Graduate Student Mentor for "Learning Statistically Accurate Dynamics of Complex Systems". Madison Experimental Mathematics (MXM) Lab project for Spring 2026. Co-mentor with Pouria Behnoudfar (project mentor lead).
The MXM Lab was founded in 2021, and aims to enhance and support undergraduate research within the Department of Mathematics and the University of Wisconsin.
This project explores how statistical information alone can be utilized to guide and enhance dynamical models. The central idea is to use statistical supervision, summary statistics such as moments, correlations, or distributional measures, as the primary observations. Rather than imposing these constraints directly on the full high-dimensional state, the project applies them indirectly through a data assimilation over a latent representation that acts as a low-dimensional control space. Adjustments are made in latent space so that, after decoding, the full-space dynamics exhibit the desired statistical properties. Importantly, the goal is not to learn or interpret the latent variables themselves, but to achieve statistically accurate behavior in the original variables. Students will implement and compare methods that update latent variables based on discrepancies between predicted and target statistics, using ensemble-based approaches. They will then evaluate how these statistical corrections affect the behavior of the full-space dynamics. The project emphasizes interpretability, computational efficiency, and principled use of weak supervision, and provides hands-on experience at the intersection of machine learning, statistics, and dynamical systems.
Recent Advances in Uncertainty Quantification and Scientific Machine Learning with Applications to Complex Dynamical Systems. Special session at the 15th AIMS Conference. Co-organised with Konstantinos Zygalakis and Nan Chen.
I have refereed/peer-reviewed papers for the following academic journals:
Journal of Atmospheric and Oceanic Technology (American Meteorological Society)
Nonlinear Processes in Geophysics (European Geosciences Union)
I have acted as a presentation reviewer/judge in the following meetings:
In case you're not sure where we might have met, here's a complete list of the conferences and workshops I have attended in person (including upcoming meetings I plan to attend).
2026
2025
2024
2023
DASSH — Diffusion-Accelerated Smoothing Using Score-Based Heuristics (WIP)
Deterministic and Stochastic Equations for the Ensemble Kalman-Bucy Smoother (WIP)
Developing a Data Assimilation Framework for Discovering the Hidden Mechanisms of Extreme Events (WIP)
Assimilative Causal Inference for General Complex Stochastic Systems (WIP)
Assimilative Causal Inference for Digital Twin Systems (On-Hold)
Data-Driven Assimilative Causal Inference (On-Hold)
Modelling the Cooking of Souvla. (On-Hold)
From left to right: Pouria, Yinling, Prof. Chen, me, and Charlotte. (Zhongrui is missing from here since he was at a conference.) Clicking on someone redirects to their academic website.