Related papers: Theoretical Foundations for the Dynamic Mode Decom…
Linear Parameter Varying (LPV) Systems are a well-established class of nonlinear systems with a rich theory for stability analysis, control, and analytical response finding, among other aspects. Although there are works on data-driven…
The identification of anomalies is a critical component of operating complex, and possibly large-scale and geo-graphically distributed cyber-physical systems. While designing anomaly detectors, it is common to assume Gaussian noise models…
In many scenarios, a state-space model depends on a parameter which needs to be inferred from data. Using stochastic gradient search and the optimal filter (first-order) derivative, the parameter can be estimated online. To analyze the…
Dynamic mode decomposition (DMD) gives a practical means of extracting dynamic information from data, in the form of spatial modes and their associated frequencies and growth/decay rates. DMD can be considered as a numerical approximation…
Current semantic segmentation models only exploit first-order statistics, while rarely exploring high-order statistics. However, common first-order statistics are insufficient to support a solid unanimous representation. In this paper, we…
With the advancement of sensing and communication in power networks, high-frequency real-time data from a power network can be used as a resource to develop better monitoring capabilities. In this work, a systematic approach based on…
Offline estimation of the dynamical model of a Markov Decision Process (MDP) is a non-trivial task that greatly depends on the data available in the learning phase. Sometimes the dynamics of the model is invariant with respect to some…
A method is presented to calculate from first principles the higher-order elastic constants of a solid material. The method relies on finite strain deformations, a density functional theory approach to calculate the Cauchy stress tensor,…
A first-principles approach to describe electron dynamics in open quantum systems driven far from equilibrium via external time-dependent stimuli is introduced. Within this approach, the driven Liouville von Neumann methodology is used to…
Identifying patterns of relations among the units of a complex system from measurements of their activities in time is a fundamental problem with many practical applications. Here, we introduce a method that detects dependencies of any…
The modeling of dynamical systems is a pervasive concern for not only describing but also predicting and controlling natural phenomena and engineered systems. Current data-driven approaches often assume prior knowledge of the relevant state…
We consider a generalization of the projecting operators method for the case of Cauchy problem for systems of 1D evolution differential equations of first order with variable coefficients. It is supposed that the coefficients dependence on…
A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new…
This note presents a unified analysis of the identification of dynamical systems with low-rank constraints under high-dimensional scaling. This identification problem for dynamic systems are challenging due to the intrinsic dependency of…
In this paper, we propose a high-order extension of the multiscale method introduced by the authors in [SIAM J. Numer. Anal., 63(4) (2025), pp. 1617--1641] for heterogeneous Stokes problems, while also providing several other improvements,…
Dynamic Mode Decomposition (DMD) describes complex dynamic processes through a hierarchy of simpler coherent features. DMD is regularly used to understand the fundamental characteristics of turbulence and is closely related to Koopman…
Predictive statistical mechanics is a form of inference from available data, without additional assumptions, for predicting reproducible phenomena. By applying it to systems with Hamiltonian dynamics, a problem of predicting the macroscopic…
We formulate a new family of high order on-surface radiation conditions to approximate the outgoing solution to the Helmholtz equation in exterior domains. Motivated by the pseudo-differential expansion of the Dirichlet-to-Neumann operator…
An attempt is given to formulate the extensions of the KP hierarchy by introducing fractional order pseudo-differential operators. In the case of the extension with the half-order pseudo-differential operators, a system analogous to the…
The higher-order gas-kinetic scheme for solving the Navier-Stokes equations has been studied in recent years. In addition to the use of higher-order reconstruction techniques, many terms are used in the Taylor expansion of the gas…