Department of Mathematics

Yue Shen will defend her dissertation “Role Extraction in Networks by Scaled Neighborhood Pattern Similarity for Scaled Stochastic Block Models\"

In this talk, we present the diffusion-model-based Ensemble Score Filter (EnSF) for accurate and efficient high-dimensional nonlinear filtering.

Nonlinear filtering, also known as data assimil... More

The incompressible fluid model is widely used in various fields in engineering and science and their numerical solutions are of prominent importance in understanding complex, natural, engineered, and ... More

Stochastic partial differential equations (SPDEs) play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced a... More

We present a hybrid data assimilation framework that combines long short-term memory (LSTM) based neural networks with the Ensemble Score Filter (EnSF) for nonlinear dynamical systems. LSTM models pro... More

Wasserstein geometric flows (WGFs) constitute a class of time-evolution partial differential equations that play a fundamental role in modeling and simulating physical systems. In this talk, we presen... More

Generative artificial intelligence models, including variational auto-encoders, normalizing flows, generative adversarial networks, and diffusion models, have dramatically advanced the realism and qua... More

Isoperimetric inequalities play a fundamental role in various areas such as analysis, probability, geometry, and even in data analysis. Among the many tools used to study isoperimetric problems, symme... More