27 citations · 285 across the 42 of their papers we have counts for
5 papers · 1 filter
Complex localization mechanisms in networks of coupled oscillators: two case studies
Zachary G. Nicolaou, Jason J. Bramburger
Localized phenomena abound in nature and throughout the physical sciences. Some universal mechanisms for localization have been characterized, such as in the snaking bifurcations o…
Data-driven Discovery of Invariant Measures
Jason J. Bramburger, Giovanni Fantuzzi
Invariant measures encode the long-time behaviour of a dynamical system. In this work, we propose an optimization-based method to discover invariant measures directly from data gat…
Synthesizing Control Laws from Data using Sum-of-Squares Optimization
Jason J. Bramburger, Steven Dahdah, James Richard Forbes
The control Lyapunov function (CLF) approach to nonlinear control design is well established. Moreover, when the plant is control affine and polynomial, sum-of-squares (SOS) optimi…
Transferability of Graph Neural Networks using Graphon and Sampling Theories
A. Martina Neuman, Jason J. Bramburger
Graph neural networks (GNNs) have become powerful tools for processing graph-based information in various domains. A desirable property of GNNs is transferability, where a trained…
Auxiliary Functions as Koopman Observables: Data-Driven Analysis of Dynamical Systems via Polynomial Optimization
Jason J. Bramburger, Giovanni Fantuzzi
We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in well-established techniques for appro…