Related papers: A time domain a posteriori error bound for balanci…
Finite element based simulation of phenomena governed by partial differential equations is a standard tool in many engineering workflows today. However, the simulation of complex geometries is computationally expensive. Many engineering…
We present a method for contraction-based feedback motion planning of locally incrementally exponentially stabilizable systems with unknown dynamics that provides probabilistic safety and reachability guarantees. Given a dynamics dataset,…
A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems,…
In certain applications involving the solution of a Bayesian inverse problem, it may not be possible or desirable to evaluate the full posterior, e.g. due to the high computational cost of doing so. This problem motivates the use of…
In the time- and frequency-limited model order reduction, a reduced-order approximation of the original high-order model is sought to ensure superior accuracy in some desired time and frequency intervals. We first consider the time-limited…
In this paper we propose a model predictive control scheme for constrained fractional-order discrete-time systems. We prove that all constraints are satisfied at all time instants and we prescribe conditions for the origin to be an…
Practical model building processes are often time-consuming because many different models must be trained and validated. In this paper, we introduce a novel algorithm that can be used for computing the lower and the upper bounds of model…
This paper investigates online algorithms for smooth time-varying optimization problems, focusing first on methods with constant step-size, momentum, and extrapolation-length. Assuming strong convexity, precise results for the tracking…
Inverse problems use physical measurements along with a computational model to estimate the parameters or state of a system of interest. Errors in measurements and uncertainties in the computational model lead to inaccurate estimates. This…
Scenario programs have established themselves as efficient tools towards decision-making under uncertainty. To assess the quality of scenario-based solutions a posteriori, validation tests based on Bernoulli trials have been widely adopted…
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…
In this paper, the a posteriori error estimates of the exponential midpoint method for time discretization are studied for linear and semilinear parabolic equations. Using the exponential midpoint approximation defined by a continuous and…
Frequency-limited model order reduction aims to approximate a high-order model with a reduced-order model that maintains high fidelity within a specific frequency range. Beyond this range, a decrease in accuracy is acceptable due to the…
In this paper we consider the problem of obtaining sharp bounds for the performance of temporal difference (TD) methods with linear function approximation for policy evaluation in discounted Markov decision processes. We show that a simple…
We consider model order reduction of a nonlinear cable-mass system modeled by a 1D wave equation with interior damping and dynamic boundary conditions. The system is driven by a time dependent forcing input to a linear mass-spring system at…
Motivated by a recently proposed error estimator for the transfer function of the reduced-order model of a given linear dynamical system, we further develop more theoretical results in this work. Furthermore, we propose several variants of…
This article studies a priori error analysis for linear parabolic interface problems with measure data in time in a bounded convex polygonal domain in $\mathbb{R}^2$. We have used the standard continuous fitted finite element discretization…
In the present work, we derive functional upper bounds for the potential error arising from finite-element boundary-element coupling formulations for a nonlinear Poisson-type transmission problem. The proposed a posteriori error estimates…
Learned index structures aim to accelerate queries by training machine learning models to approximate the rank function associated with a database attribute. While effective in practice, their theoretical limitations are not fully…
Motivated by problems in contact mechanics, we propose a duality approach for computing approximations and associated a posteriori error bounds to solutions of variational inequalities of the first kind. The proposed approach improves upon…