generative flow-field modeling

High-fidelity, computationally efficient statistical modeling of three-dimensional turbulent flows remains challenging for conventional deterministic machine learning methods, which often suffer from mean regression artifacts. Method: This paper proposes GenCFD, an end-to-end conditional score-based diffusion model for turbulence generation. Unlike standard regression approaches, GenCFD theoretically elucidates the intrinsic mechanism by which diffusion models synthesize turbulent fields, and integrates spectral-resolution-aware architecture design, joint modeling of key turbulence statistics (e.g., energy spectra, structure functions), and physics-informed generative principles. Results: Evaluated across multiple challenging turbulent flow configurations, GenCFD simultaneously achieves superior statistical fidelity and sample realism—outperforming MSE-based regression baselines with significantly reduced spectral error. The framework advances both statistical accuracy and physical plausibility in data-driven turbulence modeling. Open-source implementation is provided.

Scientific simulations often lack topological controllability in generative modeling. Method: This paper proposes a vector-field topology-guided conditional diffusion model. It is the first to embed topology signals—such as critical point locations and Poincaré indices—encoded via coordinate-based neural networks (SIRENs) into the diffusion denoising process, combined with gradient-guided sampling for explicit, precise control over 2D vector field topology. Contributions/Results: (1) Generated fields strictly satisfy user-specified critical point types and positions—achieving 100% constraint adherence; (2) Topological consistency is rigorously guaranteed while preserving fidelity to the underlying data distribution; (3) Enables topology-aware alignment across ensembles, significantly enhancing scientific exploration efficiency in fluid dynamics and related domains.

High-fidelity turbulent flow simulations—such as direct numerical simulation (DNS) and large-eddy simulation (LES)—remain computationally prohibitive for routine engineering applications. This work systematically compares three generative probabilistic models—variational autoencoders (VAEs), deep convolutional generative adversarial networks (DCGANs), and denoising diffusion probabilistic models (DDPMs)—for modeling two-dimensional Karman vortex streets, trained exclusively on LES data. Evaluation is conducted across three dimensions: statistical fidelity, spatial structure preservation, and multiscale dynamical consistency. Results demonstrate that DCGAN achieves the best overall performance in generation fidelity, inference speed, and sample efficiency—accurately reconstructing turbulent fields from limited LES data. DDPM attains higher accuracy but suffers from prohibitively slow inference; VAE trains rapidly yet yields significant structural distortions. This study establishes generative modeling as a novel, high-fidelity, low-cost surrogate paradigm for turbulence, providing a scalable, data-driven methodology for turbulent flow simulation.

This work addresses the high computational cost of traditional computational fluid dynamics (CFD), which hinders rapid exploration in indoor environmental optimization. While existing generative surrogate models can capture complex flow fields, they suffer from inefficient iterative sampling. To overcome this limitation, the study introduces, for the first time, a drifting generative framework into fluid dynamics, proposing label-conditional and spatially conditional variants that enable single-pass forward generation in the latent space of a variational autoencoder (VAE). A label-aware masking mechanism is incorporated to enforce boundary condition consistency. The method achieves flow field accuracy and physical fidelity comparable to iterative diffusion models while accelerating inference by two orders of magnitude. Moreover, it generalizes effectively to unseen geometries, establishing an efficient new paradigm for real-time CFD surrogate modeling.

High-dimensional turbulent CFD simulations face prohibitive computational costs, scarce data, and a lack of physically interpretable low-dimensional representations. Method: We propose a physics-driven, interpretable latent-space modeling framework. It introduces, for the first time, a graph-spectral-theory-based smoothness metric for physical quantities on the latent manifold and integrates it with a Gaussian Mixture Variational Autoencoder (GMVAE) to achieve structured clustering of the latent space according to key physical parameters—e.g., Reynolds number—ensuring global physical consistency. Results: Evaluated on multi-Reynolds-number 2D Navier–Stokes simulations of flow around a cylinder, the framework significantly improves clustering quality and generative robustness. The resulting low-dimensional representations enable high-fidelity reconstruction while providing explicit physical interpretability—outperforming state-of-the-art dimensionality reduction baselines across multiple quantitative metrics.

This study addresses the inverse design problem of gas turbine combustors by systematically evaluating the effectiveness of generative models in Bayesian inverse problems. For the first time in an engineering inverse design context, we benchmark conditional generative adversarial networks (cGAN), invertible neural networks (INN), conditional flow matching (CFM), and traditional Markov chain Monte Carlo (MCMC) methods, introducing a comprehensive evaluation metric that balances accuracy and diversity. Experimental results demonstrate that CFM significantly outperforms all other approaches across all metrics: it not only produces designs whose performance metrics align more closely with target specifications but also exhibits greater solution diversity and enhanced robustness to variations in training data size.

This study addresses the prohibitive computational cost of CFD simulations in automotive aerodynamics by proposing a spectral geometry-conditioned neural surrogate model for rapid flow field prediction. Methodologically, a downforce airfoil dataset is constructed, and an Airfoil2Vec encoder is introduced to fuse airfoil contours, camber, and thickness into a unified spectral representation. Efficient modeling is achieved by integrating Reynolds-Averaged Navier–Stokes (RANS) simulations with graph neural networks and neural ordinary differential equation architectures. Experimental results demonstrate that the proposed model accurately captures complex flow field characteristics while achieving orders-of-magnitude speedup over conventional CFD solvers. Furthermore, it exhibits strong generalization capabilities across diverse geometries, providing an efficient alternative for aerodynamic design optimization.

This work addresses the challenge that existing deep generative models struggle to simultaneously preserve physical consistency and high-frequency fidelity in three-dimensional aerodynamic inference, primarily due to spectral bias and gradient conflicts arising from governing equations. To overcome these limitations, the authors propose a physics-guided generative flow matching framework that constructs stable generation trajectories grounded in optimal transport theory. The approach incorporates a higher-order discrete numerical engine—operating without automatic differentiation—to alleviate gradient stiffness, and introduces a topology-aware super-resolution module (SATO) that rigorously embeds physical constraints in critical regions such as shock waves. Evaluated on the BlendedNet and NASA Rotor37 datasets, the method achieves a pressure field relative root-mean-square error of 0.0215 under sparse data conditions, significantly outperforming current neural operators while maintaining computational efficiency during inference.

This work addresses the limited generalizability of conventional neural surrogate models in computational fluid dynamics (CFD), which rely on explicit boundary conditions and struggle with scenarios involving altered boundaries or local geometric modifications. The authors reformulate steady-state CFD inference as a context-driven image inpainting task and introduce, for the first time, a reusable velocity field prior learned through self-supervision. Their approach employs a local neighborhood tokenizer to compress high-resolution velocity fields into compact spatially implicit tokens, trained via a masked autoencoder combined with latent-space flow matching. Evaluated on intracranial aneurysm hemodynamics, the method accurately reconstructs full flow fields from only sparse boundary context, significantly outperforming supervised surrogates under varying boundary conditions and distribution shifts, while enabling efficient local geometry editing and context reuse.

This work addresses the high computational cost of traditional finite element methods in simulating path-dependent constitutive models—such as plasticity—over complex geometries, and the inability of existing generative models to efficiently produce high-resolution stress fields. The authors formulate path-dependent plasticity simulation as a video generation task and propose a Transformer-based flow-matching model operating in the latent space of a variational autoencoder to generate full time-series stress fields in a single forward pass. Innovatively employing a non-Gaussian source distribution to reduce intersecting conditional transport paths, and integrating token-level load embeddings with two auxiliary networks, the method achieves high-fidelity, single-step generation without requiring distillation. Evaluated on limited training data, the approach accurately synthesizes high-resolution stress fields and demonstrates a 6–7× speedup over finite element simulations on CPUs and nearly two orders of magnitude acceleration on consumer-grade GPUs.