Related papers: Interpolatory H-infinity Model Reduction
Multi-fidelity simulation is a widely used strategy to reduce the computational cost of many-query numerical simulation tasks such as uncertainty quantification, design space exploration, and design optimization. The reduced basis approach…
We study the implicit regularization of optimization methods for linear models interpolating the training data in the under-parametrized and over-parametrized regimes. Since it is difficult to determine whether an optimizer converges to…
We introduce a new paradigm for immersed finite element and isogeometric methods based on interpolating function spaces from an unfitted background mesh into Lagrange finite element spaces defined on a foreground mesh that captures the…
We present an approach to approximate reachable sets for linear systems with bounded L-infinity controls in finite time. Our first approach investigates the boundaries of these sets and reveals an exact characterization for single-input,…
Immersed boundary methods are high-order accurate computational tools used to model geometrically complex problems in computational mechanics. While traditional finite element methods require the construction of high-quality boundary-fitted…
We revisit the linear programming approach to deterministic, continuous time, infinite horizon discounted optimal control problems. In the first part, we relax the original problem to an infinite-dimensional linear program over a measure…
Hyper-reduction methods have gained increasing attention for their potential to accelerate reduced order models for nonlinear systems, yet their comparative accuracy and computational efficiency are not well understood. Motivated by this…
Mixed H2/H-infinity control balances performance and robustness by minimizing an H2 cost bound subject to an H-infinity constraint. However, classical Riccati/LMI solutions offer limited insight into the nonconvex optimization landscape and…
Port-Hamiltonian systems result from port-based network modeling of physical systems and are an important example of passive state-space systems. In this paper, we develop the framework for model reduction of large-scale…
Machine learning approaches relying on such criteria as adversarial robustness or multi-agent settings have raised the need for solving game-theoretic equilibrium problems. Of particular relevance to these applications are methods targeting…
This paper introduces a novel approach to approximating continuous functions over high-dimensional hypercubes by integrating matrix CUR decomposition with hyperinterpolation techniques. Traditional Fourier-based hyperinterpolation methods…
The Loewner framework is an interpolatory approach for the approximation of linear and nonlinear systems. The purpose here is to extend this framework to linear parametric systems with an arbitrary number n of parameters. To achieve this, a…
We introduce and analyze a framework for function interpolation using compressed sensing. This framework - which is based on weighted $\ell^1$ minimization - does not require a priori bounds on the expansion tail in either its…
We present a suboptimal control design algorithm for a family of continuous-time parameter-dependent linear systems that are composed of interconnected subsystems. We are interested in designing the controller for each subsystem such that…
This paper presents a new method for signal reconstruction by leveraging sampled-data control theory. We formulate the signal reconstruction problem in terms of an analog performance optimization problem using a stable discrete-time filter.…
We propose a strategy for greedy sampling in the context of non-intrusive interpolation-based surrogate modeling for frequency-domain problems. We rely on a non-intrusive and cheap error indicator to drive the adaptive selection of the…
The dynamic behavior of jointed assemblies exhibiting friction nonlinearities features amplitude-dependent dissipation and stiffness. To develop numerical simulations for predictive and design purposes, macro-scale High Fidelity Models…
The fast Ewald methods are widely used to compute the point-charge electrostatic interactions in molecular simulations. The key step that introduces errors in the computation is the particle-mesh interpolation. In this work, the optimal…
The emergence of second-generation high temperature superconducting tapes has favored the development of large-scale superconductor systems. The mathematical models capable of estimating electromagnetic quantities in superconductors have…
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…