Data-Driven Modelling for Fluid Dynamics

Turbulent and chaotic flows remain among the most demanding targets for predictive simulation, central to aerodynamics, propulsion, energy systems, geophysical and biomedical applications.

Direct numerical simulation is feasible only for canonical cases, large-eddy simulation remains costly at realistic Reynolds numbers, and industrial practice still relies heavily on RANS models whose accuracy degrades outside calibrated regimes. Meanwhile, growing high-fidelity datasets, modern HPC resources, and machine-learning methods offer new ways to extract structure, identify closures, and build fast surrogates — provided models stay trustworthy, generalizable, and uncertainty-aware.

This course offers an integrated, physics-aware framework bridging classical CFD and turbulence modelling with data-driven methods, reduced-order modelling (ROM), modal analysis, and sequential data assimilation, turning large datasets into predictive, scalable digital twins.

Participants will learn to: 
(1) understand where and why RANS/LES/DNS succeed or fail; 
(2) augment turbulence models with data while enforcing physical constraints and quantifying uncertainty (field inversion, symbolic/sparse regression, Bayesian UQ); 
(3) build projection-based and data-driven ROMs for many-query CFD applications — design, optimization, control, digital twins — including POD-Galerkin, stability and pressure treatment, hyper-reduction, and geometric parametrization; 
(4) handle multi-regime and chaotic dynamics through nonlinear latent representations (autoencoders), data-driven time inference (reservoir computing, recurrent networks), and sequential/Bayesian data assimilation; and (5) apply modal decomposition (POD, SPOD, DMD/Koopman) and cluster-based ROMs to extract coherent structures from turbulent data.

The five-day course combines theory, method development, and hands-on tutorials with opensource tools (EZyRB, PINA, PyTorch, TensorFlow), plus a poster/flash-talk session for participants to present their own research.

Target audience: 

graduate students, PhD candidates, and researchers in applied mathematics, fluid mechanics, computational physics, and mechanical/aerospace engineering working on RANS/LES/DNS, turbulence closures, projection-based and data-driven ROMs, modal decomposition, or nonlinear latent modelling of complex/chaotic flows. It also targets senior researchers and industrial practitioners engaged in digital twins, real-time simulation, optimization, and uncertainty quantification who need trustworthy, scalable, physically consistent data-driven tools.

Participants will also have the opportunity to take part in a poster and flash-talk session, where they can present brief contributions highlighting applications, datasets, and open research challenges.