Department of Mathematics

Consider a complex system of a vast number of interacting agents, which can give rise to emergent collective behaviors such as bird flocking, fish swarming, and opinion formation — phenomena that ca... More

Contact Zhifeng at zdeng@fsu.edu for zoom meeting link information

In recent years, the need to quantify and control the uncertainty in physical systems has prompted a burgeoning interest in studying the evolution of the distribution of the trajectories of stochastic... More

Data-driven modeling of complex systems is a rapidly evolving field facilitated by the concurrent rise of data science. To alleviate the prohibitively expensive computational costs of repeated full-mo... More

A fundamental problem in machine learning is understanding the effect of early stopping and mini-batching on the parameters obtained and the generalization capabilities of the trained model. Even for ... More

This talk will describe how to bridge the gap between learning and safety-critical constraints through structured neural networks guided by control theory and the physics of energy systems. Using Lyap... More

In this talk, we develop and explore a foundational model for solving Partial Differential Equations (PDEs) with an emphasis on building a versatile, robust framework capable of addressing multiple PD... More

We will discuss the basics of the seminar. No formal research talk will be given.

The so-called extraordinary optical transmission (EOT) through metallic nanoholes has triggered extensive research in modern plasmonics and their applications in bio-sensing, imaging, etc. In this tal... More

The stability of steady states for complex dynamical systems are notoriously difficult problems, even for the seemingly simplest cases. For example, it is expected that the standard steady state shear... More

In his seminal paper of 1966, Vladmir Arnold recast Euler’s equation for the motion of an incompressible fluid as the geodesic equation of a right-invariant Riemannian metric on the group of volume-... More

In his seminal paper of 1966, Vladmir Arnold recast Euler’s equation for the motion of an incompressible fluid as the geodesic equation of a right-invariant Riemannian metric on the group of volume-... More

Many real-world complex systems operate far from thermodynamic equilibrium. In particular, the dissipation of entropy to maintain a system in non-equilibrium has been proposed as a unifying, organisin... More

Certain well-known dispersive partial differential equations that model the propagation of waves are known to be integrable - that is, exactly solvable. Recently, a peculiar class of integrable system... More

The theory of stochastic optimal control is a branch of applied probability which started during 90s and matured during 2000s. While it roots in theoretical economics, it became a branch of mathematic... More

We will discuss local well-posedness and ill-posedness results of some active scalar equations, including 2D incompressible Euler equations and the SQG equation. We will discuss how one can obtain ins... More

Vegetation patterns in semi-arid areas manifest either through regular or irregular vegetation patches separated by bare ground. Of particular interest are the latter structures, that exhibit a distin... More

In recent years, the main challenges in subsurface energy systems (e.g., enhanced geothermal systems and CO2 sequestration) have included issues arising from the multi-physical and multi-scale nature ... More

Data assimilation (DA) methods in the Earth Sciences, such as the

Kalman Filter (KF) and its ensemble approximation (EnKF), are usually based on Gaussian assumptions. While these statistical ap... More

In order to understand the evolution of a system, it is critical to investigate stability properties of equilibria. These are often characterized as minimizers or critical points of certain functional... More

One of the central problems for dissipative systems generated by PDEs is concerned with whether the underlying dynamics is effectively finite dimensional and can be described by a system of ODEs. To s... More

Large scale dynamics of the ocean and the atmosphere are governed by the primitive equations (PE). In this presentation, I will first review the derivation of the PE and some well-known results for th... More

We will meet for coffee at 2:45pm and hold the meeting earlier today.

Supercritical carbon dioxide (sCO2) is of interest to a wide range of engineering problems, including

carbon capture, utilization, and storage (CCUS) as well as advanced cycles for power genera... More

Community detection is a popular approach used to analyze large networks and obtain relevant statistical properties by finding community structures in networks. However, community detection algorithms... More

Among the numerous advances taking place within the discipline of machine learning, the sub-field currently known as scientific machine learning has seen encouraging developments. This branch of ML re... More

Global sensitivity analysis measures the importance of the inputs of a model to its output. Several approaches, such as Sobol sensitivity indices, derivative based global sensitivity measures (DGSM), ... More

Neural networks are usually trained with different variants of gradient descent-based optimization algorithms such as stochastic gradient descent or the Adam optimizer.  Recent theoretical work state... More

Superconductor magnets hold immense promises for strong magnets based on the fascinating nature that high current can flow with negligible Joule-heating loss dissipation. They have indeed enabled di... More

I will talk about three related topics for the 2D Rayleigh-Benard Problem: determining forms, attractor bounds, and data assimilation

In the past few decades the problem of reconstructing high-dimensional functions taking values in abstract spaces from limited samples has received increasing attention, largely due to its relevance t... More

Dr. Tam has done research on the noise of military aircraft for a number of years supported by the Office of Naval Research. Military jets operate at much higher temperatures and velocities than labor... More

Network science has emerged, in the last 20 years, as an essential framework to model and understand complex systems in a variety of disciplines. At its core, network science views a system as a set o... More

: In the talk we will describe the Navier-Stokes regularity problem (which is one of the 6 outstanding Millenium Problems), and discuss some recent efforts in achieving progress on the problem. We wil... More

This talk is based on recent works in which we study the dissipative generalized surface quasi-geostrophic equations in a supercritical regime where the order of the dissipation is small relative to o... More

In this talk we shall outline a new method to solve initial and boundary value problems that arise in physical sciences.

The idea is to use the underlying physics (such as conse... More

Supercritical carbon dioxide (sCO2) is of interest to a range of engineering problems, including carbon capture, utilization, and storage (CCUS) as well as advanced cycles for power generation. Non-id... More

We will review some basic concepts regarding the heat equation, we will quantify its regularizing effect for a well-localized initial data. On the other hand, we will see that a non-localized initial ... More

In the article by Pei, Vahab, Sussman, and Hussaini

(Journal of Scientific Computing, 2019),

an adaptive, parallel, moment-of-fluid,

space-time spectral element method (AMR-MOF-... More

Multivariate models with dependent variables are popular in financial industry, with applications to option pricing, portfolio optimization, risk management, and modeling credit portfolios. Other appl... More

Yunzheng will talk about numerical method of using backward SDEs to solve the optimal filtering problem.

Yunzheng will talk about the design of Backward SDE filter