New Model Captures Complex Flows over Long Timescales

Scientists are tackling the persistent challenge of modelling complex multiscale flows, ubiquitous in fields ranging from physics to biology and engineering. Xiao Xue, Tianyue Yang, and Mingyang Gao, all from the Centre for Computational Science at University College London, alongside Leyu Pan of Imperial College London’s Department of Earth Science and Engineering, and colleagues have developed Uni-Flow, a novel autoregressive-diffusion framework designed to simultaneously capture long-term temporal evolution and fine-scale spatial structure.

This research, a collaborative effort also involving Kewei Zhu from the University College London’s Department of Chemical Engineering, Shuo Wang from Eindhoven University of Technology’s Department of Physics, Jiuling Li, Marco F.P. ten Eikelder working with colleagues at the Institute for Mechanics, Computational Mechanics Group, Technical University of Darmstadt, and Peter V. Coveney from University College London, represents a significant advance by explicitly separating temporal evolution from spatial refinement. Validated across benchmarks including turbulent flows and patient-specific cardiovascular simulations, Uni-Flow achieves faster-than-real-time inference of complex hemodynamic phenomena, potentially transforming high-fidelity simulation from a computationally intensive process into a deployable tool with broad implications for scientific discovery in flow physics. A new technique, Uni-Flow, has been developed to model complex physical systems, offering the potential to speed up simulations across fields like fluid dynamics and healthcare. This advance could unlock real-time modelling of phenomena previously limited by computing power. Researchers are increasingly challenged by modelling the multiscale dynamics of spatiotemporal flows across physics, biology, and engineering. Despite advances in physics-informed machine learning, existing approaches struggle to simultaneously maintain long-term temporal evolution and resolve fine-scale structure in chaotic, turbulent, and physiological regimes. Researchers introduce Uni-Flow, a unified autoregressive-diffusion framework that explicitly separates temporal evolution from spatial refinement for modelling complex dynamical systems. The autoregressive component learns low-resolution latent dynamics that preserve large-scale structure and ensure stable long-horizon rollouts, while the diffusion component reconstructs high-resolution physical fields, recovering fine-scale features in a few denoising steps. Validation of Uni-Flow occurs across canonical benchmarks, including two-dimensional Kolmogorov flow, three-dimensional turbulent channel inflow generation with a quantum-informed autoregressive prior, and patient-specific simulations of aortic coarctation derived from high-fidelity lattice Boltzmann hemodynamic solvers. In the cardiovascular setting, Uni-Flow enables faster than real-time inference of pulsatile hemodynamics, reconstructing high-resolution pressure fields over physiologically relevant time horizons in seconds rather than hours. By transforming high-fidelity hemodynamic simulation from an offline, HPC-bound process into a deployable surrogate, Uni-Flow establishes a pathway to faster-than-real-time modelling of complex multiscale flows, with broad implications for scientific machine learning in flow physics. Partial differential equations (PDEs) govern the spatiotemporal evolution of many dynamical systems central to science and engineering. These systems often exhibit nonlinear, turbulent, and chaotic behaviour, and accurately capturing and computing such dynamics across disparate temporal and spatial scales is essential for advancing both fundamental understanding and practical applications. Traditionally, PDEs are solved numerically using finite difference, finite volume, and finite element discretisations, which have enabled decades of progress in computational physics and engineering. Despite these advances, resolving multiscale dynamics remains computationally prohibitive, increasingly relying on exascale computing resources and facing fundamental challenges arising from the simultaneous presence of long-term evolution and fine-scale structure. In computational fluid dynamics (CFD), large eddy simulation (LES) mitigates some of this cost by filtering unresolved small-scale motions, however, LES remains prohibitively expensive for many academic and industrial applications due to the fine grid resolution required near solid boundaries, limiting its practicality for inverse design and time-sensitive simulations. These computational constraints are particularly restrictive in physiological flow modelling, where high-fidelity solvers remain largely confined to offline analysis. Scientific machine learning (SciML) has emerged as a promising paradigm for accelerating the modelling of PDE-governed systems by learning their evolution directly from data. Recent advances have demonstrated substantial speedups in simulating complex dynamical systems, especially in regimes where traditional solvers are computationally demanding. Physics-informed machine learning (PIML) incorporates conservation laws, symmetries, and governing equations into the learning process, ensuring physical consistency while leveraging the expressive capacity of modern machine learning models. Within CFD, machine learning has been applied to enhance PDE modelling through subgrid-scale closures and turbulence modelling, where resolving all flow scales is impractical. Reinforcement learning has been used to adaptively tune closure terms, while physics-informed neural networks embed PDE residuals directly into loss functions. These approaches reflect a broader trend toward hybridising data-driven learning with numerical solvers, allowing machine learning models to respect governing physical constraints. Recent work has focused on learning the spatiotemporal evolution of entire fields, utilising recurrent neural architectures, such as long short-term memory (LSTM) networks, to capture temporal dependencies but often struggling with long-horizon stability. Neural operator frameworks, including the Fourier Neural Operator and DeepONet, provide a general approach for learning mappings between infinite-dimensional function spaces, enabling efficient solutions of parametric PDEs. Despite their promise, most autoregressive and operator-learning models suffer from long-term instability, where accumulated errors degrade physical realism or cause predictions to collapse towards trivial states. Efforts to stabilise chaotic dynamics through invariant-measure preservation and constrained learning have largely been limited to simplified or low-resolution systems. In general, such approaches have struggled to preserve the correct macroscopic dynamics, with machine-learned surrogate models often diverging from the true long-term behaviour. A complementary line of work has explored diffusion models for reconstructing high-resolution physical fields, originally developed for image synthesis and restoration, and demonstrating strong performance in recovering fine-scale structure and multiscale features in complex flows. However, diffusion models lack inherent temporal modelling capabilities. Uni-Flow addresses this by decoupling temporal evolution from spatial refinement, enabling efficient modelling of both large-scale dynamics and fine-scale features. Real-time haemodynamic simulation via decoupling of temporal evolution and spatial refinement Across canonical benchmarks and complex physiological regimes, Uni-Flow consistently delivered faster-than-real-time inference of complex multiscale flows. Specifically, patient-specific simulations of aortic coarctation, previously requiring hours of high-performance computing time, now complete in seconds. This speed-up transforms high-fidelity hemodynamic simulation from an offline process into a deployable surrogate model. Uni-Flow achieved this by decoupling temporal evolution from spatial refinement. In two-dimensional Kolmogorov flow, the low-resolution autoregressive component accurately captured dominant shear-layer dynamics, while the subsequent diffusion-based refinement addressed under-resolution of fine-scale vortices. Time-averaged kinetic energy spectra demonstrated consistent inertial scaling, though a slight underestimation occurred at higher wavenumbers. Statistical alignment between predicted and ground-truth vorticity distributions was confirmed via quantile-quantile comparisons, showing minor deviations in the tails. Moving to three-dimensional turbulent channel flow, Uni-Flow sustained long-horizon dynamics while selectively reconstructing fine-scale structure, essential for practical scientific simulations demanding both temporal stability and spatial accuracy. Turbulence data generation and Uni-Flow methodology implementation Uni-Flow explicitly separates temporal evolution from spatial refinement, addressing limitations in existing physics-informed approaches that struggle with both long-term prediction and fine-scale resolution. High-fidelity turbulent inflow data was generated using the lattice Boltzmann method, simulating a three-dimensional turbulent channel flow at a friction Reynolds number of Reτ = 180. Instantaneous velocity fields from the mid-plane were extracted, creating a dataset of 320 trajectories, each with 192 × 192 spatial dimensions, and divided into training, validation, and test subsets following an 80/10/10 split. To ensure stable and expressive latent temporal dynamics, a quantum-informed Koopman operator was employed, trained on a 20-qubit quantum device, showcasing a pathway towards hybrid quantum-classical surrogates. High-resolution fields were subsequently reconstructed using Denoising Diffusion Implicit Models (DDIM) sampling with 40 denoising steps. By combining these elements, Uni-Flow aims to transform high-fidelity simulation from an offline process into a deployable surrogate, enabling faster-than-real-time modelling of complex multiscale flows. Validating the framework involved comparing time-averaged velocity fields, instantaneous streamwise velocity fields, and streamwise energy spectra between reference data. 👉 More information 🗞 Uni-Flow: a unified autoregressive-diffusion model for complex multiscale flows 🧠 ArXiv: https://arxiv.org/abs/2602.15592 Tags: