Ming Zhong

Research

Recovering governing structure from scientific data

I develop mathematical and computational methods for ill-posed inverse problems in scientific machine learning, especially the recovery of low-dimensional governing structure from high-dimensional, noisy, partial, or under-resolved observations.

01

Learning governing dynamics from high-dimensional observations

I seek low-dimensional laws hidden in high-dimensional data. My work develops nonparametric and structure-aware methods for identifying interaction kernels, environmental forces, latent variables, and stochastic dynamics from trajectories, equilibrium configurations, and partial observations.

  • Interaction-law learning from trajectories and collective steady states
  • Joint discovery of interaction variables, kernels, and environmental effects
  • System identification for SDEs and stochastic PDEs with structured noise
  • Applications to self-organization, celestial mechanics, and biological systems
02

Inverse problems for partially observed scientific systems

I study systems in which observations reveal only part of the evolving state or a composite quantity. Residential burglary dynamics provides a central model problem: the observable crime activity couples hidden attractiveness and population fields, so successful forward simulation does not by itself imply identifiable inverse recovery.

  • Joint state and parameter recovery from direct and indirect observations
  • Identifiability under limited spatial and temporal sampling
  • Finite-element learning methods with PDE-compatible regularization
  • Applications to urban crime, hidden-state recovery, and uncertainty analysis
03

Numerical and computational foundations of scientific machine learning

Reliable recovery requires approximations and optimization methods that respect the governing mathematics. I study stability, approximation error, conditioning, and computational cost across physics-informed neural networks, random features, Gaussian processes, and traditional numerical methods.

  • Stable training for stiff and hyperbolic PDEs
  • Dimension and domain co-decomposition for interpretable approximation
  • Physics-informed random features, Gaussian processes, and hybrid solvers
  • Applications to power systems, supernova simulation, and conservation laws

Support & recognition

NSF CCF Algorithmic Foundations

A Bayesian Paradigm for Physics-Informed Machine Learning · Co-PI · 2022–2026.

Ralph E. Powe Junior Faculty Enhancement Award

Data-driven Modeling of Emergent Behaviors in Social Sciences · PI · 2024–2025.

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