6 papers
A joint optimization approach to identifying sparse dynamics using least squares kernel collocation
Alexander W. Hsu, Ike Griss Salas, Jacob M. Stevens-Haas +3
We develop an all-at-once modeling framework for learning systems of ordinary differential equations (ODE) from scarce, partial, and noisy observations of the states. The proposed…
A Proximal Method for Composite Optimization with Smooth and Convex Components
Samet Uzun, Dayou Luo, Behçet AçıkmeÅe +1
We introduce prox-convex for minimizing , where and are convex, and are smooth, and each component of is convex (possibly nonsmooth).…
On-line learning of dynamic systems: sparse regression meets Kalman filtering
Gianluigi Pillonetto, Akram Yazdani, Aleksandr Aravkin
Learning governing equations from data is central to understanding the behavior of physical systems across diverse scientific disciplines, including physics, biology, and engineeri…
Sparse and nonparametric estimation of equations governing dynamical systems with applications to biology
G. Pillonetto, A. Giaretta, A. Aravkin +2
Data-driven discovery of model equations is a powerful approach for understanding the behavior of dynamical systems in many scientific fields. In particular, the ability to learn m…
Optimization Outperforms Unscented Techniques for Nonlinear Smoothing
Payton Howell, Aleksandr Aravkin
We review optimization-based approaches to smoothing nonlinear dynamical systems. These approaches leverage the fact that the Extended Kalman Filter and corresponding smoother can…
Sparse-mode Dynamic Mode Decomposition for Disambiguating Local and Global Structures
Sara M. Ichinaga, Steven L. Brunton, Aleksandr Y. Aravkin +1
The dynamic mode decomposition (DMD) is a data-driven approach that extracts the dominant features from spatiotemporal data. In this work, we introduce sparse-mode DMD, a new varia…