Location

Dimora Sella (https://www.dimorasella.com), Strada Vicinale Valverde 63 07041 - Alghero (SS), Italy - Sardinia

About the course

The course addresses the increasing need for advanced training in theoretical, computational, optimization, stochastic, and data-driven methods that are becoming essential across many areas of fluid mechanics research. Designed for PhD students, postdoctoral researchers, and early-career scientists, the course will provide participants with methodological tools that are broadly applicable across ERCOFTAC disciplines.

The school will be held at a single venue where all participants will stay throughout the course. This format is intended to promote not only high-quality teaching but also close interaction between students and lecturers. Mornings will be devoted to lectures and discussions, while afternoons will focus on hands-on activities, practical exercises, group work and recitation sessions.

By bringing together leading experts and young researchers, the course will foster scientific exchange, collaboration, and the development of a common methodological framework across fluid mechanics

Preliminary course modules

Module I – Data and Operator Decompositions

SVD, Schur decomposition, eigenvalues, NMF, block-diagonalization, sparsity promotion, low-rank decompositions, Fourier, Gabor and wavelet transforms, Hilbert transform, Hilbert–Huang transform, inverse Abel transform.

Module II – Optimization

Variational methods; adjoint-based optimization; optimization under uncertainty;exotic norms (mixedness, Huber); derivative-free optimization; constrained optimization; global convergence.

Module III – Iterative and Approximate Methods

Randomized algorithms; Krylov methods; Arnoldi; deflation; implicit restarting; geometric and algebraic multigrid.

Module IV – Stochastic Methods and Uncertainty

Distribution evolution; Fokker–Planck equation; Wiener and Poisson processes; Ornstein–Uhlenbeck processes; Gaussian mixture models; introduction to stochastic PDEs.

Additional Cross-Cutting Topics

Data assimilation, Kalman filtering, reduced-order modelling, practical implementation using experimental and numerical datasets.

Application

To be opened in due time.

Organisers