Hongli (Bob) Zhao

Jones 307

5747 S Ellis Avenue, Chicago IL

Chicago, IL 60637

I am a 4th year PhD student at Computational and Applied Mathematics at University of Chicago, advised by Prof. Mihai Anitescu.

Prior to Chicago, I graduated from UC Berkeley in Applied Math, and Data Science. During undergraduate studies, I was very fortunate to have worked with Prof. Daniel Tartakovsky and Prof. Lin Lin. I also participated in BeBOP (Summer 2021), organized by Prof. James Demmel.

I am broadly interested in developing scalable numerical methods for scientific computing, with a particular focus on characterizing uncertainty in physical systems subject to randomness.

Interests

Structured matrix and tensor computations
Rare events simulation (e.g. cascading failures)
Optimal control and deep learning

Education

PhD in Computational and Applied Math. University of Chicago (CCAM), 2021-Present
BA in Applied Math and Data Science. UC Berkeley, 2018-2021

Email: honglizhaobob [at] uchicago.edu

News & Activities

Jun 5, 2023	Mathematical and Scientific Machine Learning at ICERM
May 15, 2023	Portland, Oregon. Global Sensitivity Analysis in High Dimensional Parameter Spaces Program description. Session Link & Abstract Slides: Please find the research talk via this link
Feb 14, 2023	CTF Workshop at UW AI Institute in Dynamical Systems

Recent Publications

Arxiv

Data-Driven Estimation of Failure Probabilities in Correlated Structure-Preserving Stochastic Power System Models

Hongli Zhao, Tyler E. Maltba, D. Adrian Maldonado, and 2 more authors

2024

arXiv Bib

@misc{zhao2024datadriven,
  title = {Data-Driven Estimation of Failure Probabilities in Correlated Structure-Preserving Stochastic Power System Models},
  author = {Zhao, Hongli and Maltba, Tyler E. and Maldonado, D. Adrian and Constantinescu, Emil and Anitescu, Mihai},
  year = {2024},
  eprint = {2401.02555},
  archiveprefix = {arXiv},
  primaryclass = {cs.CE},
}

SIAM SISC
Data-driven Closures & Assimilation for Stiff Multiscale Random Dynamics

Tyler E. Maltba, Hongli Zhao, and D. Adrian Maldonado

2023

Abs arXiv Bib

We introduce a data-driven and physics-informed framework for propagating uncertainty in stiff, multiscale random ordinary differential equations (RODEs) driven by correlated (colored) noise. Unlike systems subjected to Gaussian white noise, a deterministic equation for the joint probability density function (PDF) of RODE state variables does not exist in closed form. Moreover, such an equation would require as many phase-space variables as there are states in the RODE system. To alleviate this curse of dimensionality, we instead derive exact, albeit unclosed, reduced-order PDF (RoPDF) equations for low-dimensional observables/quantities of interest. The unclosed terms take the form of state-dependent conditional expectations, which are directly estimated from data at sparse observation times. However, for systems exhibiting stiff, multiscale dynamics, data sparsity introduces regression discrepancies that compound during RoPDF evolution. This is overcome by introducing a kinetic-like defect term to the RoPDF equation, which is learned by assimilating in sparse, low-fidelity RoPDF estimates. Two assimilation methods are considered, namely nudging and deep neural networks, which are successfully tested against Monte Carlo simulations.
@misc{stiff-closures, title = {Data-driven Closures \& Assimilation for Stiff Multiscale Random Dynamics}, author = {Maltba, Tyler E. and Zhao, Hongli and Maldonado, D. Adrian}, year = {2023}, eprint = {2312.10243}, archiveprefix = {arXiv}, primaryclass = {math.DS}, }