73 citations · 369 across the 22 of their papers we have counts for
24 papers
Learning Dynamical Systems with the Spectral Exterior Calculus
Suddhasattwa Das, Dimitrios Giannakis, Yanbing Gu +1
We present a data-driven framework for learning dynamical systems on compact Riemannian manifolds based on the spectral exterior calculus (SEC). This approach represents vector fie…
Conditional expectation using compactification operators
Suddhasattwa Das
The separate tasks of denoising, least squares expectation, and manifold learning can often be posed in a common setting of finding the conditional expectations arising from a prod…
The categorical basis of dynamical entropy
Suddhasattwa Das
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continu…
Data-driven discovery of quasiperiodically driven dynamics
Suddhasattwa Das, Shakib Mustavee, Shaurya Agarwal
The analysis of a timeseries can provide many new perspectives if it is accompanied by the assumption that the timeseries is generated from an underlying dynamical system. For exam…
Learning theory for dynamical systems
Tyrus Berry, Suddhasattwa Das
The task of modelling and forecasting a dynamical system is one of the oldest problems, and it remains challenging. Broadly, this task has two subtasks - extracting the full dynami…
Uncovering Quasi-periodic Nature of Physical Systems: A Case Study of Signalized Intersections
Suddhasattwa Das, Shakib Mustavee, Shaurya Agarwal
This paper presents a novel approach to analyze quasiperiodically driven dynamical systems. It aims to develop a complete data-driven framework for modeling such unknown dynamics.…
A Linear Dynamical Perspective on Epidemiology: Interplay Between Early COVID-19 Outbreak and Human Mobility
Shakib Mustavee, Shaurya Agarwal, Chinwendu Enyioha +1
This paper investigates the impact of human activity and mobility (HAM) in the spreading dynamics of an epidemic. Specifically, it explores the interconnections between HAM and its…
Computability of topological pressure on compact shift spaces beyond finite type
Michael Burr, Suddhasattwa Das, Christian Wolf +1
We investigate the computability (in the sense of computable analysis) of the topological pressure on compact shift spaces for continuous potentials $ϕ:X\to {\…
An information-geometric approach to feature extraction and moment reconstruction in dynamical systems
Suddhasattwa Das, Dimitrios Giannakis, Enikő Székely
We propose a dimension reduction framework for feature extraction and moment reconstruction in dynamical systems that operates on spaces of probability measures induced by observab…
On harmonic Hilbert spaces on compact abelian groups
Suddhasattwa Das, Dimitrios Giannakis
Harmonic Hilbert spaces on locally compact abelian groups are reproducing kernel Hilbert spaces (RKHSs) of continuous functions constructed by Fourier transform of weighted s…
Lie group valued Koopman eigenfunctions
Suddhasattwa Das
Every continuous-time flow on a topological space has associated to it a Koopman operator, which operates by time-shifts on various spaces of functions, such as , , or fu…
Reproducing kernel Hilbert space compactification of unitary evolution groups
Dimitrios Giannakis, Suddhasattwa Das, Joanna Slawinska
A framework for coherent pattern extraction and prediction of observables of measure-preserving, ergodic dynamical systems with both atomic and continuous spectral components is de…
Koopman spectra in reproducing kernel Hilbert spaces
Suddhasattwa Das, Dimitrios Giannakis
Every invertible, measure-preserving dynamical system induces a Koopman operator, which is a linear, unitary evolution operator acting on the space of observables associated…
Solving the Babylonian Problem of quasiperiodic rotation rates
Suddhasattwa Das, Yoshitaka Saiki, Evelyn Sander +1
A trajectory is quasiperiodic if the trajectory lies on and is dense in some -dimensional torus, and there is a choice of coordinates on the…
Extraction and Prediction of Coherent Patterns in Incompressible Flows through Space-Time Koopman Analysis
Dimitrios Giannakis, Suddhasattwa Das
We develop methods for detecting and predicting the evolution of coherent spatiotemporal patterns in incompressible time-dependent fluid flows driven by ergodic dynamical systems.…
Delay-coordinate maps and the spectra of Koopman operators
Suddhasattwa Das, Dimitrios Giannakis
The Koopman operator induced by a dynamical system is inherently linear and provides an alternate method of studying many properties of the system, including attractor reconstructi…
Almost-sure quasiperiodicity in countably many co-existing circles
Suddhasattwa Das
In many dynamical systems, countably infinitely many invariant tori co-exist. The occurrence of quasiperiodicity on any one of these tori is sometimes sufficient to establish stron…
Quantitative Quasiperiodicity
Suddhasattwa Das, Yoshitaka Saiki, Evelyn Sander +1
The Birkhoff Ergodic Theorem concludes that time averages, i.e., Birkhoff averages, of a function along a length ergodic trajectory of a fu…
Measuring quasiperiodicity
Suddhasattwa Das, Chris B. Dock, Yoshitaka Saiki +4
The Birkhoff Ergodic Theorem asserts under mild conditions that Birkhoff averages (i.e. time averages computed along a trajectory) converge to the space average. For sufficiently s…
Multi-chaos from Quasiperiodicity
Suddhasattwa Das, James A Yorke
One of the common characteristics of chaotic maps or flows in high dimensions is "unstable dimensional variability", in which there are periodic points whose unstable manifolds hav…
Indestructible dynamics of torus maps
Suddhasattwa Das, James Yorke
Given a -dimensional torus map , where is an integer-matrix and and is a periodic function, we find conditions on under which is semi-conjug…
Quantitative Quasiperiodicity
Suddhasattwa Das, Yoshitaka Saiki, Evelyn Sander +1
The Birkhoff Ergodic Theorem concludes that time averages, that is, Birkhoff averages, of a function along an ergodic trajectory of a function …
Avoiding extremes using Partial Control
Suddhasattwa Das, James Yorke
Dynamical systems can be prone to severe fluctuations due to the presence of chaotic dynamics. This paper explains for a toy chaotic economic model how such a system can be regulat…
Super convergence of ergodic averages for quasiperiodic orbits
Suddhasattwa Das, James A. Yorke
By definition, a map quasiperiodic on a set if the map is conjugate to a pure rotation. Suppose we have a trajectory that we suspect is quasiperiodic. How do we determi…