336 citations · 3.5k across the 72 of their papers we have counts for
79 papers
Non-Destructive Detection of Early Drought Stress via Spectral Submanifold Analysis
Sunghwan Jung, Isabella Thiel, Jisoo Yuk +1
Non-destructive early detection of water stress is critical for precision agriculture, yet current detection methods are often labor-intensive or destructive. We propose a rapid, n…
Nonautonomous Spectral Submanifolds for Model Reduction of Nonlinear Mechanical Systems under Parametric Resonance
Thomas Thurnher, George Haller, Shobhit Jain
We use the recent theory of Spectral Submanifolds (SSM) for model reduction of nonlinear mechanical systems subject to parametric excitations. Specifically, we develop expressions…
Variational construction of tubular and toroidal streamsurfaces for flow visualization
Mingwu Li, Bálint Kaszás, George Haller
Approximate streamsurfaces of a 3D velocity field have recently been constructed as isosurfaces of the closest first integral of the velocity field. Such approximate streamsurfaces…
Nonlinear Model Reduction to Fractional and Mixed-Mode Spectral Submanifolds
George Haller, Bálint Kaszás, Aihui Liu +1
A primary spectral submanifold (SSM) is the unique smoothest nonlinear continuation of a nonresonant spectral subspace of a dynamical system linearized at a fixed point. Passin…
Interplay between advective, diffusive, and active barriers in Rayleigh-Bénard flow
Nikolas Aksamit, Robert Hartmann, Detlef Lohse +1
Our understanding of the material organization of complex fluid flows has recently benefited from mathematical developments in the theory of objective coherent structures. These me…
Model reduction for nonlinearizable dynamics via delay-embedded spectral submanifolds
Joar Axås, George Haller
Delay embedding is a commonly employed technique in a wide range of data-driven model reduction methods for dynamical systems, including the Dynamic mode decomposition (DMD), the H…
The Objective Deformation Component of a Velocity Field
Bálint Kaszás, Tiemo Pedergnana, George Haller
For an arbitrary velocity field defined on a finite, fixed spatial domain, we find the closest rigid-body velocity field to in the …
Approximate streamsurfaces for flow visualization
Stergios Katsanoulis, Florian Kogelbauer, Roshan Kaundinya +2
Instantaneous features of three-dimensional velocity fields are most directly visualized via streamsurfaces. It is generally unclear, however, which streamsurfaces one should pick…
Data-Driven Spectral Submanifold Reduction for Nonlinear Optimal Control of High-Dimensional Robots
John Irvin Alora, Mattia Cenedese, Edward Schmerling +2
Modeling and control of high-dimensional, nonlinear robotic systems remains a challenging task. While various model- and learning-based approaches have been proposed to address the…
Using Spectral Submanifolds for Nonlinear Periodic Control
Florian Mahlknecht, John Irvin Alora, Shobhit Jain +4
Very high dimensional nonlinear systems arise in many engineering problems due to semi-discretization of the governing partial differential equations, e.g. through finite element m…
Model reduction for constrained mechanical systems via spectral submanifolds
Mingwu Li, Shobhit Jain, George Haller
Dynamical systems are often subject to algebraic constraints in conjunction to their governing ordinary differential equations. In particular, multibody systems are commonly subjec…
Fast data-driven model reduction for nonlinear dynamical systems
Joar Axås, Mattia Cenedese, George Haller
We present a fast method for nonlinear data-driven model reduction of dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs). We use observed data to locate…
Dynamics-based machine learning of transitions in Couette flow
Bálint Kaszás, Mattia Cenedese, George Haller
We derive low-dimensional, data-driven models for transitions among exact coherent states (ECSs) in one of the most studied canonical shear flows, the plane Couette flow. These one…
Data-Driven Modeling and Prediction of Non-Linearizable Dynamics via Spectral Submanifolds
Mattia Cenedese, Joar Axås, Bastian Bäuerlein +2
We develop a methodology to construct low-dimensional predictive models from data sets representing essentially nonlinear (or non-linearizable) dynamical systems with a hyperbolic…
Quasi-Objective Eddy Visualization from Sparse Drifter Data
Alex P. Encinas Bartos, Nikolas O. Aksamit, George Haller
We employ a recently developed single-trajectory Lagrangian diagnostic tool, the trajectory rotation average , to visualize oceanic vortices (or eddies…
Data-driven Nonlinear Model Reduction to Spectral Submanifolds in Mechanical Systems
Mattia Cenedese, Joar Axås, Haocheng Yang +2
While data-driven model reduction techniques are well-established for linearizable mechanical systems, general approaches to reducing non-linearizable systems with multiple coexist…
Nonlinear analysis of forced mechanical systems with internal resonance using spectral submanifolds, Part II: Bifurcation and quasi-periodic response
Mingwu Li, George Haller
In Part I of this paper, we have used spectral submanifold (SSM) theory to construct reduced-order models for harmonically excited mechanical systems with internal resonances. In t…
Objective Momentum Barriers in Wall Turbulence
Nikolas O. Aksamit, George Haller
We use the recent frame-indifferent theory of diffusive momentum transport to identify internal barriers in wall-bounded turbulence. Formed by the invariant manifolds of the Laplac…
Nonlinear analysis of forced mechanical systems with internal resonance using spectral submanifolds, Part I: Periodic response and forced response curve
Mingwu Li, Shobhit Jain, George Haller
We show how spectral submanifold theory can be used to construct reduced-order models for harmonically excited mechanical systems with internal resonances. Efficient calculations o…
How to Compute Invariant Manifolds and their Reduced Dynamics in High-Dimensional Finite-Element Models
Shobhit Jain, George Haller
Invariant manifolds are important constructs for the quantitative and qualitative understanding of nonlinear phenomena in dynamical systems. In nonlinear damped mechanical systems,…
Integral Equations & Model Reduction For Fast Computation of Nonlinear Periodic Response
Gergely Buza, George Haller, Shobhit Jain
We propose a reformulation for the integral equations approach of Jain, Breunung \& Haller [Nonlinear Dyn. 97, 313--341 (2019)] to steady-state response computation for periodicall…
Using Spectral Submanifolds for Optimal Mode Selection in Model Reduction
Gergely Buza, Shobhit Jain, George Haller
Model reduction of large nonlinear systems often involves the projection of the governing equations onto linear subspaces spanned by carefully-selected modes. The criteria to selec…
Universal Upper Estimate for Prediction Errors under Moderate Model Uncertainty
Bálint Kaszás, George Haller
We derive universal upper estimates for model-prediction error under moderate but otherwise unknown model uncertainty. Our estimates give upper bounds on the leading order trajecto…
Stability of Forced-Damped Response in Mechanical Systems from a Melnikov Analysis
Mattia Cenedese, George Haller
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent…