This paper proposes a novel approach for learning a data-driven quadratic manifold from
high-dimensional data, then employing this quadratic manifold to derive efficient physics …

Nearly all model-reduction techniques project the governing equations onto a linear
subspace of the original state space. Such subspaces are typically computed using methods …

Conventional reduced order modeling techniques such as the reduced basis (RB) method
(relying, eg, on proper orthogonal decomposition (POD)) may incur in severe limitations …

A quadratic approximation manifold is presented for performing nonlinear, projection-based,
model order reduction (PMOR). It constitutes a departure from the traditional affine subspace …

Inspired by our previous work on a quadratic approximation manifold [1], we propose in this
paper a computationally tractable approach for combining a projection-based reduced-order …

Numerical simulation of parametrized differential equations is of crucial importance in the
study of real-world phenomena in applied science and engineering. Computational methods …

This work presents a model reduction approach for problems with coherent structures that
propagate over time, such as convection-dominated flows and wave-type phenomena …

Transport-dominated phenomena provide a challenge for common mode-based model
reduction approaches. We present a model reduction method, which is suited for these kinds …

In this paper, we propose a general framework for projection-based model order reduction
assisted by deep neural networks. The proposed methodology, called ROM-net, consists in …

We propose a general---ie, independent of the underlying equation---registration method for
parameterized model order reduction. Given the spatial domain Ω⊂R^d and the manifold …