[02493] Advanced Modelling of Complex Nonlinear Systems
Session Time & Room : 4E (Aug.24, 17:40-19:20) @G704
Type : Proposal of Minisymposium
Abstract : Complex nonlinear systems with millions and even billions of parameters appear in various fields of science and engineering. These include mechanics, fluid dynamics, and deep neural networks. In order to better understand, predict and optimize the solutions, new mathematical models are required.
In this mini-symposium, we plan to present several approaches from different fields related to modeling large high-dimensional nonlinear systems. This will foster better synergy and collaboration of researchers from various disciplines. Researchers from advanced signal processing, applied mathematics, and fluid mechanics will discuss their contributions. We anticipate new insights and analogies will be gained following this exchange of ideas.
[03289] A Minimal Set of Koopman Eigenfunctions -- Analysis and Numerics
Author(s) :
Ido Cohen (Technion - Israel Institute of Technology)
Abstract : In this talk, we present the most concise linear representation of nonlinear systems based on the theory of Koopman Operator. Here, we define the “basis” of Koopman eigenfunctions from which the whole spectrum of the Koopman operator can be generated and the dynamic is accurately reconstructed. Numerically, the curse of dimensionality in samples vanishes since the inherent geometry constraints. Thus, the suggested method yields the most reduced representation from samples justifying the term \emph{minimal set}.
[03525] Acoustic Streaming
Author(s) :
James Friend (University of California San Diego)
Abstract : Acoustic streaming is a nonlinear effect from an acoustic wave that can generate rapid fluid flows. We show a new, mathematically challenging approach to its analysis that overcomes past limitations, recasting traditional separation of scales in one variable to separation of spatiotemporal scales, with careful treatment of partial derivatives and the definition of compatibility equations to ensure closure. We provide closed-form solutions to transient acoustic streaming for the first time.
[04735] The Underlying Correlated Dynamics in Neural Training
Author(s) :
Guy Gilboa (Technion)
Rotem Turjeman (Technion)
Tom Berkov (Technion)
Ido Cohen (Technion)
Abstract : We propose a model of neural-net training which dramatically reduces the dimensionality. Our algorithm, Correlation Mode Decomposition (CMD), yields groups of highly correlated parameters. We achieve a remarkable dimensionality reduction with this approach, where a network of 11M parameters like ResNet-18 can be modeled well using just a few modes. Retraining the network using our model induces a regularization which yields better generalization capacity on the test set.
[05114] A Nonstochastic Control Approach to Optimization
Author(s) :
Xinyi Chen (Princeton University and Google AI)
Elad Hazan (Princeton University and Google AI)
Abstract : Selecting the best hyperparameters, such as the learning rate and momentum, is an important but nonconvex problem. We propose an online nonstochastic control methodology for optimization that can circumvent this nonconvexity and obtain certain global guarantees. The problem of learning the best optimizer can be framed as a feedback control problem over the choice of optimizers. Our method guarantees that we can compete with the best optimizer in hindsight from a class of methods on a given sequence of problems.
