Related papers: Data-Driven Spectral Submanifold Reduction for Non…
We present a general and modular algorithmic framework for path planning of robots. Our framework combines geometric methods for exact and complete analysis of low-dimensional configuration spaces, together with practical, considerably…
Providing efficient and accurate parametrizations for model reduction is a key goal in many areas of science and technology. Here we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal…
Dynamic control of a soft-body robot to deliver complex behaviors with low-dimensional actuation inputs is challenging. In this paper, we present a computational approach to automatically generate versatile, underactuated control policies…
We present a data-driven approach to efficiently approximate nonlinear transient dynamics in solid-state systems. Our proposed machine-learning model combines a dimensionality reduction stage with a nonlinear vector autoregression scheme.…
In this contribution, we discuss the modeling and model reduction framework known as the Loewner framework. This is a data-driven approach, applicable to large-scale systems, which was originally developed for applications to linear…
Recently, many reinforcement learning techniques were shown to have provable guarantees in the simple case of linear dynamics, especially in problems like linear quadratic regulators. However, in practice, many reinforcement learning…
Hyperspectral images (HSI) contain a wealth of information over hundreds of contiguous spectral bands, making it possible to classify materials through subtle spectral discrepancies. However, the classification of this rich spectral…
The deformable and continuum nature of soft robots promises versatility and adaptability. However, control of modular, multi-limbed soft robots for terrestrial locomotion is challenging due to the complex robot structure, actuator mechanics…
A central challenge in neuroscience is understanding how neural system implements computation through its dynamics. We propose a nonlinear time series model aimed at characterizing interpretable dynamics from neural trajectories. Our model…
Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains…
Dimensionality reduction (DR) techniques map high-dimensional data into lower-dimensional spaces. Yet, current DR techniques are not designed to explore semantic structure that is not directly available in the form of variables or class…
The problem of constructing data-based, predictive, reduced models for the Kuramoto-Sivashinsky equation is considered, under circumstances where one has observation data only for a small subset of the dynamical variables. Accurate…
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…
Feature selection of high-dimensional labeled data with limited observations is critical for making powerful predictive modeling accessible, scalable, and interpretable for domain experts. Spectroscopy data, which records the interaction…
Magnetically actuated fish-like robots offer promising solutions for underwater exploration due to their miniaturization and agility; however, precise control remains a significant challenge because of nonlinear fluid dynamics, flexible fin…
In this work, we study distance metric learning (DML) for high dimensional data. A typical approach for DML with high dimensional data is to perform the dimensionality reduction first before learning the distance metric. The main…
We apply two recently formulated mathematical techniques, Slow-Fast Decomposition (SFD) and Spectral Submanifold (SSM) reduction, to a von Karman beam with geometric nonlinearities and viscoelastic damping. SFD identifies a global slow…
Low-dimensional representations of underdamped systems often provide insightful grasps and analytical tractability. Here, we build such representations via information projections, obtaining an optimal model that captures the most…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
Data-driven modeling techniques have been explored in the spatial-temporal modeling of complex dynamical systems for many engineering applications. However, a systematic approach is still lacking to leverage the information from different…