Related papers: A-priori error estimation for space-time Galerkin …
We consider high-dimensional asset price models that are reduced in their dimension in order to reduce the complexity of the problem or the effect of the curse of dimensionality in the context of option pricing. We apply model order…
Advection-Diffusion-Reaction (ADR) Partial Differential Equations (PDEs) appear in a wide spectrum of applications such as chemical reactors, concentration flows, and biological systems. A large number of these applications require the…
The increasing size and complexity of modern power systems have led to a high-dimensional mathematical model for transient stability studies, rendering full-scale simulations computationally burdensome. While dimensionality reduction is…
We consider second order explicit and implicit two-step time-discrete schemes for wave-type equations. We derive optimal order aposteriori estimates controlling the time discretization error. Our analysis, has been motivated by the need to…
This paper proposes a supervised machine learning framework for the non-intrusive model order reduction of unsteady fluid flows to provide accurate predictions of non-stationary state variables when the control parameter values vary. Our…
In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…
Model order reduction (MOR) is often applied to spatially-discretized partial differential equations to reduce their order and hence decrease computational complexity. A reduced system can be obtained, e.g., by time-limited balanced…
In this paper we present a novel approach for the design of high order general boundary conditions when approximating solutions of the Euler equations on domains with curved boundaries, using meshes which may not be boundary conformal. When…
Most model reduction methods reduce the state dimension and then temporally evolve a set of coefficients that encode the state in the reduced representation. In this paper, we instead employ an efficient representation of the entire…
Reduced order methods (ROMs) for the incompressible Navier--Stokes equations, based on proper orthogonal decomposition (POD), are studied that include snapshots which approach the temporal derivative of the velocity from a full order mixed…
We study the numerical approximation by space-time finite element methods of a multi-physics system coupling hyperbolic elastodynamics with parabolic transport and modeling poro- and thermoelasticity. The equations are rewritten as a…
In this paper, we consider model order reduction (MOR) methods for problems with slowly decaying Kolmogorov $n$-widths as, e.g., certain wave-like or transport-dominated problems. To overcome this Kolmogorov barrier within MOR, nonlinear…
In this work a stabilised and reduced Galerkin projection of the incompressible unsteady Navier-Stokes equations for moderate Reynolds number is presented. The full-order model, on which the Galerkin projection is applied, is based on a…
We are interested in numerically approximating the solution ${\bf U}(t)$ of the large dimensional semilinear matrix differential equation $\dot{\bf U}(t) = { \bf A}{\bf U}(t) + {\bf U}(t){ \bf B} + {\cal F}({\bf U},t)$, with appropriate…
In this paper, we prove uniform error bounds for proper orthogonal decomposition (POD) reduced order modeling (ROM) of Burgers equation, considering difference quotients (DQs), introduced in [26]. In particular, we study the behavior of the…
Parametric partial differential equations (PDEs) are fundamental for modeling a wide range of physical and engineering systems influenced by uncertain or varying parameters. Traditional neural network-based solvers, such as Physics-Informed…
We provide rigorous and computable a-posteriori error estimates for first order finite-volume approximations of nonlinear systems of hyperbolic conservation laws in one spatial dimension. Our estimators rely on recent stability results by…
In this work, we address parametric non-stationary fluid dynamics problems within a model order reduction setting based on domain decomposition. Starting from the optimisation-based domain decomposition approach, we derive an optimal…
This work proposes a statistically enhanced framework to address the instability and limited predictive capability of conventional Galerkin-Proper Orthogonal Decomposition (Galerkin-POD) models. The method reformulates the correction of the…
We introduce a residual-based a posteriori error estimator for a novel $hp$-version interior penalty discontinuous Galerkin method for the biharmonic problem in two and three dimensions. We prove that the error estimate provides an upper…