Related papers: Error Estimation and Stopping Criteria for Krylov-…
Compressed sensing typically deals with the estimation of a system input from its noise-corrupted linear measurements, where the number of measurements is smaller than the number of input components. The performance of the estimation…
Data-driven reduced order modeling of chaotic dynamics can result in systems that either dissipate or diverge catastrophically. Leveraging non-linear dimensionality reduction of autoencoders and the freedom of non-linear operator inference…
With a specific emphasis on control design objectives, achieving accurate system modeling with limited complexity is crucial in parametric system identification. The recently introduced deep structured state-space models (SSM), which…
We consider estimation and control in linear time-varying dynamical systems from the perspective of regret minimization. Unlike most prior work in this area, we focus on the problem of designing causal estimators and controllers which…
This paper presents an interpolatory framework for time-limited $H_2$ optimal model order reduction named Limited Time Iterative Rational Krylov Algorithm (LT-IRKA). The algorithm yields high fidelity reduced order models over limited time…
Solving optimal stopping problems by backward induction in high dimensions is often very complex since the computation of conditional expectations is required. Typically, such computations are based on regression, a method that suffers from…
Projection-based model order reduction of dynamical systems usually introduces an error between the high-fidelity model and its counterpart of lower dimension. This unknown error can be bounded by residual-based methods, which are typically…
This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…
Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of…
We investigate an optimization problem governed by an elliptic partial differential equation with uncertain parameters. We introduce a robust optimization framework that accounts for uncertain model parameters. The resulting non-linear…
We consider the problem of sequential evaluation, in which an evaluator observes candidates in a sequence and assigns scores to these candidates in an online, irrevocable fashion. Motivated by the psychology literature that has studied…
This paper considers the implicit Euler discretization of Levant's arbitrary order robust exact differentiator in presence of sampled measurements. Existing implicit discretizations of that differentiator are shown to exhibit either…
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…
In this paper we compute families of reduced order models that match a prescribed set of moments of a highly dimensional linear time-invariant system. First, we fully parametrize the models in the interpolation points and in the free…
Momentum methods play a significant role in optimization. Examples include Nesterov's accelerated gradient method and the conditional gradient algorithm. Several momentum methods are provably optimal under standard oracle models, and all…
A decision maker records measurements of a finite-state Markov chain corrupted by noise. The goal is to decide when the Markov chain hits a specific target state. The decision maker can choose from a finite set of sampling intervals to pick…
We provide a unifying framework for $\mathcal{L}_2$-optimal reduced-order modeling for linear time-invariant dynamical systems and stationary parametric problems. Using parameter-separable forms of the reduced-model quantities, we derive…
In a standard classification framework a set of trustworthy learning data are employed to build a decision rule, with the final aim of classifying unlabelled units belonging to the test set. Therefore, unreliable labelled observations,…
We consider linear model reduction in both the control and state variables for unconstrained linear-quadratic optimal control problems subject to time-varying parabolic PDEs. The first-order optimality condition for a state-space reduced…
Model predictive controllers use dynamics models to solve constrained optimal control problems. However, computational requirements for real-time control have limited their use to systems with low-dimensional models. Nevertheless,…