PERSON] et al. [1] demonstrated that a fully convolutional NN with an ED model can effectively learn laminar flow data around a car shape inside a rectangular channel. [PERSON] et al.