Related papers: Optimized Sampling for Multiscale Dynamics
Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…
Forward uncertainty quantification in dynamical systems is challenging due to non-smooth or locally oscillating nonlinear behaviors. Spline dimensional decomposition (SDD) addresses such nonlinearity by partitioning input coordinates via…
Dynamic spectrum management (DSM) has been recognized as a key technology to significantly improve the performance of digital subscriber line (DSL) broadband access networks. The basic concept of DSM is to coordinate transmission over…
Probabilistic Manifold Decomposition (PMD)\cite{doi:10.1137/25M1738863}, developed in our earlier work, provides a nonlinear model reduction by embedding high-dimensional dynamics onto low-dimensional probabilistic manifolds. The PMD has…
This paper proposes a mode multigrid (MMG) method, and applies it to accelerate the convergence of the steady state flow on unstructured grids. The dynamic mode decomposition (DMD) technique is used to analyze the convergence process of…
Radiation-induced photocurrent in semiconductor devices can be simulated using complex physics-based models, which are accurate, but computationally expensive. This presents a challenge for implementing device characteristics in high-level…
This paper presents a method of data-driven parametric Dynamic Mode Decomposition (p-DMD) to derive a linear parameter-varying reduced-order model (LPV-ROM) for the nonlinear aeroelasticity of highly flexible aircraft. It directly uses the…
The ability to monitor and interpret of hardware system events and behaviors are crucial to improving the robustness and reliability of these systems, especially in a supercomputing facility. The growing complexity and scale of these…
While many time-dependent network design problems can be formulated as time-indexed formulations with strong relaxations, the size of these formulations depends on the discretization of the time horizon and can become prohibitively large.…
The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…
In this study, we investigated the stability of dynamic mode decomposition (DMD) algorithms to noisy data. To achieve a stable DMD algorithm, we applied the truncated total least squares (T-TLS) regression and optimal truncation level…
Diffusion models have gained attention for their ability to represent complex distributions and incorporate uncertainty, making them ideal for robust predictions in the presence of noisy or incomplete data. In this study, we develop and…
With the growing complexity in architecture and the size of large-scale computing systems, monitoring and analyzing system behavior and events has become daunting. Monitoring data amounting to terabytes per day are collected by sensors…
Flexible spacecraft structures present significant challenges for physical and control system design due to nonlinear dynamics, mission constraints, environmental variables, and changing operational conditions. This paper presents a…
Linear Dynamical System (LDS) is an elegant mathematical framework for modeling and learning multivariate time series. However, in general, it is difficult to set the dimension of its hidden state space. A small number of hidden states may…
Distributed optimization has been widely used as one of the most efficient approaches for model training with massive samples. However, large-scale learning problems with both massive samples and high-dimensional features widely exist in…
Dictionary learning is a challenge topic in many image processing areas. The basic goal is to learn a sparse representation from an overcomplete basis set. Due to combining the advantages of generic multiscale representations with learning…
Residual Dynamic Mode Decomposition (ResDMD) offers a method for accurately computing the spectral properties of Koopman operators. It achieves this by calculating an infinite-dimensional residual from snapshot data, thus overcoming issues…
We present a nonlinear dynamical approximation method for time-dependent Partial Differential Equations (PDEs). The approach makes use of parametrized decoder functions, and provides a general, and principled way of understanding and…
We present Stochastic Dynamic Mode Decomposition (SDMD), a novel data-driven framework for approximating the Koopman semigroup in stochastic dynamical systems. Unlike existing methods, SDMD explicitly incorporates sampling time into its…