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Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly…

Suppressing vibrations in mechanical systems, usually described by second-order dynamical models, is a challenging task in mechanical engineering in terms of computational resources even nowadays. One remedy is structure-preserving model…

We present a framework for constructing a structured realization of a linear time-invariant dynamical system solely from a discrete sampling of an input and output trajectory of the system. We estimate the transfer function of the original…

Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…

Transfer learning has emerged as a highly sought-after and actively pursued research area within the statistical community. The core concept of transfer learning involves leveraging insights and information from auxiliary datasets to…

World models have been recently proposed as sandbox environments in which AI agents can be trained and evaluated before deployment. While realistic world models often have high computational demands, this can often be alleviated by…

We first consider the problem of approximating a few eigenvalues of a rational matrix-valued function closest to a prescribed target. It is assumed that the proper rational part of the rational matrix-valued function is expressed in the…

We discuss structure-preserving model order reduction for port-Hamiltonian systems based on an approximation of the full-order state by a linear combination of ansatz functions which depend themselves on the state of the reduced-order…

To better understand the overlapping modular organization of large networks with respect to flow, here we introduce the map equation for overlapping modules. In this information-theoretic framework, we use the correspondence between…

In this paper, we consider the structure-preserving model order reduction problem for multi-input/multi-output bilinear control systems by tangential interpolation. We propose a new type of tangential interpolation problem for structured…

Due to the substantial scale of Large Language Models (LLMs), the direct application of conventional compression methodologies proves impractical. The computational demands associated with even minimal gradient updates present challenges,…

Using nonlinear projections and preserving structure in model order reduction (MOR) are currently active research fields. In this paper, we provide a novel differential geometric framework for model reduction on smooth manifolds, which…

While many approaches exist in the literature to learn low-dimensional representations for data collections in multiple modalities, the generalizability of multi-modal nonlinear embeddings to previously unseen data is a rather overlooked…

In this paper, designs and analyses of compressive recognition systems are discussed, and also a method of establishing a dual connection between designs of good communication codes and designs of recognition systems is presented. Pattern…

Recent research has shown growing interest in modeling hypergraphs, which capture polyadic interactions among entities beyond traditional dyadic relations. However, most existing methodologies for hypergraphs face significant limitations,…

We propose new linear combinations of compositions of a basic second-order scheme with appropriately chosen coefficients to construct higher order numerical integrators for differential equations. They can be considered as a generalization…

Many countries are currently challenged with the extensive integration of renewable energy sources, which necessitates vast capacity expansion measures. These measures in turn require comprehensive power flow studies, which are often…

We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…

Existing ML models are known to be highly over-parametrized, and use significantly more resources than required for a given task. Prior work has explored compressing models offline, such as by distilling knowledge from larger models into…

The reduced-order modeling of a system from data (also known as system identification) is a classical task in system and control theory and well understood for standard linear systems with the so-called Loewner framework as one of many…