Author

P. Koumoutsakos

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Preprint Oct 2026

Discovery of Singularities in Partial Differential Equations Using Adaptive Numerical Discretizations

We compute self-similar singularity profiles of partial differential equations (PDEs) using adaptive numerical discretizations based on optimizing a discrete loss (ODIL). The fields are represented in overlapping local Chebyshev patches joined with a mapped asymptotic patch. After factoring out the leading power laws o...

A. Yang, Lucas Amoudruz, P. Koumoutsakos · 0 citations

Preprint Aug 2026

A hybrid proper orthogonal decomposition and diffusion framework for reduced-order forecasting of turbulent flow dynamics

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 de...

Rodrigo Abad'ia-Heredia, Xiangrui Zou, M. López-Martín et al. · 0 citations