Publications

2024

1. In Progress

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

   Hongli Zhao, and  others

   2024

   Bib

   @article{tail-probabilities,
     author = {Zhao, Hongli and others},
     title = {Data-Driven Estimation of Correlated Failure Probabilities in Structure-Preserving Stochastic Power System Models},
     year = {2024},
   }

2023

1. Arxiv

   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},
   }

2. Arxiv

   Model discovery for nonautonomous translation-invariant problems

   Hongli Zhao, and Daniel M. Tartakovsky

   2023

   Abs arXiv

   Discovery of mathematical descriptors of physical phenomena from observational and simulated data, as opposed to from the first principles, is a rapidly evolving research area. Two factors, time-dependence of the inputs and hidden translation invariance, are known to complicate this task. To ameliorate these challenges, we combine Lagrangian dynamic mode decomposition with a locally time-invariant approximation of the Koopman operator. The former component of our method yields the best linear estimator of the system’s dynamics, while the latter deals with the system’s nonlinearity and non-autonomous behavior. We provide theoretical estimators (bounds) of prediction accuracy and perturbation error to guide the selection of both rank truncation and temporal discretization. We demonstrate the performance of our approach on several non-autonomous problems, including two-dimensional Navier-Stokes equations.

3. Arxiv

   Tensorizing flows: a tool for variational inference

   Yuehaw Khoo, Michael Lindsey, and Hongli Zhao

   2023

   arXiv Bib

   @misc{khoo2023tensorizing,
     title = {Tensorizing flows: a tool for variational inference},
     author = {Khoo, Yuehaw and Lindsey, Michael and Zhao, Hongli},
     year = {2023},
     eprint = {2305.02460},
     archiveprefix = {arXiv},
     primaryclass = {cs.LG},
   }

4. Springer RMS

   High-dimensional density estimation with tensorizing flow

   Yinuo Ren, Hongli Zhao, Yuehaw Khoo, and 1 more author

   Research in the Mathematical Sciences, 2023

   Abs Bib

   We propose the tensorizing flow method for estimating high-dimensional probability density functions from observed data. Our method combines the optimization-less feature of the tensor-train with the flexibility of flow-based generative models, providing an accurate and efficient approach for density estimation. Specifically, our method first constructs an approximate density in the tensor-train form by efficiently solving the tensor cores from a linear system based on kernel density estimators of low-dimensional marginals. Subsequently, a continuous-time flow model is trained from this tensor-train density to the observed empirical distribution using maximum likelihood estimation. Numerical results are presented to demonstrate the performance of our method.

   @article{tensorizing-flow-density-estimation,
     author = {Ren, Yinuo and Zhao, Hongli and Khoo, Yuehaw and Ying, Lexing},
     date = {2023/06/21},
     date-added = {2023-11-12 23:24:21 -0600},
     date-modified = {2023-11-12 23:24:21 -0600},
     doi = {10.1007/s40687-023-00395-x},
     id = {Ren2023},
     isbn = {2197-9847},
     journal = {Research in the Mathematical Sciences},
     number = {3},
     pages = {30},
     title = {High-dimensional density estimation with tensorizing flow},
     url = {https://doi.org/10.1007/s40687-023-00395-x},
     volume = {10},
     year = {2023},
     bdsk-url-1 = {https://doi.org/10.1007/s40687-023-00395-x},
   }

2022

1. Springer CN

   Autonomous learning of nonlocal stochastic neuron dynamics

   Tyler E. Maltba, Hongli Zhao, and Daniel M. Tartakovsky

   Cognitive Neurodynamics, 2022

   Abs arXiv Bib

   Neuronal dynamics is driven by externally imposed or internally generated random excitations/noise, and is often described by systems of random or stochastic ordinary differential equations. Such systems admit a distribution of solutions, which is (partially) characterized by the single-time joint probability density function (PDF) of system states. It can be used to calculate such information-theoretic quantities as the mutual information between the stochastic stimulus and various internal states of the neuron (e.g., membrane potential), as well as various spiking statistics. When random excitations are modeled as Gaussian white noise, the joint PDF of neuron states satisfies exactly a Fokker-Planck equation. However, most biologically plausible noise sources are correlated (colored). In this case, the resulting PDF equations require a closure approximation. We propose two methods for closing such equations: a modified nonlocal large-eddy-diffusivity closure and a data-driven closure relying on sparse regression to learn relevant features. The closures are tested for the stochastic non-spiking leaky integrate-and-fire and FitzHugh-Nagumo (FHN) neurons driven by sine-Wiener noise. Mutual information and total correlation between the random stimulus and the internal states of the neuron are calculated for the FHN neuron.

   @article{autonomous,
     author = {Maltba, Tyler E. and Zhao, Hongli and Tartakovsky, Daniel M.},
     date = {2022/06/01},
     date-added = {2023-11-12 23:10:10 -0600},
     date-modified = {2023-11-12 23:10:10 -0600},
     doi = {10.1007/s11571-021-09731-9},
     id = {Maltba2022},
     isbn = {1871-4099},
     journal = {Cognitive Neurodynamics},
     number = {3},
     pages = {683--705},
     title = {Autonomous learning of nonlocal stochastic neuron dynamics},
     url = {https://doi.org/10.1007/s11571-021-09731-9},
     volume = {16},
     year = {2022},
     bdsk-url-1 = {https://doi.org/10.1007/s11571-021-09731-9},
   }