Zobrazeno 1 - 10
of 45
pro vyhledávání: '"Otto, Samuel E."'
Publikováno v:
Journal of Computational Physics, Volume 516, 2024, 113371.
The ability to measure differences in collected data is of fundamental importance for quantitative science and machine learning, motivating the establishment of metrics grounded in physical principles. In this study, we focus on the development of su
Externí odkaz:
http://arxiv.org/abs/2404.14347
There is a mystery at the heart of operator learning: how can one recover a non-self-adjoint operator from data without probing the adjoint? Current practical approaches suggest that one can accurately recover an operator while only using data genera
Externí odkaz:
http://arxiv.org/abs/2401.17739
Symmetry is present throughout nature and continues to play an increasingly central role in physics and machine learning. Fundamental symmetries, such as Poincar\'{e} invariance, allow physical laws discovered in laboratories on Earth to be extrapola
Externí odkaz:
http://arxiv.org/abs/2311.00212
Recently developed reduced-order modeling techniques aim to approximate nonlinear dynamical systems on low-dimensional manifolds learned from data. This is an effective approach for modeling dynamics in a post-transient regime where the effects of in
Externí odkaz:
http://arxiv.org/abs/2307.15288
Data-driven models for nonlinear dynamical systems based on approximating the underlying Koopman operator or generator have proven to be successful tools for forecasting, feature learning, state estimation, and control. It has become well known that
Externí odkaz:
http://arxiv.org/abs/2209.09977
Data-driven reduced-order models often fail to make accurate forecasts of high-dimensional nonlinear dynamical systems that are sensitive along coordinates with low-variance because such coordinates are often truncated, e.g., by proper orthogonal dec
Externí odkaz:
http://arxiv.org/abs/2207.14387
Reduced-order modeling techniques, including balanced truncation and $\mathcal{H}_2$-optimal model reduction, exploit the structure of linear dynamical systems to produce models that accurately capture the dynamics. For nonlinear systems operating fa
Externí odkaz:
http://arxiv.org/abs/2106.01211
Autor:
Otto, Samuel E., Rowley, Clarence W.
Sensor placement and feature selection are critical steps in engineering, modeling, and data science that share a common mathematical theme: the selected measurements should enable solution of an inverse problem. Most real-world systems of interest a
Externí odkaz:
http://arxiv.org/abs/2101.11162
In recent years, the success of the Koopman operator in dynamical systems analysis has also fueled the development of Koopman operator-based control frameworks. In order to preserve the relatively low data requirements for an approximation via Dynami
Externí odkaz:
http://arxiv.org/abs/2003.07094
We propose a framework that elucidates the input-output characteristics of flows with complex dynamics arising from nonlinear interactions between different time scales. More specifically, we consider a periodically time-varying base flow, and perfor
Externí odkaz:
http://arxiv.org/abs/1911.10179