Past talks
Fall 2021
December 2nd
Hosted by: Binan Gu, NJIT
Topic: Dynamics of the Spherical Spin Glass
Abstract: This talk will discuss my work to characterize the glassy dynamical phase transition in the spherical p-spin glass. This is a paradigmatic model of a high-dimesional stochastic gradient descent in a disordered energy landscape. I use Large Deviations theory to obtain limiting population density equations describing the dynamics.
November 17th
Speaker: Binan Gu, NJIT
Topic: On Continuum Limit of PageRank
Abstract: I will discuss the paper by Jeff Calder et. al. on the continuum limit of PageRank, a direct follow-up from my talk two weeks ago. PageRank is a ranking vector quantifying the importance of nodes in a graph (or webpages in the world wide web, or subsets thereof). This vector can be interpreted as the dominant eigenvector of the transition matrix of a modified random walk (with restarts), i.e. the stationary distribution. Calder et. al. aims to study the continuum limit of the PageRank algorithm as the number of nodes goes to infinity in some rescaled fashion and provides a governing PDE that captures the spatial dependence of the PageRank score. In this talk, we investigate the ground work for this finding, point out the necessary knowledge needed for this derivation and many other similar problems, and connect to mean-field limits of stochastic games.
November 11th
Speaker: Hamza M. Ruzayqat, Postdoctoral Research Fellow at King Abdullah University of Science and Technology (KAUST)
Topic: Particle Filter in High Dimensions
Abstract: One of the most important applications of fluid dynamics models is numerical weather prediction. Modern numerical weather prediction combines sophisticated nonlinear fluid dynamics models with increasingly accurate high-dimensional data. This process is called data assimilation (or filtering) and it is performed every day at all major operational weather centers across the world. Data assimilation is not limited to fluid dynamics, but it has many applications in statistics and engineering. Filtering in general is a very challenging task as analytical solutions are typically not available and many numerical approximation methods can have a cost that scales exponentially with the dimension. In this talk I will focus upon the class of algorithms that are based on sequential Monte Carlo (SMC) methods. I will present a new method (lagged particle filter) that aims to reduce the cost to O(Nd2), where N is the number of simulated samples in the SMC algorithm and d is the dimension. The bias of our approximation is shown to be uniformly controlled in the dimension and exponentially small in time.
November 4th
Speaker: Binan Gu, NJIT
Topic: PageRank, its related centrality measures and connection to diffusion on large graphs
Abstract: In this talk, I will introduce the well-known PageRank, discuss the notion of centrality and lastly connect to graph partitioning schemes involving modified diffusions on very large graphs.
October 28th
Hosted by: Binan Gu
Topic: Topological Data Analysis Applied to Interaction Networks in Particulate Systems
Abstract: Particulate systems are very common in nature and in a variety of technologically relevant applications.
Many of these systems are composed of particles that remain in contact for relatively long periods.
These contacts form a network, whose properties are important for the purpose of understanding the system
as a whole. However, the contact network provides only partial information about the interaction between the
particles. In order to obtain a deeper understanding of a particulate system, the strength of the contacts needs
to be considered. This naturally leads to the concept of interaction networks appearing on mesoscale.
The properties of these structures are of fundamental importance for the purpose of revealing the underlying physical
causes of many phenomena, ranging from the interaction fields of colloidal systems to earthquakes. This presentation
focuses on applications of algebraic topology, and in particular of persistent homology, to analysis of such interaction networks.
The considered approach allows to simplify the complicated interaction network to a set of topological quantities that describe
their global properties. Furthermore, this approach allows to explore not only static but also dynamic properties of interaction
networks, so that time dependence of these networks can be quantified as well.
October 21st
Topic: Sparsity Constraints: Applications, Approximations, and Algorithms
Abstract: I'll give an opinionated overview of sparsity constraints as they are applied in the contexts of compressed sensing, matrix completion, matrix compression, and image deblurring. I'll review common approximations of such constraints and a few classes of algorithms for computing approximate solutions.
October 14th
Speaker: Georg Stadler, Courante Institute of Mathematical Sciences, NYU
Hosted by: Binan Gu
Topic: Optimal control of systems governed by PDEs with uncertain parameters
Abstract: I will review two formulations of optimization problems under
uncertainty. The uncertainty enters the problem through the governing
equation, typically a PDE. I am planning to show various application
examples to illustrate in what contexts these formulations can be
useful.
October 7th
Speaker: Connor Robertson, NJIT
Topic: Neural networks for function approximation and data-driven modeling
Abstract: Artificial neural networks have demonstrated an impressive capacity for classification and prediction in many fields. Applications in public facing fields such as text and image processing have stirred up massive public and academic interest in machine learning generally. This excitement has more recently begun to influence scientific techniques for modeling physical systems. In this talk, I will discuss the use of a variety of neural network architectures for function approximation and data-driven modeling of physical systems. In particular, I will focus on the recent efforts to include ``interpretable'' elements in the network architecture that wholly or partially remove the “black box” from around neural networks. The architectures I will discuss include: convolutional neural networks, autoencoders, recurrent and residual neural networks, physics informed neural networks, reservoir computers, symbolic networks, and hybrid combinations of differential equations and neural networks. I will both give an overview of these popular methods and highlight their strengths and weaknesses as compared to their traditional counterparts in modeling and simulation.
September 30th
Topic: Full Waveform Inversion Using the Wasserstein Metric
Abstract: We consider the problem of full waveform inversion, which seeks to use surface measurements to determine the structure of the earth's subsurface. While this inverse problem can easily be formulated as an optimization problem, the resulting objective function is often highly non-convex and difficult to minimize in practice. We discuss the use of the Wasserstein metric for measuring the misfit between seismic signals. This talk will focus on two questions. (1) What properties of the Wasserstein metric make it a good choice of misfit for this particular application? (2) How can we use the adjoint state method to quickly construct the gradients that are needed for efficient optimization?
September 23rd
Hosted by: Binan Gu
Topic: Image Sharpening via Sobolev Gradient Flows
Abstract: The most obvious way to blur an image anisotropically is by using the heat equation (or Gaussian convolutions). What if we wanted to sharpen the image? It is well known that the backwards heat equation is ill-posed. So what other backwards "heat"-like evolution equations are available? Here we discuss a variational approach that yields a nice PDE for forward and backward blurring/sharpening.
September 16th
Topic: Introduction to Kalman filtering and data assimilation
Abstract: Being able to solve a high dimensional data science problem is becoming an expected skill of most practical applied mathematicians today. In this talk, we’ll discuss the filtering problem which asks us how to establish a “best estimate” for the true value of a system despite us only having access to an incomplete or potentially noisy set of observations. We will discuss how the ensemble Kalman filter (EnKF), first developed in the 90’s, has become a popular algorithm for solving filtering problems common in different geoscientific applications where state dimensions can be in the order of millions.
September 9th
Speaker: Binan Gu, NJIT
Topic: Stochastic Temporal Networks
Abstract: Dynamics on temporal networks are ubiquitous in our daily life, ranging from social interactions, trade networks, power grids, cardiovascular systems and machine learning with graphical methods. At the same time, the underlying structure of the connections can be inherent random, only allowing communication from time to time in a stochastic fashion. In this talk, I will survey the building block of a stochastic temporal network with simple examples such as the Poisson random walk on undirected graph, and discuss the finding of a generalised Montroll-Weiss formula for continuous-time random walks on temporally stochastically varying graphs.
September 2nd
Hosted by: Binan Gu
Topic: Computing the Distance Between Probability Measures: Wasserstein vs. Fisher-Rao
Spring 2021
May 13th
Hosted by: Binan Gu
Topic: Proximal Policy Gradient Alg. for Reinforcement Learning
May 6th
Topic: A discussion of open problems related to stochastic gradient descent
April 29th
Hosted by: Binan Gu
Topic: Algorithmic thresholds for principal component analysis of tensors
Abstract: We study the algorithmic thresholds for principal component analysis of Gaussian tensors with a planted rank-one spike, via Langevin dynamics and gradient descent. I consider N stochastic particles moving randomly over the N-sphere. The advection term is a gradient descent: the gradient is biased towards a particular point on the sphere - think of this as the ‘North Pole’. Another component of the gradient consists of an all-to-all interaction term: each interaction involves p particles and is modulated by a static random weight. This random Hamiltonian is an archetype for a high-dimensional disordered energy landscape. We want to efficiently estimate the location of the north-pole signal, despite the static disorder due to the random Hamiltonian, and white noise perturbing each of the particles. To do this I determine autonomous limiting equations that predict the relative influence of the north-pole signal, the static disorder, and the white noise.
April 22nd
Hosted by: Binan Gu
Topic: Functional Data Analysis via Deep Neural Networks
Abstract: In functional data analysis, data are displayed as smooth curves, surfaces, or hypersurfaces evaluated at a finite subset of design points. Functional data usually demonstrate complex underlying structures, hence, classic statistical approaches encounter challenges. In this talk, I will describe some recent progress on functional data analysis via deep learning, which is proven superior in handling the complex functional data.
April 15th
Hosted by: Binan Gu
Topic: Stochastic Gradient Descent (SGD)
April 8th
Speaker: Binan Gu, NJIT
Topic: Diffusion Approximations and Nonconvex Optimization
March 25th
Topic: Nesterov’s method for accelerated gradient descent
May 13th
Hosted by: Binan Gu
Topic: Semi-Supervised Learning Using Gaussian Fields and Harmonic Functions
May 13th
Hosted by: Binan Gu
Topic: Solving High-Dim. Parabolic PDE Using Deep Learning
May 13th
Topic: Deep Learning for Mean-Field Games II
May 13th
Hosted by: Binan Gu
Topic: Deep Learning for Mean-Field Games I
May 13th
Speaker: Binan Gu, NJIT
Topic: On the Energy Landscape of Deep Networks
May 13th
Hosted by: Binan Gu
Topic: Deep Residual Networks: Optimal Control Point of View
Fall 2020
December 11th
Topic: Reinforcement Learning
December 4th
Hosted by: Binan Gu
Topic: Learning Frameworks
November 20th
Hosted by: Binan Gu
Topic: Sampling Theory
November 13th
Speaker: Binan Gu, NJIT
Topic: Graph-Based Models & Model Selection
November 6th
Hosted by: Binan Gu
Topic: GAN/WGAN
October 30th
Hosted by: Binan Gu
Topic: Matrix Completion and Sparse Recovery
October 23rd
Topic: Bayesian Statistics & Machine Learning
October 16th
Hosted by: Binan Gu
Topic: Dimension Reduction
October 9th
Speaker: Binan Gu, NJIT
Topic: Graph-Based Learning
October 2nd
Hosted by: Binan Gu
Topic: Information Geometry and Learning
September 25th
Hosted by: Binan Gu
Topic: Why does the stochastic gradient descent work?