欲計算流體流經物體後產生的速度、壓力變化，可使用計算流體力學（Computational Fluid Dynamics, CFD），CFD利用離散方法求解連續方程式、動量方程式和能量方程式等，得到流體在初始和邊界條件下的模擬結果，是現代工程設計的重要技術之一。然而在超音速條件下，由於其流場複雜性、壓縮性導致的非線性行為，需要更高精度的數值方法和更細緻的網格劃分，使得該類設計工作的計算成本高昂，技術門檻相對較高。
而在做外型、結構等最佳化設計時，每次的設計變更也都需要經由此複雜冗長的過程才得以初步驗證性能，導致設計進程被嚴重拖慢，因此，如何降低模擬計算時的計算成本，是在近年工業界以及學術界的一大課題。
而近年來隨著圖形運算單元（GPU）的迅速發展，利用類神經網路進行預測任務的技術已十分成熟，例如應用於語音助理的大型語言模型（Large Language Model, LLM）、自駕車用於周遭環境感知，基於卷積網路的物件感測模型，到用於圖像風格、畫質轉換的生成對抗網路（Generative Adversarial Networks, GANS），這些應用都在各領域取得飛躍性的發展成果。
在計算流體力學或空氣動力學領域中，使用卷積神經網路於預測一些常用的性能指標，例如升阻力係數、物體表面壓力分佈，甚至到完整流場的數值分布，都在近年取得良性發展，在此領域利用該技術來預測以往需要長時間取得的模擬結果變得可行。經過良好調整後的神經網路模型，預測結果可以作為參考，以便將更多心力投入於細部設計和最佳化方法等課題上。
本研究以超音速流條件下，不同三維凸起物搭配馬赫數所產生的表面壓力、與來流方向垂直之任意截面上的速度、靜壓、總壓等物理場作為資料庫，利用深度學習技術來訓練、驗證並最終測試其準確度。

This study introduces an innovative method to predict 3D flow field with higher resolution. In the problem of supersonic flow around a bump, by inputting the height at different location on the bump (heightmap), the deep learning model can predict flow field data including pressure, velocity and density. Unlike conventional methods using volumetric data, this research exclusively employs multiple slices to represent the 3D flow field, enabling accurate predictions solely across slices and locations.
The deep learning model is trained to predict data from two different view angles, top-view data and slice data, in this study. The outcomes of predicting top-view data show that conventional deep learning architectures, such as autoencoder or UNet, exhibit proficient performance in managing this task. However, when focusing on the primary objective of this study, which involves predicting slice data from various viewpoints, utilizing only the heightmap for predictions leads to unforeseen and unexpected results. In response to this challenge, we aim to tackle the problem by introducing local features that encompass the geometric contours of the slices. These local features will be used in conjunction with the heightmap (global features) as inputs for the model. The additional input information not only successfully resolved this issue and drive the development of a novel architecture named “dimensional features UNet” (DF-UNet). The newly proposed network architecture has two encoders handling local features and heightmap separately. The results show that both traditional UNet and DF-UNet can predict flow field on any slice, furthermore the newly proposed DF-UNet has the improvement of 10% compared to traditional UNet in the prediction of slice data.

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