Using nonlinear projections and preserving structure in model order reduction (MOR) are
currently active research fields. In this paper, we provide a novel differential geometric …

Modeling in applied science and engineering targets increasingly ambitious objectives,
which typically yield increasingly complex models. Despite major advances in computations …

Linearity of Koopman operators and simplicity of their estimators coupled with model-
reduction capabilities has lead to their great popularity in applications for learning dynamical …

Computing reduced-order models using non-intrusive methods is particularly attractive for
systems that are simulated using black-box solvers. However, obtaining accurate data …

Many engineering applications rely on the evaluation of expensive, non-linear high-
dimensional functions. In this paper, we propose the RONAALP algorithm (Reduced Order …

The ability to measure differences in collected data is of fundamental importance for
quantitative science and machine learning, motivating the establishment of metrics …

Conventional physics-based modeling techniques involve high effort, eg, time and expert
knowledge, while data-driven methods often lack interpretability, structure, and sometimes …

In this work we propose a novel method to ensure important entropy inequalities are
satisfied semi-discretely when constructing reduced order models (ROMs) on nonlinear …

Accurate and efficient prediction of airfoil aerodynamic coefficients is essential for improving
aircraft performance. However, current research often encounters significant challenges in …

We propose a method based on autoencoders to reconstruct attractors from recorded
footage, preserving the topology of the underlying phase space. We provide theoretical …