The efficient implementation of reduced basis methods relying on a high fidelity discretization method to compute the elements of the reduced basis, requires to enter within the code, offline, so that the online solution can be produced very rapidly. Since this is sometimes impossible, in particular for codes used in industrial framework, we have proposed a Non Invasive alternative where the...
In this talk, I will survey reduced order model (ROM) closures and
stabilizations for under-resolved turbulent flows. Over the past
decade, several closure and stabilization strategies have been
developed to tackle the ROM inaccuracy in the convection-dominated,
under-resolved regime, i.e., when the number of degrees of freedom is
too small to capture the complex underlying dynamics. I...
The problem of estimating the state of a physical system is ubiquitous in science. However observations are always limited so that the high-dimensional state cannot be observed and the associated mathematical problem is ill-posed. Popular workarounds include dimension reduction and regularization by imposing some structure to the class of elements in which the estimation is sought.
We here...
A quadratic approximation manifold is presented for performing nonlinear, projection-based, model order reduction (PMOR). It constitutes a departure from the traditional affine subspace approximation aimed at mitigating the Kolmogorov barrier for nonlinear PMOR, particularly for convection-dominated transport problems. It builds on the data-driven approach underlying the traditional...
Partial differential equations (PDEs) that model convection-dominated phenomena often arise in engineering practice and scientific applications, ranging from the study of high-speed, turbulent flow over vehicles to wave propagation through solid media. The solutions of these equations are characterized by local features or disturbances that propagate throughout the domain as time evolves or a...
Reduced-order models (ROM) are of paramount importance for physical understanding, data
compression, estimation, control and optimization. Over a century ago, simple dynamical models
of coherent structures have been facilitated by stability theory (Orr-Sommerfeld equation
1907) and by vortex models (von K arm an 1911). Data-driven reduced-order modeling of coherent
structures has been...
We present several contributions related to Tensor methods for high-dimensional problems and discuss how they are inherently related to model reduction.
In particular, we will show several ways to introduce a principle of adaptivity, making tensor representations more suitable to parsimoniously represent certain solutions sets. In the last part of the talk, a contribution on a possible way to...
Different methods have been proposed in the scientific panorama to offer a compromise between modeling accuracy and computational efficiency. Reduced order models represent a widespread solution in such a direction. In this presentation, we focus on the Hierarchical Model (HiMod) reduction technique, which proved to be an effective approach to discretize CFD configurations where a principal...
