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{Seminar} @ CDS: 06th January : “Learning physics-based data-driven reduced-order models and obtaining nonlinear systems’ stability limits.”

06 Jan @ 11:00 AM -- 12:00 PM

Department of Computational and Data Sciences

Department Seminar


SPEAKER     :  Aniketh Kalur, Postdoctoral fellow at the Oden Institute

TITLE            : Learning physics-based data-driven reduced-order models and obtaining nonlinear systems’ stability limits.

Date & Time :  January 06, 2023, 11:00 AM.

Venue              : #102, CDS Seminar Hall.





Obtaining data-driven nonlinear reduced-order models (ROMs) relies on projecting the high-dimensional system onto a linear subspace—also called a linear dimensionality reduction technique. However, intrinsically nonlinear systems seldom evolve on linear subspaces, so the ROMs obtained from linear dimensionality reduction techniques do not effectively generalize outside the training dataset. In the first part of this talk, I will present a data-driven nonlinear dimensionality reduction framework such that the resulting ROMs trajectories evolve on a quadratic (nonlinear) subspace. The proposed framework is non-intrusive, requiring only the system’s trajectory data, and does not need access or modification to the high-fidelity code. Additionally, the ROMs are obtained by solving a least-squares regression problem while retaining the linear-quadratic structure of the original high-dimensional system. The proposed quadratic manifold-based ROMs will enable a richer reconstruction of the system trajectories and enable accurate future-state predictions.

After obtaining nonlinear ROMs, especially for fluid flows, it is critical to identify the stability limit, i.e., determine when the transition to turbulence will occur in the resulting nonlinear model. In the second part of the talk, I will introduce a quadratic constraints framework for obtaining stability limits and bounds for nonlinear systems with theoretical guarantees. The proposed framework accounts for nonlinear interactions by encoding physics-based properties of the system as quadratic constraints—without explicitly modeling the nonlinear term. The problem of obtaining stability bounds for nonlinear systems boils down to solving Lyapunov matrix inequalities with quadratic constraints while ensuring the stability bounds are rigorous and have theoretical guarantees. Finally, I will demonstrate the framework’s effectiveness in obtaining stability bounds for fluid flows like the Channel flow and the Couette flow.



Aniketh Kalur is a postdoctoral fellow at the Oden Institute for Computational Engineering and Sciences at the University of Texas at Austin in Prof. Karen Willcox’s research group. His research interests lie at the intersection of control theory, computational sciences, data-driven methods, and scientific machine learning. Dr. Kalur obtained his Ph.D. from the University of Minnesota, Twin Cities, where he developed techniques for getting stability bounds for nonlinear systems like fluid flows using tools from robust control theory. He obtained a master’s degree in aerospace engineering at the University at Buffalo, where he worked on developing adaptive control laws for spacecrafts in formation flying. He also developed algorithms to classify space debris in orbit effectively.


Host Faculty: Prof. Sashikumaar Ganesan

                                                                             ALL ARE WELCOME


06 Jan
11:00 AM -- 12:00 PM
Event Category:


Room No: 102 (Seminar Hall of CDS)