Professor Stuart's research is focused on the development of foundational mathematical and algorithmic frameworks for the seamless integration of models with data. He works in the Bayesian formulation of inverse problems for differential equations, and in data assimilation for dynamical systems.
I am broadly interested in applied analysis, with a particular focus on partial differential equations, optimal transportation, and their applications to data science.
My research addresses issues at the heart of computational engineering, sciences, and medicine: to understand, enhance, and control the quality, validity, and reliability of simulation-based predictions of complex physical systems. I have worked on various uncertainty quantification and optimization problems associated with models governed by parametric partial differential equations. I have extensively worked on application problems associated with computational polymer science. I am currently working on constitutive modeling for solid mechanics.
My research interests include data assimilation, stochastic process models, graph-based machine learning and active learning. My previous researches applied graph-based active learning to image classification and segmentation problems, while also extending methods by developing novel batch active learning approaches. Earlier this year, I also explored the integration of large language models with knowledge graphs. Currently, my primary research focus is on data assimilation.
My research interests are related to developing numerical methods for partial differential equations, with an emphasis on problems in fluid mechanics. My current research is focused on developing and applying data assimilation methods to fluid flows involving shocks. Previously, I have worked towards developing efficient numerical methods to predict boundary layer transition, and on projection-based model reduction methods.My research interests are related to developing numerical methods for partial differential equations, with an emphasis on problems in fluid mechanics. My current research is focused on developing and applying data assimilation methods to fluid flows involving shocks. Previously, I have worked towards developing efficient numerical methods to predict boundary layer transition, and on projection-based model reduction methods.
My research develops statistical and machine learning methods to model spatial and time varying processes from data; specifically in physical, biological and engineering problems where nonlocal effects are present. Examples include inference of Green’s functions, autoregressive or memory kernel models, and fractional order or higher-order equations. I am also interested in finding compressed interpretable representations of partially observed systems, which often introduce nonlocal interactions in the observed coordinates as well as in time. My prior work applied optimal transport algorithms to trajectory inference and biological matching, and I am now exploring how dynamical systems can be compared using optimal transport metrics.
I am primarily interested in developing efficient Bayesian inference techniques for probabilistic models such as Gaussian processes and stochastic (partial) differential equations, with the goal of making them applicable in real-world applications. Methods I have considered include variational inference, inclusion of physical or geometric/topological inductive biases, and deep learning methodologies. Prior to this, I have also done research at the intersection of geometric and statistical mechanics, as well as analysis of stochastic fluid PDEs.
My research interests lie at the intersection of computational science and applied mathematics. I work on problems involving data assimilation to improve models of dynamical systems.
I am interested in the development and characterization of data-driven methods — particularly those using the formalism of dynamical systems — and applications of these methods to make disciplinary contributions to (geophysical) fluid dynamics and atmosphere-ocean science. Previously, I developed data-driven methods for spectral approximations of Koopman operators and used these methods to study oscillations in the earth’s atmosphere.
My research interests are in numerical algorithms for PDEs, mean field games, and gaussian processes.
My work lies at the intersection of data assimilation, stochastic analysis, dynamical systems, computational statistics and machine learning. In general, I am interested in using theoretical insights from analysis to develop novel computationally efficient numerical algorithms.
My research delves into the area of high-dimensional chaotic dynamical systems. I am particularly interested in extreme events, data assimilation, uncertainty quantification, and the application of machine learning to uncover constitutive laws. Currently, my focus is on studying the predictability of earthquakes and Slow Slip Events (SSEs). In the intersection of mathematics, geophysics, and data science, my work aims to shed light on complex, high-dimensional systems that have the potential to improve our understanding and ability to predict natural phenomena.
Ervik’s research interests broadly encompass stochastic models for the climate. He has a background in applied mathematics and is currently working on developing stochastic closures for subgrid-scale cloud models. The goal of this research is to develop a model that more faithfully incorporates uncertainty. As part of this, he also works on methods for robust parameter estimation and uncertainty quantification.
I am interested in problems at the intersection of mechanics, data-driven modelling, statistics and machine learning. Currently, I am working on multiscale modelling problems and learning thermodynamically stable material constitutive laws from data.
My research interests lie at the intersection of computer science and applied mathematics. I work on data-driven methods for computational problems in natural science.
My research interests lie in the intersection of: Optimization, Optimal Control and Reinforcement Learning with a focus on applications in robotics and PDE-constrained optimization.
Research Interests in Applied analysis and simulation: Partial differential equations, optimization, deterministic modelling, inverse problems, numerical analysis and implementation; Uncertainty quantification and probabilistic techniques: Bayesian inverse problems, optimal design, scalability of algorithms, machine learning.
My research lies at the intersection of fluid dynamics, data-driven modeling, and interdisciplinary applications. I currently focus on ensemble data assimilation and machine learning for flows dominated by shocks and chemical reactions. More broadly, my work integrates data with physical models to advance predictive accuracy for complex, nonlinear, and high-dimensional systems through novel and rigorous methodologies.
