Related papers: Kernel Learning for Robust Dynamic Mode Decomposit…
This work proposes a Stochastic Variational Deep Kernel Learning method for the data-driven discovery of low-dimensional dynamical models from high-dimensional noisy data. The framework is composed of an encoder that compresses…
Surrogate modelling is widely applied in computational science and engineering to mitigate computational efficiency issues for the real-time simulations of complex and large-scale computational models or for many-query scenarios, such as…
Controlling systems with complex, nonlinear dynamics poses a significant challenge, particularly in achieving efficient and robust control. In this paper, we propose a Dyna-Style Reinforcement Learning control framework that integrates…
The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…
A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system…
We present Latent Diffeomorphic Dynamic Mode Decomposition (LDDMD), a new data reduction approach for the analysis of non-linear systems that combines the interpretability of Dynamic Mode Decomposition (DMD) with the predictive power of…
Kernel-based subspace clustering, which addresses the nonlinear structures in data, is an evolving area of research. Despite noteworthy progressions, prevailing methodologies predominantly grapple with limitations relating to (i) the…
Learning models of dynamical systems characterized by specific stability properties is of crucial importance in applications. Existing results mainly focus on linear systems or some limited classes of nonlinear systems and stability…
Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either…
The Dynamic-Mode Decomposition (DMD) is a well established data-driven method of finding temporally evolving linear-mode decompositions of nonlinear time series. Traditionally, this method presumes that all relevant dimensions are sampled…
A significant challenge in many fields of science and engineering is making sense of time-dependent measurement data by recovering governing equations in the form of differential equations. We focus on finding parsimonious ordinary…
Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…
The sparse identification of nonlinear dynamics (SINDy) has been established as an effective method to learn interpretable models of dynamical systems from data. However, for high-dimensional slow-fast dynamical systems, the regression…
We propose a kernel-spectral embedding algorithm for learning low-dimensional nonlinear structures from high-dimensional and noisy observations, where the datasets are assumed to be sampled from an intrinsically low-dimensional manifold and…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…
Hybrid systems are traditionally difficult to identify and analyze using classical dynamical systems theory. Moreover, recently developed model identification methodologies largely focus on identifying a single set of governing equations…
Discovering governing equations of complex dynamical systems directly from data is a central problem in scientific machine learning. In recent years, the sparse identification of nonlinear dynamics (SINDy) framework, powered by heuristic…
Dynamic Mode Decomposition (DMD) is a powerful tool for extracting spatial and temporal patterns from multi-dimensional time series, and it has been used successfully in a wide range of fields, including fluid mechanics, robotics, and…
Machine learning models can represent climate processes that are nonlocal in horizontal space, height, and time, often by combining information across these dimensions in highly nonlinear ways. While this can improve predictive skill, it…
Extracting coherent patterns is one of the standard approaches towards understanding spatio-temporal data. Dynamic mode decomposition (DMD) is a powerful tool for extracting coherent patterns, but the original DMD and most of its variants…