Forecasting turbulent flow dynamics requires a balance between predictive fidelity and computational efficiency. Diffusion-based generative models can represent complex spatiotemporal dynamics, but their application to high-dimensional turbulent flows remains computationally expensive. In contrast, proper orthogonal decomposition (POD) provides compact, physically interpretable reduced-order representations, although aggressive modal truncation can remove relevant flow structures. This work introduces a hybrid reduced-order generative forecasting framework that combines POD with Generative Learning of Effective Dynamics (G-LED). The method performs temporal prediction in a physics-based modal space and uses diffusion-based reconstruction to recover physically meaningful flow-field representations. It is assessed using experimental measurements of the turbulent wake behind a circular cylinder. Three configurations are compared: full-field G-LED, global POD-G-LED, and localized POD-G-LED. Full-field G-LED provides the highest fidelity, preserving richer vorticity fluctuations and more consistent turbulent kinetic energy distributions, but requires approximately 17 h for diffusion-model training, 7 h for Transformer training, and 3 min to predict 100 future snapshots. By transferring prediction to a reduced POD space, global POD-G-LED reduces these costs to approximately 8 h, 2 h, and 50 s, respectively, while retaining dominant wake organization and coherent energetic structures. A localized POD-G-LED formulation assigns different modal resolutions to distinct wake regions and improves vorticity statistics and energetic distributions relative to the global reduced-order configuration. These results show that coupling physics-based modal representations with diffusion-based generative reconstruction offers an effective route to efficient turbulent-flow forecasting.
Data-driven learning provides a promising route for accelerating computational fluid dynamics, yet transient flow prediction remains challenging because models must simultaneously capture evolving temporal dynamics and cross-scale spatial structures while generalizing across geometries and operating conditions. In this work, we study one-step-ahead prediction of two-dimensional incompressible transient flows from historical snapshots and propose Multi-Scale Spatiotemporal Flow (MuST-Flow), a physics-informed multi-scale spatiotemporal network for recurrent forecasting of velocity and pressure fields. The central idea of MuST-Flow is to couple cross-scale feature extraction with physical regularization, enabling the model to better resolve localized high-gradient flow structures while maintaining physically consistent evolution. Specifically, MuST-Flow adopts a multi-scale spatiotemporal convolutional design with dilated receptive fields to learn hierarchical flow representations and incorporates a hybrid loss derived from the residuals of the incompressible Navier–Stokes equations to encourage mass and momentum consistency during training. To evaluate generalization beyond fixed configurations, the proposed method is assessed on transient hydrofoil flow data under cross-geometry testing with varied operating conditions. Experimental results show that MuST-Flow achieves the lowest mean absolute error, highest structural similarity, and lowest speed and velocity-direction errors among both generic spatiotemporal prediction baselines and flow-oriented neural-operator baselines, while maintaining competitive divergence and Navier–Stokes residuals. These results demonstrate its effectiveness as an efficient surrogate modeling framework for two-dimensional incompressible transient flow prediction.
Yan Liu, Jie Liu, Xinhai Chen et al.· The Physics of Fluids· 0 citations
We use a large database of direct numerical simulations to investigate the transition of the Rayleigh--Taylor instability to turbulence and its evolution toward a late-time self-similar regime. In addition to tracking the growth of the mixing layer through the mean heavy-fluid concentration profile, we analyze one-dimensional profiles of turbulent kinetic energy and dissipation, two key quantities in classical turbulent-mixing models. We consider two reduced-order modeling strategies that differ in where nonlinearity is introduced: either in the construction of the latent space or in the description of its temporal evolution. The first method uses a linear encoder--decoder obtained using Proper Orthogonal Decomposition (POD), with nonlinear reduced dynamics learned by a physics-informed neural network (PINN). The second uses a nonlinear encoder--decoder learned by an autoencoder, while constraining the latent dynamics to remain linear and satisfy physical constraints. Both approaches achieve satisfactory performance in reconstructing, interpolating, and extrapolating the dynamics of the Rayleigh--Taylor instability.
Téo Granger, B. Nadiga, B. Gréa et al.· 0 citations
Accurately capturing unsteady flow dynamics remains challenging for physics-informed neural networks because nonlinear convection, multiscale structures, boundary effects, and accumulated temporal errors can degrade long-time prediction accuracy. This work proposes a physics-informed convolutional leaky-integrator recurrent network for capturing time-dependent flow fields. By combining local convolutions with learnable leaky memory, the proposed method provides a compact recurrent time-marching model with fewer parameters than multi-gate recurrent architectures. To support long-time prediction, the temporal domain is decomposed into overlapping windows coupled by consistency constraints, governing-equation residuals are evaluated using finite-difference differentiation matrices, and prescribed boundary conditions are enforced through hard constraints. The framework is evaluated on incompressible Navier–Stokes flows, including forced two-dimensional flow and the pre-merger interaction of two co-rotating vortices in a no-slip square cavity. Numerical results show that the proposed method reconstructs velocity and vorticity fields with low errors and provides temporally consistent solutions over the tested intervals. For the co-rotating-vortex case, vortex-core kinematics, vorticity statistics, circulation, restricted enstrophy, and the second moment of vorticity are evaluated. The proposed method captures the mutual rotation and gradual approach of the vortex cores and reproduces the principal trends in vorticity redistribution and restricted-enstrophy decay. Compared with the Convolutional Long Short-Term Memory variant, the proposed method achieves errors of the same order of magnitude while using fewer trainable parameters and requiring shorter runtimes in the main recurrent comparisons. Additional tests in Appendix B illustrate its applicability to selected nonlinear evolutionary partial differential equations.
Ziyi Zhen, Yan Zhang, Hui Xu· The Physics of Fluids· 0 citations
Granular flows are ubiquitous in natural and industrial systems, yet their complex dynamics remain difficult to characterize. For inverse problems involving unknown inlet, outlet, and wall boundary conditions, where CFD simulations are challenging, reconstructing complete flow fields from sparse observations constitutes a challenging inverse problem. In this study, a physics-informed neural network framework driven by both physical mechanisms and measurement data is developed to reconstruct the steady-state full-field distribution of granular flows in a pipe. The proposed approach integrates sparse measurement data with governing equations and constitutive relations and is trained using high-fidelity datasets generated by CFD solutions of a continuum model. The framework incorporates a dimensionless loss formulation, physics-informed initialization, dynamic global weighting, and a locally weighted granular temperature data-loss strategy. These treatments enable accurate reconstruction of the complete flow-field evolution. This work establishes a robust methodological framework for flow-field reconstruction in complex granular flow systems.
Predictive, fast reduced-order models are essential for fusion devices like ITER, where real-time transport forecasting, optimisation, and control cannot depend on costly first-principles turbulence simulations alone. We tackle this problem with the LaQuey Mahajan, Rutherford, and Tang equation, a reduced trapped-ion mode turbulence model equivalent, after nondimensionalisation, to the Kuramoto–Sivashinsky equation. We use a geometry-aware reduced-order framework over a two-parameter space of damping and dissipation. Local proper orthogonal decomposition bases extracted from direct numerical simulation are used to build Galerkin reduced models. Frozen bases remain accurate when turbulent structures vary smoothly, but they deviate near transitional regimes where fluctuation content reorganises. Grassmann-manifold analysis shows that subspace proximity does not always guarantee physical accuracy: transport may be reproduced even when fine-scale structure is not. Adaptive, parameter-dependent bases obtained by manifold interpolation significantly improve robustness and recover both large-scale and fine-scale fidelity. Overall, the results show that transport accuracy, structural fidelity, and basis geometry are complementary validation criteria for plasma surrogates, and they support efficient predictive models for ITER-scale optimisation and control.
David Garrido González, N. Saura, Adel Saleh et al.· Plasma Physics and Controlle...· 0 citations
Multiscale fluid flows often contain localized flow structures, such as viscous shock layers, wet-dry fronts, steady viscous wakes, decaying vortical structures, and vortex-shedding patterns, whose accurate prediction requires the simultaneous preservation of global conservation trends and small-scale gradients. This study examines these flow-physics requirements through a physics-informed wavelet-Fourier (PIWF) representation for multiscale fluid dynamics. Instead of relying on a single monolithic neural approximator, the formulation separates two complementary components of the flow field within a physics-informed neural representation: long-range coherent modes through a Fourier-basis branch and localized steep-gradient or vortical features through a compactly supported wavelet branch. The outputs are fused with a residual multilayer perceptron using channel attention, and the governing equations, initial conditions, and boundary conditions are imposed directly through the physics-informed loss. The model is assessed on five canonical fluid-dynamics problems: Burgers'equation, the shallow water equations, Kovasznay flow, Taylor--Green vortex flow, and two-dimensional cylinder wake flow. The results show that PIWF improves the resolution of shock-like gradients, wet--dry interfaces, steady wake fields, decaying vortical structures, vorticity extrema, and broadband wake spectra relative to standard physics-informed neural networks and physics-informed Kolmogorov--Arnold networks. These findings indicate that a wavelet-Fourier physics-informed representation can provide a useful route for analyzing multiscale flow phenomena when high-fidelity interior reference data are limited or unavailable.
Chao Wang, Shilong Li, Yunpeng Wang et al.· 0 citations
