Exploring Artificial Intelligence Network with Application to Fluid Simulation

Abstract

Artificial neural networks (ANNs) are mathematical models inspired by the human brain and are widely used in machine learning (ML) for regression and classification tasks. When extended to multiple layers, ANNs form deep learning (DL) models capable of handling large-scale data; however, conventional multilayer perceptrons often suffer from overfitting and inefficiency when applied to high-dimensional image data. Convolutional neural networks (CNNs) address these limitations by learning hierarchical spatial features through localized convolutional operations, significantly reducing the number of trainable parameters while improving prediction accuracy. Owing to their ability to capture spatial patterns, CNNs have shown strong potential in computational fluid dynamics (CFD), where traditional direct numerical simulation (DNS) of the Navier–Stokes equations is computationally expensive for turbulent flows. Recent ML frameworks such as JAX-CFD and ΦFlow demonstrate that CNN-based models can approximate high-resolution CFD results on coarse grids with substantially reduced computational cost. Despite this progress, the scarcity of large, accurate datasets remains a major challenge for training reliable ML-based fluid solvers, as DNS-based data generation is resource intensive. This dissertation introduces the mathematical foundations of ANNs and CNNs, followed by an investigation of their application to CFD. It demonstrates how JAX-CFD and ΦFlow can be used both to accelerate fluid simulations and to generate high-quality datasets, supporting the long-term goal of replacing DNS with efficient ML-based approaches.