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Arjun Vijaywargiya (University of Texas at Austin)5/18/26, 3:45 PMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
Standard projection-based model reduction for dynamical systems incurs closure error because it only accounts for instantaneous dependence on the resolved state. From the Mori–Zwanzig (MZ) perspective, projecting the full dynamics onto a low-dimensional resolved subspace induces additional noise and memory terms arising from the dynamics of the unresolved component in the orthogonal...
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Tomoki Koike (Georgia Institute of Technology)5/18/26, 4:10 PMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
Modeling and simulation of real-world applications often involve dynamical systems with large degrees of freedom, requiring substantial computational time and resources. Projection-based model reduction enables efficient simulation of such dynamical systems by constructing low-dimensional surrogate models from high-dimensional data. Specifically, Operator Inference (OpInf) learns such reduced...
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Dr Mattia Manucci (Karlsruhe Institute of Technology)5/18/26, 4:35 PMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
In this talk, we present an efficient strategy to approximate the solutions of large-scale generalized Lyapunov equations (GLEs) while providing rigorous error guarantees. The motivation for this study stems from the use of GLEs in model order reduction (MOR) of switched linear systems (SLS) in control form. Specifically, we analyze how inaccuracies in the computed GLE solution influence the...
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Till Peters (TU Braunschweig, Institute for Numerical Analysis)5/18/26, 5:00 PMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
Today, mathematical modeling is dominated by increasingly high-dimensional and complex dynamical systems. One special type of structure is the bilinear state equation, which either naturally appears in various applications or results from the Carleman bilinearization of the underlying nonlinear dynamics. Recently, dynamical systems with quadratic outputs have also gained significant attention...
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Petar Mlinarić (University of Zagreb)5/19/26, 11:00 AMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
Vector fitting is a widely used method for least-squares rational approximation that approaches the nonlinear least-squares problem with a sequence of linear least-squares problems. By contrast, the iterative rational Krylov algorithm (IRKA) is a method for a continuous least-squares approximation, originally formulated as a fixed-point iteration and with a recent interpretation as a...
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Reetish Padhi (Virginia Tech)5/19/26, 11:25 AMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
We develop the theoretical framework for extending the quadrature based balanced truncation (QuadBT) method to linear systems with quadratic outputs (LQO). QuadBT which was originally designed for data-driven balanced truncation of standard linear systems with linear outputs only. We show that by sampling the extended impulse responses (kernels) and their derivatives (in the time domain) or...
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Sam Bender5/19/26, 11:50 AMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
We consider single-input, single-output systems with time-varying, periodic parameters:
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ẋ(t) = A(t)x(t) + b(t)u(t),
y(t) = c(t) x(t),
where A(t) ∈ ℝⁿˣⁿ and b(t), c(t) ∈ ℝⁿ all have period T.
Such systems arise when modeling phenomena in fluid dynamics, structural mechanics, and electronic circuits. In particular, linearization around known periodic orbits of a nonlinear model produces a... -
Cade Ballew (University of Washington)5/19/26, 3:45 PMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
The Akhiezer iteration is a new iterative method for solving indefinite linear systems and computing matrix functions. The iteration uses orthogonal polynomial recurrence coefficients to efficiently compute the action of a matrix polynomial to a vector without computing inner products. It features an a priori computable convergence rate and is often faster in practice than standard Krylov...
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Rudi Smith (Virginia Tech)5/19/26, 4:10 PMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
Continuous-time algebraic Lyapunov equations are linear matrix equations of the form
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$$ \begin{equation*} A X E^{\mathsf{H}} + E X A^{\mathsf{H}} = -W \end{equation*} $$ where $A, E \in \mathbb{C}^{n \times n}$ are large-scale sparse coefficient matrices and $W = B R B^{\mathsf{H}}$ represents an indefinite right-hand side defined by the low-rank factor $B \in \mathbb{C}^{n \times... -
Dan E. Folescu (Virginia Tech)5/19/26, 4:35 PMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
Modal truncation has long been a fundamental approach of model order reduction: to systematically eliminate eigenmodes of a dynamical system that contribute little to the modeling behavior over a given time/frequency range. Typically, this procedure requires the ability to access and utilize intrusive state-space information about the underlying full-order system, which can be infeasible for...
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Emmanuel Ameh (Cornell University)5/19/26, 5:00 PMNumerical Linear Algebra Tools for Model Order ReductionMinisymposium Talk
Data-driven reduced-order models (ROMs) could enable near-optimal control for very high-dimensional nonlinear dynamical systems, with applications in active flow control such as relaminarizing turbulent flows and recovering from aerodynamic stall. With initial conditions far away from the desired steady state solving the resulting Hamilton-Jacobi-Bellman (HJB) equation, which defines the value...
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