Related papers: Identification of Dominant Subspaces for Linear St…
In this paper, we investigate the extrapolation capabilities of implicit deep learning models in handling unobserved data, where traditional deep neural networks may falter. Implicit models, distinguished by their adaptability in layer…
In this paper, we propose new algebraic Gramians for continuous-time linear switched systems, which satisfy generalized Lyapunov equations. The main contribution of this work is twofold. First, we show that the ranges of those Gramians…
When approximating a function that depends on a parameter, one encounters many practical examples where linear interpolation or linear approximation with respect to the parameters prove ineffective. This is particularly true for responses…
We provide algorithmically verifiable necessary and sufficient conditions for fundamental system theoretic properties of discrete time linear systems subject to data losses. More precisely, the systems in our modeling framework are subject…
The paper presents a model reduction framework geared towards the analysis and design of systems that switch and oscillate. While such phenomena are ubiquitous in nature and engineering, model reduction methods are not well developed for…
After training complex deep learning models, a common task is to compress the model to reduce compute and storage demands. When compressing, it is desirable to preserve the original model's per-example decisions (e.g., to go beyond top-1…
We introduce a novel model order reduction method for large-scale linear switched systems (LSS) where the coefficient matrices are affected by a low-rank switching. The key idea is to replace the LSS by a non-switched system with extended…
We develop an interpolation-based modeling framework for parameter-dependent partial differential equations arising in control, inverse problems, and uncertainty quantification. The solution is discretized in the physical domain using…
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…
Many real-world systems are modelled using complex ordinary differential equations (ODEs). However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like Proper Orthogonal…
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…
The problem of estimating parameters of switched affine systems with noisy input-output observations is considered. The switched affine models is transformed into a switched linear one by removing its intersection subspace, which is…
We consider an optimization problem related to semi-active damping of vibrating systems. The main problem is to determine the best damping matrix able to minimize influence of the input on the output of the system. We use a minimization…
Machine learning systems, especially with overparameterized deep neural networks, can generalize to novel test instances drawn from the same distribution as the training data. However, they fare poorly when evaluated on out-of-support test…
In this paper we consider different model reduction techniques for systems with moving loads. Due to the time-dependency of the input and output matrices, the application of time-varying projection matrices for the reduction offers new…
In the paper we consider the linear underdetermined system of a special type. Systems of this type appear in non-homogeneous network flow programming problems in the form of systems of constraints and can be characterized as systems with a…
An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…
Network partitioning has gained recent attention as a pathway to enable decentralized operation and control in large-scale systems. This paper addresses the interplay between partitioning, observability, and sensor placement (SP) in dynamic…
We study the problem of transfer learning, observing that previous efforts to understand its information-theoretic limits do not fully exploit the geometric structure of the source and target domains. In contrast, our study first…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…