Related papers: Accurate error estimation for model reduction of n…
Within this article, we develop a residual type a posteriori error estimator for a time discrete quasi-static phase-field fracture model. Particular emphasize is given to the robustness of the error estimator for the variational inequality…
Two asymptotically exact a posteriori error estimates are proposed for eigenvalues by the nonconforming Crouzeix--Raviart and enriched Crouzeix-- Raviart elements. The main challenge in the design of such error estimators comes from the…
Based on the auxiliary subspace techniques, a hierarchical basis a posteriori error estimator is proposed for the Stokes problem in two and three dimensions. For the error estimator, we need to solve only two global diagonal linear systems…
The purpose of this work is the design and analysis of a reliable and efficient a posteriori error estimator for the so-called pointwise tracking optimal control problem. This linear-quadratic optimal control problem entails the…
The state-of-the art proof of a global inf-sup condition on mixed finite element schemes does not allow for an analysis of truly indefinite, second-order linear elliptic PDEs. This paper, therefore, first analyses a nonconforming finite…
The depth of networks plays a crucial role in the effectiveness of deep learning. However, the memory requirement for backpropagation scales linearly with the number of layers, which leads to memory bottlenecks during training. Moreover,…
In this paper, we propose an acceleration framework for a class of iterative methods using the Reduced Order Method (ROM). Assuming that the underlying iterative scheme generates a rich basis for the solution space, we construct the next…
In this paper we introduce a novel certified shape optimization strategy - named Certified Descent Algorithm (CDA) - to account for the numerical error introduced by the Finite Element approximation of the shape gradient. We present a…
The a priori error analysis of reduced order models (ROMs) for fluids is relatively scarce. In this paper, we take a step in this direction and conduct numerical analysis of the recently introduced time relaxation ROM (TR-ROM), which uses…
Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…
We present an iterative framework to improve the amortized approximations of posterior distributions in the context of Bayesian inverse problems, which is inspired by loop-unrolled gradient descent methods and is theoretically grounded in…
POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear parametrized partial differential equations, combining (i) a preliminary dimensionality…
The indirect approach to continuous-time system identification consists in estimating continuous-time models by first determining an appropriate discrete-time model. For a zero-order hold sampling mechanism, this approach usually leads to a…
This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function. It concerns Symplectic Euler solutions of the Hamiltonian…
The known a posteriori error analysis of hybrid high-order methods (HHO) treats the stabilization contribution as part of the error and as part of the error estimator for an efficient and reliable error control. This paper circumvents the…
Reduced-order models that accurately abstract high fidelity models and enable faster simulation is vital for real-time, model-based diagnosis applications. In this paper, we outline a novel hybrid modeling approach that combines machine…
Real-world systems are often characterized by high-dimensional nonlinear dynamics, making them challenging to control in real time. While reduced-order models (ROMs) are frequently employed in model-based control schemes, dimensionality…
Purpose: Simulation-based digital twins represent an effort to provide high-accuracy real-time insights into operational physical processes. However, the computation time of many multi-physical simulation models is far from real-time. It…
Estimation of actual errors from the residue in iterative solutions is necessary for efficient solution of large problems when their condition number is much larger than one. Such estimators for conjugate gradient algorithms used to solve…
Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…