27 citations · 285 across the 42 of their papers we have counts for
44 papers
Finite-Data Error Bounds for Approximating the Koopman Operator: Sampling Measures, Super-Polynomial Convergence and Regularization
Daniel Fassler, Rachel Morris, Jason Bramburger +1
The Koopman operator is a well-established framework for lifting nonlinear dynamical systems to an infinite-dimensional space where dynamics are linear. Extended Dynamic Mode Decom…
The Spectral Skeleton of Chaos: Koopman Wave Packets on Poincaré Sections
Jason J. Bramburger, Shiloh-Sheray Gagnon, Rachel Morris +1
A Poincaré section replaces a flow by a return map, but for a chaotic system this map is usually known only from sampled crossings. We show that coarse transport can be read direct…
Stability of localized solutions to lattice dynamical systems
Bocheng Ruan, Jack M. Hughes, Jason J. Bramburger
Localized patterns are spatially confined structures that arise in lattice dynamical systems and play an important role in physics, biology, and materials science. While their exis…
Weighted Birkhoff Averages Accelerate Data-Driven Methods
Maria Bou-Sakr-El-Tayar, Jason J. Bramburger, Matthew J. Colbrook
Many data-driven algorithms in dynamical systems rely on ergodic averages that converge painfully slowly. One simple idea changes this: taper the ends. Weighted Birkhoff averages c…
Data-Driven Stabilisation of Unstable Periodic Orbits of the Three-Body Problem
Owen M. Brook, Jason J. Bramburger, Davide Amato +1
Many different models of the physical world exhibit chaotic dynamics, from fluid flows and chemical reactions to celestial mechanics. The study of the three-body problem (3BP) and…
On the lattice property of the Koopman operator spectrum
Jason J. Bramburger
The Koopman operator has become a celebrated tool in modern dynamical systems theory for analyzing and interpreting both models and datasets. The linearity of the Koopman operator…
Learning graphons from data: Random walks, transfer operators, and spectral clustering
Stefan Klus, Jason J. Bramburger
Many signals evolve in time as a stochastic process, randomly switching between states over discretely sampled time points. Here we make an explicit link between the underlying sto…
Bounding Escape Rates and Approximating Quasi-Stationary Distributions of Brownian Dynamics
Jason J. Bramburger
Throughout physics Brownian dynamics are used to describe the behaviour of molecular systems. When the Brownian particle is confined to a bounded domain, a particularly important q…
Capturing the critical coupling of large random Kuramoto networks with graphons
Jason Bramburger, Matt Holzer
Collective oscillations and patterns of synchrony have long fascinated researchers in the applied sciences, particularly due to their far-reaching importance in chemistry, physics,…
Reconstruction of frequency-localized functions from pointwise samples via least squares and deep learning
A. Martina Neuman, Andres Felipe Lerma Pineda, Jason J. Bramburger +1
Recovering frequency-localized functions from pointwise data is a fundamental task in signal processing. We examine this problem from an approximation-theoretic perspective, focusi…
Localized synchronous patterns in weakly coupled bistable oscillators
Erik Bergland, Jason J Bramburger, Bjorn Sandstede
Motivated by numerical continuation studies of coupled mechanical oscillators, we investigate branches of localized time-periodic solutions of one-dimensional chains of coupled osc…
Real-Time Motion Detection Using Dynamic Mode Decomposition
Marco Mignacca, Simone Brugiapaglia, Jason J. Bramburger
Dynamic Mode Decomposition (DMD) is a numerical method that seeks to fit timeseries data to a linear dynamical system. In doing so, DMD decomposes dynamic data into spatially coher…
Localized Patterns
Jason J. Bramburger, Dan J. Hill, David J. B. Lloyd
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-under…
Persistence of steady-states for dynamical systems on large networks
Jason J. Bramburger, Matt Holzer, Jackson Williams
The goal of this work is to identify steady-state solutions to dynamical systems defined on large, random families of networks. We do so by passing to a continuum limit where the a…
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…
Universal Dynamics of Damped-Driven Systems: The Logistic Map as a Normal Form for Energy Balance
J. Nathan Kutz, Aminur Rahman, Megan R. Ebers +2
Damped-driven systems are ubiquitous in engineering and science. Despite the diversity of physical processes observed in a broad range of applications, the underlying instabilities…
Dihedral rings of patterns emerging from a Turing bifurcation
Dan J. Hill, Jason J. Bramburger, David J. B. Lloyd
Collective organisation of patterns into ring-like configurations has been well-studied when patterns are subject to either weak or semi-strong interactions. However, little is kno…
Saddle Transport and Chaos in the Double Pendulum
Kadierdan Kaheman, Jason J. Bramburger, J. Nathan Kutz +1
Pendulums are simple mechanical systems that have been studied for centuries and exhibit many aspects of modern dynamical systems theory. In particular, the double pendulum is a pr…
The Experimental Multi-Arm Pendulum on a Cart: A Benchmark System for Chaos, Learning, and Control
Kadierdan Kaheman, Urban Fasel, Jason J. Bramburger +3
The single, double, and triple pendulum has served as an illustrative experimental benchmark system for scientists to study dynamical behavior for more than four centuries. The pen…
Localized patterns in planar bistable weakly coupled lattice systems
Jason J. Bramburger, Bjorn Sandstede
Localized planar patterns in spatially extended bistable systems are known to exist along intricate bifurcation diagrams, which are commonly referred to as snaking curves. Their an…