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Zlatko Drmac (Faculty of Science, University of Zagreb)5/19/26, 2:00 PMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
The Dynamic Mode Decomposition (DMD) is a powerful and versatile numerical method for data driven analysis of nonlinear dynamical systems, with a wide spectrum of applications. It can be used for model order reduction, analysis of latent structures in the dynamics, and e.g. for forecasting and control. The theoretical bedrock upon which the more general Extended DMD (EDMD) framework is built...
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Cankat Tilki (Virginia Tech)5/19/26, 2:25 PMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
We present an in-depth analysis of the Koopman operator using wavelet transform. Based on this analysis, we construct an invariant subspace for the Koopman operator and introduce wavelet-based observables that span this subspace. Moreover, on this subspace, we study the Koopman operator and its eigendecomposition. To approximate its action numerically over this subspace, we combine Extended...
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Amy de Castro (University of Utah)5/19/26, 2:50 PMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
Constructing low-order approximations to a high-dimensional manifold is a well-studied field as these types of problems arise naturally from the solution of parametric partial differential equations in multi-query or optimization contexts. Full-order approximations, although the most accurate approach to reconstructing a solution manifold, incur too high of an expense in these scenarios....
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Geshuo Wang (University of Washington)5/20/26, 10:45 AMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
The numerical solution of kinetic equations is challenging due to the high dimensionality of the underlying phase space. In this paper, we develop a dynamical low-rank method based on the projector-splitting integrator in tensor-train (TT) format. The key idea is to discretize the three-dimensional velocity variable using tensor trains while treating the spatial variable as a parameter,...
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Feliks Nueske (Max-Planck-Institute DCTS Magdeburg)5/20/26, 11:10 AMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
In this talk, I will present recent work on analysing time series data for complex dynamics. Extended dynamic mode decomposition (EDMD, Williams et al, 2015) is a widely used algorithm to learn a linear surrogate model for the statistics of an evolving dynamics, based on the Koopman operator framework. For high-dimensional systems, choosing a suitable basis set can become challenging, as...
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David Bindel (Cornell University)5/20/26, 11:35 AMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
Stellarators are non-axisymmetric magnetic field configurations used to confine plasmas. Within a stellarator, particles roughly follow magnetic field lines, and the magnetic fields in stellarators can be organized into different regions according to the dynamics of field line flows, with regions of nested flux surfaces potentially interspersed with islands or regions of chaos. While can...
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Matthias Voigt (UniDistance Suisse)5/21/26, 11:00 AMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
Kernel methods approximate nonlinear maps in a data-driven way by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel Hilbert space (RKHS), determined solely by the chosen kernel and the dataset, whose elements identify the basis elements. Consequently, the projection operator...
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Alejandro Diaz (Sandia National Laboratories)5/21/26, 11:25 AMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
This talk presents an interpretable, non-intrusive reduced-order modeling technique for parameterized problems using regularized kernel interpolation. Parameterized reduced-order models (ROMs) enable the rapid approximation of PDE solutions corresponding to a given parameter, thus accelerating uncertainty quantification or inverse problem workflows requiring many PDE solves. Existing...
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Peter Benner5/21/26, 11:50 AMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
Learning compact surrogate models from data has become a major application area of machine learning techniques. Such models are required to describe dynamical behavior of processes in the presence of time series data and the absence of explicit mechanistic models. This may be the case if only measurement data is available or simulation data is obtained via proprietary software. Prominent...
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Jorge Reyes (Virginia Tech)5/21/26, 2:00 PMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
This talk focuses on the numerical analysis of regularized projection-based reduced-order models (ROMs) for turbulent fluid flows. Direct numerical simulations are well known to be computationally infeasible for routine simulations in computational fluid dynamics, particularly at high Reynolds numbers. Reduced-order models offer an efficient low-dimensional framework capable of producing fast...
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Robin Herkert (University of Stuttgart)5/21/26, 2:25 PMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
Large-scale Hamiltonian dynamics are governed by
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$$ \dot x = J\nabla H(x),\quad J=\begin{bmatrix}0&I\\-I&0\end{bmatrix}, $$
and arise from spatial discretizations of conservative PDEs as well as in molecular and multibody models. In multi-query, control, and real-time settings, projection-based model order reduction (MOR) is essential, but generic reduced spaces may destroy the... -
Sarswati Shah5/21/26, 2:50 PMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
In this work, we propose a reduced-order modeling (ROM) framework for conservation laws that operates in the Cumulative Distribution Transform (CDT) domain. The CDT maps nonnegative, unit-mass states to an $L^2$ Hilbert space, in which pure translations become affine lines and $W_2$ (optimal transport) distances coincide with Euclidean distances. This linearization dramatically improves the...
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Boris Kramer (University of California San Diego)5/21/26, 3:15 PMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
Hamilton-Jacobi-Bellman partial differential equations (HJB PDEs) arise in various settings in optimal control and model order reduction, and their solutions are notoriously difficult to acquire. For linear time-invariant systems, the HJB PDEs of interest typically simplify to matrix algebraic equations, such as the algebraic Riccati equation or the matrix Lyapunov equation, for which many...
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Paul Van Dooren (Universite catholique de Louvain)5/22/26, 8:45 AMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
We show how to use tangential interpolation techniques to construct structured linearizations for several types of structured rational matrices. The classes studied in this paper are square rational matrices that are either Hermitian, or skew-Hermitian, or complex symmetric, or complex skew-symmetric, upon evaluation on one of the following three curves~: the real axis, the imaginary axis and...
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Ion Victor Gosea (Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany)5/22/26, 9:10 AMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
We extend the Loewner framework to multivariate (static and dynamic) functions with an arbitrary number $n$ of variables [1]. We present the following facts:
(i) That $n$-variable rational functions (and realization), described in the barycentric basis, can be constructed to interpolate and/or approximate/compress any tensorized $n$-D data or $n$-variate function;
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(ii) That these... -
Steffen W. R. Werner (Virginia Tech)5/22/26, 9:35 AMLinear Algebra Foundations for Data-driven Modeling and Model Order ReductionMinisymposium Talk
Learning dynamical systems from data has emerged as a pivotal area of research, bridging the realms of mathematics, engineering, and data science. Of particular importance is the construction of models with meaningful internal structure that allows interpretability and explainability of the results. In the case of mechanical and electro-mechanical processes, dynamical systems are typically...
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