• Speaker: Round table conversation
• Title: Preparing for Fall - teaching modalities
• Date: 07/14/2021
• Time: 10:00 AM - 12:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Tsvetanka Sendova (tsendova@msu.edu)

No abstract available.

• Speaker: Qi (Rose) Yu , University of California, San Diego
• Title: University of California, San Diego
• Date: 07/15/2021
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

Applications such as climate science and transportation require learning complex dynamics from large-scale spatiotemporal data. Existing machine learning frameworks are still insufficient to learn spatiotemporal dynamics as they often fail to exploit the underlying physics principles. Representation theory can be used to describe and exploit the symmetry of the dynamical system. We will show how to design neural networks that are equivariant to various symmetries for learning spatiotemporal dynamics. Our methods demonstrate significant improvement in prediction accuracy, generalization, and sample efficiency in forecasting turbulent flows and predicting real-world trajectories. This is joint work with Robin Walters, Rui Wang, and Jinxi Li.

• Speaker: Yaniv Plan, University of British Columbia
• Title: A family of measurement matrices for generalized compressed sensing
• Date: 07/22/2021
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

We consider the problem of recovering a structured signal x that lies close to a subset of interest T in R^n, from its random noisy linear measurements y = B A x + w, i.e., a generalization of the classic compressed sensing problem. Above, B is a fixed matrix and A has independent sub-gaussian rows. By varying B, and the sub-gaussian distribution of A, this gives a family of measurement matrices which may have heavy tails, dependent rows and columns, and singular values with large dynamic range. Typically, generalized compressed sensing assumes a random measurement matrix with nearly uniform singular values (with high probability), and asks: How many measurements are needed to recover x? In our setting, this question becomes: What properties of B allow good recovery? We show that the “effective rank” of B may be used as a surrogate for the number of measurements, and if this exceeds the squared Gaussian complexity of T-T then accurate recovery is guaranteed. We also derive the optimal dependence on the sub-gaussian norm of the rows of A, to our knowledge this was not known previously even in the case when B is the identity. We allow model mismatch and inexact optimization with the aim of creating an easily accessible theory that specializes well to the case when T is the range of an expansive neural net.

• Speaker: Mengsen Zhang, UNC Chapel Hill
• Title: Transitions and their topological signatures in social and brain dynamics
• Date: 07/26/2021
• Time: 2:00 PM - 3:00 PM
• Place: Online (virtual meeting)
• Contact: Shelley Kandola (kandola2@msu.edu)

Understanding biological and social interactions in a dynamical system framework amounts to identifying stable patterns of activity and tracking transitions between them. When the system’s dimension is low (few interacting elements), one can often visually inspect the time series and write down the relevant variables and differential equations. Once we venture into higher dimensions, this traditional modeling approach becomes intractable: what constitutes a “stable pattern” or a “transition” in the empirical data depends on the spatiotemporal scales at which we look at the system. We show how persistent homology serves as a natural tool for characterizing such multiscale dynamics in rhythmic social interaction. Furthermore, a key goal of studying transitions is to understand the relations between distinct stable dynamic patterns – they provide access to the global organization of the dynamical system. We show how existing topological data analysis (TDA) tools can be adapted to understand the network of transitions in brain dynamics. The talk focuses on the empirical and dynamical-system context in which TDA is applied in the hope of eliciting new conversations across the boundary of empirical science, dynamical systems modeling, and TDA.

• Speaker: Round table conversation
• Title: Preparing for Fall - teaching modalities - Part II
• Date: 07/28/2021
• Time: 10:00 AM - 12:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Tsvetanka Sendova (tsendova@msu.edu)

No abstract available.

• Speaker: Wotao Yin, UCLA
• Title: Learning to Optimize: Fixed-Point Network
• Date: 07/29/2021
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Olga Turanova (turanova@msu.edu)

Many applications require repeatedly solving a certain optimization problem, each time with new but similar data. “Learning to optimize” or L2O is an approach to develop algorithms that solve these similar problems very efficiently. L2O-generated algorithms have achieved significant success in signal processing and inverse-problem applications. This talk introduces the motivation for L2O and gives a quick overview of different types of L2O approaches for continuous optimization. Then, we will introduce Fixed Point Networks (FPNs), which incorporate fixed-point iterations into deep neural networks and provide abilities such as physics-based inversion, data-driven regularization, encoding hard constraints, and infinite depth. The FPNs are easy to train with a new Jacobian-free back propagation (JFB) scheme.