Related papers: Kernel Learning for Robust Dynamic Mode Decomposit…
Identification of nonlinear dynamical systems has been popularized by sparse identification of the nonlinear dynamics (SINDy) via the sequentially thresholded least squares (STLS) algorithm. Many extensions SINDy have emerged in the…
Dynamical systems are ubiquitous within science and engineering, from turbulent flow across aircraft wings to structural variability of proteins. Although some systems are well understood and simulated, scientific imaging often confronts…
Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…
We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…
Model Interpretation aims at the extraction of insights from the internals of a trained model. A common approach to address this task is the characterization of relevant features internally encoded in the model that are critical for its…
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…
There is a broad need in the neuroscience community to understand and visualize large-scale recordings of neural activity, big data acquired by tens or hundreds of electrodes simultaneously recording dynamic brain activity over minutes to…
A low-dimensional dynamical system is observed in an experiment as a high-dimensional signal; for example, a video of a chaotic pendulums system. Assuming that we know the dynamical model up to some unknown parameters, can we estimate the…
In order to identify one system (module) in an interconnected dynamic network, one typically has to solve a Multi-Input-Single-Output (MISO) identification problem that requires identification of all modules in the MISO setup. For…
Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which…
Modeling and controlling complex spatiotemporal dynamical systems driven by partial differential equations (PDEs) often necessitate dimensionality reduction techniques to construct lower-order models for computational efficiency. This paper…
Metric and kernel learning are important in several machine learning applications. However, most existing metric learning algorithms are limited to learning metrics over low-dimensional data, while existing kernel learning algorithms are…
We demonstrate that the integration of the recently developed dynamic mode decomposition (DMD) with a multi-resolution analysis allows for a decomposition method capable of robustly separating complex systems into a hierarchy of…
Data-driven methodologies are nowadays ubiquitous. Their rapid development and spread have led to applications even beyond the traditional fields of science. As far as dynamical systems and differential equations are concerned, neural…
Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information and…
Diffusion models have emerged as a powerful class of generative models for molecular design, capable of capturing complex structural distributions and achieving high fidelity in 3D molecule generation. However, their widespread use remains…
Remote sensing image segmentation faces persistent challenges in distinguishing morphologically similar categories and adapting to diverse scene variations. While existing methods rely on implicit representation learning paradigms, they…
Sparse linear models are one of several core tools for interpretable machine learning, a field of emerging importance as predictive models permeate decision-making in many domains. Unfortunately, sparse linear models are far less flexible…
Data-driven methods of model identification are able to discern governing dynamics of a system from data. Such methods are well suited to help us learn about systems with unpredictable evolution or systems with ambiguous governing dynamics…
In order to fully utilize "big data", it is often required to use "big models". Such models tend to grow with the complexity and size of the training data, and do not make strong parametric assumptions upfront on the nature of the…