相关论文: Non-intrusive Data-driven ADI-based Low-rank Balan…

Balanced truncation (BT) is a model reduction method that utilizes a coordinate transformation to retain eigen-directions that are highly observable and reachable. To address realizability and scalability of BT applied to highly stiff and…

On the basis of input-output time-domain data collected from a complex simulator, this paper proposes a constructive methodology to infer a reduced-order linear, bilinear or quadratic time invariant dynamical model reproducing the…

As a special type of bilinear systems, K-power bilinear systems possess a special coupled structure along with nice properties in practice. In this paper, we investigate the data-driven counterpart of balanced truncation for K-power…

The alternating direction implicit (ADI) methods are computationally efficient and numerically effective tools for computing low-rank solutions of large-scale linear matrix equations. It is known in the literature that the low-rank ADI…

Structured reduced-order modeling is a central component in the computer-aided design of control systems in which cheap-to-evaluate low-dimensional models with physically meaningful internal structures are computed. In this work, we develop…

Parametric model order reduction by matrix interpolation allows for efficient prediction of the behavior of dynamic systems without requiring knowledge about the underlying parametric dependency. Within this approach, reduced models are…

Balanced truncation is a well-established model order reduction method which has been applied to a variety of problems. Recently, a connection between linear Gaussian Bayesian inference problems and the system-theoretic concept of balanced…

In this work, we develop implicit rank-adaptive schemes for time-dependent matrix differential equations. The dynamic low rank approximation (DLRA) is a well-known technique to capture the dynamic low rank structure based on Dirac-Frenkel…

This paper presents a weakly intrusive strategy for computing a low-rank approximation of the solution of a system of nonlinear parameter-dependent equations. The proposed strategy relies on a Newton-like iterative solver which only…

In this article, we show that the projection-free, snapshot-based, balanced truncation method can be applied directly to unstable systems. We prove that even for unstable systems, the unmodified balanced proper orthogonal decomposition…

Subspace learning and matrix factorization problems have great many applications in science and engineering, and efficient algorithms are critical as dataset sizes continue to grow. Many relevant problem formulations are non-convex, and in…

Continuous-time algebraic Lyapunov equations have become an essential tool in various applications. In the case of large-scale sparse coefficient matrices and indefinite constant terms, indefinite low-rank factorizations have successfully…

We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system…

An interpolation method for discretising continuous-time Linear Time Invariant (LTI) models is proposed in this paper. It consists first in using the Loewner interpolation framework on a specific set of frequency data and secondly to…

Low-rank structure is a common implicit assumption in many modern reinforcement learning (RL) algorithms. For instance, reward-free and goal-conditioned RL methods often presume that the successor measure admits a low-rank representation.…

We present GRAPHIC, a new angular differential imaging (ADI) reduction pipeline where all geometric image operations are based on Fourier transforms. To achieve this goal the entire pipeline is parallelised making it possible to reduce…

Learning the dynamics of a process given sampled observations at several time points is an important but difficult task in many scientific applications. When no ground-truth trajectories are available, but one has only snapshots of data…

AI algorithms at the edge demand smaller model sizes and lower computational complexity. To achieve these objectives, we adopt a green learning (GL) paradigm rather than the deep learning paradigm. GL has three modules: 1) unsupervised…

Large-scale linear, time-invariant (LTI) dynamical systems are widely used to characterize complicated physical phenomena. We propose a two-stage algorithm to reduce the order of a large-scale LTI system given samples of its transfer…

The non-Hermitian models, which are symmetric under parity (P) and time-reversal (T) operators, are the cornerstone for the fabrication of new ultra-sensitive optoelectronic devices. However, providing the gain in such systems usually…