Use of Convolutional Neural Networks for Multifidelity CFD Problems

Abstract

Abstract. In recent years, there has been a growing interest in applying deep learning techniques to Computational Fluid Dynamics (CFD), particularly for accelerating simulations and enhancing data resolution. This work explores the use of Convolutional Neural Networks (CNNs) to reconstruct high-resolution CFD fields from low-resolution inputs. A U-Net architecture was selected due to its proven ability to capture both global context and fine-scale features through its encoder–decoder structure combined with skip connections, facilitating detailed reconstructions. The study focuses on two canonical CFD problems: a bump-in-a-duct configuration and a hydrogen combustion chamber. These cases were chosen to encompass both non-reactive and reactive flow regimes and to test the generalization capability of the model under different physical conditions. The network was trained to predict high-resolution pressure, axial velocity, and heat of reaction fields from their corresponding low-resolution versions, thus performing a super-resolution task. Due to the limited size of the available dataset, several regularization techniques were employed to improve model robustness, including Dropout layers and Batch Normalization. Additionally, different data normalization strategies were tested, such as Z-normalization and Min–Max scaling, to enhance training stability and ensure faster convergence. A multi-network approach was also developed to separately handle the prediction of pressure fields and that of axial velocity and heat release rate, mitigating the risk of feature mixing and allowing each network to specialize in learning specific patterns. The datasets were generated using two solvers: a custom Fortran-based code solving the non-dimensional Euler equations, and the commercial CFD software Ansys Fluent for more complex reactive flow simulations. This combination enabled the creation of a multifidelity database, covering a wide range of fluid dynamic behaviors and ensuring better generalization capabilities during training and validation phases. The training process involved careful hyperparameter optimization, early stopping strategies, and loss function selection to prevent overfitting and maximize prediction quality. Quantitative assessments demonstrated prediction errors on the order of a few percent, while qualitative analyses confirmed the ability of the models to accurately reconstruct the flow structures, even in complex reacting flows. The final phase of the project focused on identifying potential future developments of the proposed framework, particularly exploring the capability of the U-Net architecture to address a broader class of problems. One promising direction involves extending the methodology to correct two-dimensional solutions in order to approximate three-dimensional flow fields. This approach consists of training the network with the 2D planes extracted from the full 3D simulations. Furthermore, techniques such as data augmentation could be implemented to improve the model’s generalization and robustness. The main contribution of this work includes the dataset generation, the design and implementation of the U-Net architecture, the training framework, and the performance evaluation. The results highlight the promising role of CNN-based surrogate models in enhancing CFD simulation capabilities and accelerating future engineering workflows by enabling fast and accurate predictions across different fidelity levels.