Dry eye disease is caused by a breakdown of a uniform tear film, which occurs when the layer of tears experiences breakup. To better understand this ocular condition, the dynamics of the tear film can be studied using fluorescence imaging.   Many parameters affect tear film thickness and fluorescent intensity distributions over time; exact values or…

The capability of using imperfect statistical reduced-order models to capture crucial statistics in complex turbulent systems is investigated. Much simpler and more tractable block-diagonal models are proposed to approximate the complex and high-dimensional turbulent dynamical equations using both parameterization and machine learning strategies. A systematic framework of correcting model errors with empirical information theory is…

Gaussian processes (GPs) are popular models for random functions in computational and applied mathematics, statistics, machine learning and data science. However, GP methodology scales poorly to large data-sets due to the need to factorize a dense covariance matrix. In spatial statistics, a standard approach to surmount this challenge is to represent Matérn GPs using finite…

The objective of this talk is to introduce a fairness interpretability framework for measuring and explaining the bias in classification and regression models at the level of a regressor distribution. In our work, we measure the model bias across sub-population distributions in the model output using the Wasserstein metric. To properly quantify the contributions of…

Stochastic optimization problems with deterministic constraints commonly appear in machine learning, finance, and engineering applications. This talk presents a new adaptive solution strategy for this important class of problems. The aim is to decrease the computational cost while maintaining an optimal convergence rate. The guiding principle is to adjust the batch size (or sample size)…

There is a well-established linear algebraic lens for studying consensus dynamics on networks, which has yielded significant theoretical results in areas like distributed computing, modeling of opinion dynamics, and ranking methods.  Recently, strong connections have been made between problems of consensus dynamics on networks and classical iterative methods in numerical linear algebra.  This talk will…

Analysis of physical and engineering systems is characterized by unique computational challenges associated with high dimensionality of parameter spaces, large cost of simulations or experiments, as well as existence of uncertainty. For a wide range of these problems the goal is to either quantify uncertainty and compute risk for critical events, optimize parameters or control…

Mean field games (MFGs) study strategic decision-making in large populations where individual players  interact via specific mean-field quantities. They have recently gained enormous popularity as powerful research tools with vast applications. For example, the Nash equilibrium of MFGs forms a pair of PDEs, which connects and extends variational optimal transport problems. This talk will present…

Realistic image generation has benefited from recent groundbreaking advances in the ML community. At the core of generative models lies the capability to sample high-dimensional distributions with relatively small support and a priori unknown shape. In many scientific applications, this capability is a limiting factor that has led to modeling choices that circumvent the sampling…

At the heart of modern deep learning is the deep neural nets accompanied by stochastic optimization and sampling algorithms. These architectures and algorithms have an explicit flavor. In particular, traditional deep nets compose affine and simple nonlinear transformations, defining an explicit function for representation learning. The explicit deep nets lack flexibility and adaptivity for modeling…

Photoacoustic tomography (PAT) is a non-invasive imaging modality that requires recovering the initial data of the wave equation from certain measurements of the solution outside the object. In the standard PAT, the measured data consist of time-dependent signals measured on an observation surface. In contrast, the measured data from the recently invented full-field detection technique…

A major challenge in the study of dynamical systems is that of model discovery: turning data into reduced order models that are not just predictive, but provide insight into the nature of the underlying dynamical system that generated the data. We introduce a number of data-driven strategies for discovering nonlinear multiscale dynamical systems and their…

For social networks, nodes encode social entities, such as people, twitter accounts, etc., while edges encode relationship or events between entities. Opinion dynamics model opinion evolution as dynamical processes on social networks. Traditional models of opinion dynamics consider how opinions evolve either on time-independent networks or on temporal networks with edges that follow Poisson statistics.…

Data or patterns (e.g., signals and images) emanating from physical sensors often exhibit complicated nonlinear structures in high dimensional spaces, which post challenges in constructing effective models and interpretable machine learning algorithms.  When data is generated through deformations of certain templates, transport transforms often linearize data clusters which are non-linear in the original domain. We…

Suppose we observe very few entries from a large matrix. Can we predict the missing entries, say assuming the matrix is (approximately) low rank ? We describe a very simple method to solve this matrix completion problem. We show our method is able to recover matrices from very few entries and/or with ill conditioned matrices,…

Tensor method can be used for compressing high-dimensional functions arising from partial differential equations (PDE). In this talk, we focus on using these methods for the simulation of transition processes between metastable states in chemistry applications, for example in molecular dynamics. To this end, we also propose a novel generative modeling procedure using tensor-network without…

Operator networks have emerged as promising deep learning tools for approximating the solution to partial differential equations (PDEs). These networks map input functions that describe material properties, forcing functions and boundary data to the solution of a PDE, i.e., they learn the solution operator of the PDE. In this talk, we consider a new type…

Operator networks have emerged as promising deep learning tools for approximating the solution to partial differential equations (PDEs). These networks map input functions that describe material properties, forcing functions and boundary data to the solution of a PDE, i.e., they learn the solution operator of the PDE. In this talk, we consider a new type…

Deep learning method has emerged as a competitive mesh-free method for solving partial differential equations (PDEs). The idea is to represent solutions of PDEs by neural networks to take advantage of the rich expressiveness of neural networks representation. In this talk, we will explore the applicability of this powerful framework to the kinetic equation, which…

In this talk, I will present 3 problems on fluid structure interaction: 1) Flight stability of wedges: Recent experiments have shown that cones of intermediate apex angles display orientational stability with apex leading in flight. Here we show in experiments and simulations that analogous results hold in the two-dimensional context of solid wedges or triangular prisms in planar…