Intelligent fluid flows: A survey of deep learning methods for turbulent flows, multiphase flows, and combustion

Scientific deep learning (SciDL), an emerging interdisciplinary field at the interface of deep learning (DL) and computational science, is poised to revolutionize modeling approaches in fluid mechanics. This survey presents a comprehensive overview of recent advances in SciDL methodologies tailored to complex fluid flow regimes, with a particular emphasis on turbulent flows , multi-phase flows , and combustion . These regimes represent some of the most formidable challenges in fluid dynamics, characterized by strong nonlinearities, high dimensionality, and multiscale interactions. While conventional numerical solvers remain foundational, their computational demands and limitations in real-time prediction and uncertainty quantification motivate the integration of data-driven techniques. We begin by introducing the core methodologies in SciDL, including Physics-Informed Neural Networks (PINNs), operator learning, hybrid modeling strategies, and generative models for forward and inverse problems in fluid mechanics. The survey then explores domain-specific applications: in turbulent flows , DL has driven progress in closure modeling, reduced-order models, active flow control; in multi-phase flows , neural networks have advanced the modeling of droplet, particle, and bubble dynamics through improved interface tracking and Phase Field methods, and high-fidelity flow field reconstruction using different DL architectures; and in combustion , SciDL has enabled efficient surrogate modeling of chemical kinetics and inverse problems. By synthesizing these developments, this work aims to bridge the gap between traditional fluid dynamicists and modern machine learning (ML) practitioners, offering a curated and technically rigorous perspective on the state of the field. We further discuss critical challenges, including issues of interpretability, generalizability, data scarcity, and numerical robustness, and outline key directions for future research, such as neural operators for turbulence modeling, data-driven discovery of constitutive laws in combusting flows, and multi-fidelity frameworks for uncertainty-aware simulations. This survey underscores the transformative potential of SciDL in enabling next-generation predictive, efficient, and adaptive modeling tools in fluid mechanics.