Seminars
Spring, 2023
Controlling Populations of Neural Oscillators
Jeff Moehlis
Professor and Chair, Department of Mechanical Engineering
University of California at Santa Barbara
Santa Barbara, CA
Many challenging problems that consider the analysis and control of neural brain rhythms have been motivated by the advent of deep brain stimulation as a therapeutic treatment for a wide variety of neurological disorders. In a computational setting, neural rhythms are often modeled using large populations of coupled, conductance-based neurons. Control of such models comes with a long list of challenges: the underlying dynamics are nonnegligibly nonlinear, high dimensional, and subject to noise; hardware and biological limitations place restrictive constraints on allowable inputs; direct measurement of system observables is generally limited; and the resulting systems are typically highly underactuated. In this talk, I highlight a collection of recent analysis techniques and control frameworks that have been developed to contend with these difficulties. Particular emphasis is placed on the problem of desynchronization for a population of pathologically synchronized neural oscillators, a problem that is motivated by applications to Parkinson's disease where pathological synchronization is thought to contribute to the associated motor control symptoms.
Jeff Moehlis received a Ph.D. in Physics from UC Berkeley in 2000, and was a Postdoctoral Researcher in the Program in Applied and Computational Mathematics at Princeton University from 2000-2003. He joined the Department of Mechanical Engineering at UC Santa Barbara in 2003, and is currently Chair of this department. He was also recently the Chair of the Program in Dynamical Neuroscience at UC Santa Barbara. He has been a recipient of a Sloan Research Fellowship in Mathematics and a National Science Foundation CAREER Award, and was Program Director of the SIAM Activity Group in Dynamical Systems from 2008-2009. Jeff's current research includes applications of dynamical systems and control techniques to neuroscience, cardiac dynamics, and collective behavior. He has published over 100 journal / conference proceedings articles on these and other topics including shear flow turbulence, microelectromechanical systems, energy harvesting, and dynamical systems with symmetry.
Wednesday, January 18, 2023
3:30 PM
Stauffer Science Lecture Hall, Room 102 (SLH 102)
The Zoom webinar is at https://usc.zoom.us/j/95805178776?pwd=aEtTRnQ2MmJ6UWE4dk9UMG9GdENLQT09.
host: Nguyen
Machine Learning for Scientific Discovery, with Examples in Fluid Mechanics
Steven L. Brunton
Professor of Mechanical Engineering
Department of Mechanical Engineering
University of Washington
Seattle, WA
Accurate and efficient nonlinear dynamical systems models are essential to understand, predict, estimate, and control complex natural and engineered systems. In this talk, I will explore how machine learning may be used to develop these models purely from measurement data. We explore the sparse identification of nonlinear dynamics (SINDy) algorithm, which identifies a minimal dynamical system model that balances model complexity with accuracy, avoiding overfitting. This approach tends to promote models that are interpretable and generalizable, capturing the essential “physics” of the system. We also discuss the importance of learning effective coordinate systems in which the dynamics may be expected to be sparse. This sparse modeling approach will be demonstrated on a range of challenging modeling problems, for example in fluid dynamics. Because fluid dynamics is central to transportation, health, and defense systems, we will emphasize the importance of machine learning solutions that are interpretable, explainable, generalizable, and that respect known physics.
Steven L. Brunton is a Professor of Mechanical Engineering at the University of Washington. He is also Adjunct Professor of Applied Mathematics and Computer science, and a Data Science Fellow at the eScience Institute. Steve received the B.S. in mathematics from Caltech in 2006 and the Ph.D. in mechanical and aerospace engineering from Princeton in 2012. His research combines machine learning with dynamical systems to model and control systems in fluid dynamics, biolocomotion, optics, energy systems, and manufacturing. He received the Army and Air Force Young Investigator Program (YIP) awards and the Presidential Early Career Award for Scientists and Engineers (PECASE). Steve is also passionate about teaching math to engineers as co-author of three textbooks and through his popular YouTube channel, under the moniker “eigensteve”.
Wednesday, January 25, 2023
3:30 PM
Stauffer Science Lecture Hall, Room 102 (SLH 102)
The Zoom webinar is at https://usc.zoom.us/j/95805178776?pwd=aEtTRnQ2MmJ6UWE4dk9UMG9GdENLQT09.
host: Nguyen
Dynamical Weighs: Learning Smooth Latent-Dynamics for Advection-Dominated Systems via Consistency-Constrained Hyper-Networks
Leonardo Zepeda-Núñez
Senior Research Scientist
Google Research
and
Assistant Professor
Department of Mathematics
University of Wisconsin-Madison
Madison, Wisconsin
We present a data-driven, space-time continuous framework to learn surrogate models for complex physical systems described by partial differential equations (PDEs). Our approach involves constructing hypernetwork-based latent dynamical models directly on the parameter space of a compact representation network specially tailored to the state space of the target system. The framework leverages the expressive power of the network with a specially designed consistency-inducing regularization to obtain latent trajectories that are both low-dimensional and smooth. These properties render our surrogate models highly efficient at inference time.
We demonstrate the effectiveness of our approach on advection-dominated systems. These systems have slow-decaying Kolmogorov n-widths that hinders standard methods, including reduced order modeling, from producing high-fidelity simulations at low cost. We show that our method is able to generate accurate multi-step rollout predictions at high efficiency, for several one- and two-dimensional PDEs. The resulting rollouts are shown to be stable and reflect statistics that are consistent with the ground truths.
Leonardo Zepeda-Núñez is a Senior Research Scientist at Google Research and an Assistant Professor of Mathematics at the University of Wisconsin-Madison. He has held postdoctoral positions at Lawrence Berkeley Lab and University of California, working with Lin Lin and Hongkai Zhao respectively. He received a Ph.D. in Mathematics from MIT in 2015 under the direction of Laurent Demanet, an M.Sc. from University of Paris VI in 2010, and a Diploma from École Polytechnique in 2009. His research emcompases scientific machine learning with applications to weather and climate, electronic structure computations, wave-based inverse problems, and fast PDE solvers for wave phenomena.
Wednesday, February 8, 2023
3:30 PM
Stauffer Science Lecture Hall, Room 102 (SLH 102)
The Zoom webinar is at https://usc.zoom.us/j/98775609685?pwd=a2lSd01oY0o2KzA4VWphbGxjWk5Qdz09.
host: Ronney
host: Ronney
Adaptive Scale-Similar Closure: Toward the Most General Stabilized Subgrid Model for Multi-Physics LES
Werner J.A. Dahm
ASU Foundation Professor of Aerospace and Mechanical Engineering
School for Engineering of Matter, Transport and Energy
Arizona State University
Tempe, AZ
This seminar presents an adaptive scale-similar closure approach that can dynamically represent any subgrid term accurately and stably even at the smallest resolved scales of a simulation. The approach is based on scale similarity and generalized representations from the complete and minimal tensor representation theory of Smith (1971). At each point, the local tensor polynomial coefficients adapt to the local turbulence state via system identification at a test-filter scale and rescaling to the LES-scale. The methodology is demonstrated by applying it to the subgrid stress and subgrid scalar flux. Resulting fields for the subgrid terms and production rates are nearly indistinguishable from corresponding true fields, and are far more accurate than traditional subgrid models. Stability is ensured by a physics-based rational Boolean stabilization method, which uses the local subgrid production and subgrid redistribution rates to determine how individual subgrid components must be rescaled to provide local backward-transfer reduction or forward-transfer amplification. This produces only very small changes in the highly accurate fields for the subgrid terms and production rates that result from this new closure methodology. Together, adaptive scale-similar closure and rational Boolean stabilization essentially solve two key problems that have previously limited the accuracy of multi-physics large eddy simulations.
Werner J.A. Dahm is Professor Emeritus of Aerospace Engineering at the University of Michigan, where he was on the faculty for 25 years, and since 2010 has been the ASU Foundation Professor of Mechanical and Aerospace Engineering at Arizona State University. Previously he served in the Pentagon as the Chief Scientist of the U.S. Air Force, and in numerous senior technical advisory roles, including on the Air Force Scientific Advisory Board since 2005 and as Chair of the Board from 2014-2017. He is an AIAA Fellow, an APS Fellow, and recipient of the Air Force Decoration for Exceptional Civilian Service and the Secretary of the Air Force Distinguished Public Service Award.
Wednesday, September 14, 2022
3:30 PM
Seaver Science Library, Room 202 (SSL 202)
The webinar will also be on Zoom at
https://usc.zoom.us/j/98775609685?pwd=a2lSd01oY0o2KzA4VWphbGxjWk5Qdz09.
host: Ronney
host: Nguyen
host: Pahlevan
host: Nguyen
host: Spedding
host: Plucinsky
Published on August 2nd, 2017
Last updated on January 31st, 2023