Non-smooth dynamical systems, such as an oscillating beam rubbing against a wall, also have low-dimensional attracting spectral submanifolds (SSMs). But those SSMs, and the reduced models they carry, are only piecewise smooth. Movie: Leonardo Bettini Paper: doi.org/10.1016/j.ijno…

Bacterial Barriers (Part 1): New manuscript with Ranjiangshang Ran in Journal of Fluid Mechanics shows how interactions between swimming bacteria and flow elliptic Lagrangian coherent structures George Haller form Lagrangian vortex boundaries (i.e., mixing barriers). See it at bit.ly/3RaXOWI

Model Reduction and Machine Learning for Solids, Fluids and Controls (Udine, Italy, Sept. 9-13). Summer school by Bala Balachandran, Charbel Farhat, Michael Graham, George Haller, Shobhit Jain and Gianluigi Rozza. Register here: lnkd.in/eTDmhZc6

Data-driven linearization (DDL) explains dynamic mode decomposition (DMD) as a first-order, approximate linearization of the dynamics on a dominant spectral submanifold. DDL then refines this linearization to higher orders with increased accuracy. link.springer.com/article/10.100…

A Ph.D. position is available at ETH Zurich in Data-Driven Nonlinear Model Reduction (a.k.a. Dynamics-Based Machine Learning) and its applications to large-scale physical problems. Interested candidates may apply here: jobs.ethz.ch/job/view/JOPG_…

Puzzling period-3 response in forced fluid sloshing turns out to arise from a nonlinear resonance. Predicted by a data-driven, 4D SSM-reduced model, extracted directly from a video of the experiment. nature.com/articles/s4159…

We can now extract simple and predictive reduced-order models for nonlinear dynamical systems directly from videos! doi.org/10.1007/s11071…

Data-Driven Model Reduction for Dynamical Systems Montestigliano Spring School for Graduate Students 13th - 19th April 2025, Montestigliano, Italy Register till February 3, 2025 ercoftac.org/events/ercofta…

A 2D SSM-reduced model accurately predicts the motion of the full, nonlinear, finite-element model of a plate in a random pressure field. General theory of random SSMs (random spectral submanifolds) with examples here: doi.org/10.1016/j.jsv.…

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I'm humbled and honored. Thank you!

Data-driven, nonlinear, SSM-based model-predictive control of soft robots outperforms other model reduction approaches by a large margin, as shown in rdcu.be/ecgH4. Collaborators at @stanford and ETH Zurich: John Alora, Mattia Cenedese, and Marco Pavone

Data-driven nonlinear modelling on spectral submanifolds (SSMs) can uncover problems in the experimental data collection, rather than just fit to the available data. Here, a mismatch between the SSM-predicted forced response and results from the actual experiment revealed a

Just published by SIAM: An introduction to the theory and applications of spectral submanifolds, with a large collection of equation- and data-driven examples in model reduction, system identification, and control. epubs.siam.org/doi/10.1137/1.…

A smooth, data-driven reduced model using Spectral Submanifolds (SSMs) outperform all other competing approaches on a non-smooth tribomechadynamics benchmark challenge problem: link.springer.com/article/10.100…

We now have another open Ph.D. position at ETH Zurich in data-driven nonlinear reduced-order modelling, with applications in system ID and control. Interested candidates may apply here: jobs.ethz.ch/job/view/JOPG_…

Manifold-based reduced models of nonlinear systems can be significantly extended using Padé approximation. This yields more accuracy with fewer unknowns on larger domains, even from experimental data: nature.com/articles/s4146…