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A list of all the posts and pages found on the site. For you robots out there is an XML version available for digesting as well.
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Posts
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portfolio
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publications
A Stochastic Mortar Mixed Finite Element Method for Flow in Porous Media with Multiple Rock Types
Published in SIAM, 2011
We propose a new way (Sparse Grid) to solve the Darcy’s equation with stochastic permeability.
Recommended citation: Ganis, B. and Yotov, I. and Zhong, M. (2011). "A Stochastic Mortar Mixed Finite Element Method for Flow in Porous Media with Multiple Rock Types." SIAM Journal on Scientific Computing. 33(3): 1439 - 1474. https://epubs.siam.org/doi/10.1137/100790689
Hierarchical Reconstruction Method for Solving Ill-posed Linear Inverse Problems
Published in DRUM, 2016
We develop a multi-scale solver based on hierarchical reconstruction to recover data for compressed sensing, de-convolusion, and linear regressoin.
Recommended citation: Zhong, M. (2016). "Hierarchical Reconstruction Method for Solving Ill-posed Linear Inverse Problems." DRUM. https://drum.lib.umd.edu/handle/1903/18280
Iterative Refinement of A Modified Lavrentiev Regularization Method for De-convolution of the Discrete Helmholtz Type Differential Filter
Published in arXiv, 2018
We propose an iterative solver to do de-convolusion for Large Eddy Simulation.
Recommended citation: Mays, N. and Zhong, M. (2018). "Iterative Refinement of A Modified Lavrentiev Regularization Method for De-convolution of the Discrete Helmholtz Type Differential Filter." arXiv. https://arxiv.org/abs/1801.08913
Time Relaxation with Iterative Modified Lavrentiev Regularization
Published in arXiv, 2018
We combine an iterative solver with time relaxaton model for LES.
Recommended citation: Zhong, M. (2018). "Time Relaxation with Iterative Modified Lavrentiev Regularization." arXiv. https://arxiv.org/abs/11809.09517
Nonparametric inference of interaction laws in systems of agents from trajectory data
Published in PNAS, 2019
We develop a learning theory to model self organization from obsrevation data.
Recommended citation: Lu, F. and Zhong, M. and Tang, S. and Maggioni, M. (2019). "Nonparametric inference of interaction laws in systems of agents from trajectory data." PNAS. 116(29): 14424 - 14433. https://www.pnas.org/doi/10.1073/pnas.1822012116
Data-driven discovery of emergent behaviors in collective dynamics
Published in Physica D, 2020
We study the steady state behavior of our learning algorithm.
Recommended citation: Zhong, M. and Miller, J. and Maggioni, M. (2020). "Data-driven discovery of emergent behaviors in collective dynamics." Physica D: Nonlinear Phenomena. 116(29): 14424 - 14433. https://www.sciencedirect.com/science/article/abs/pii/S0167278919308152?via%3Dihub
Learning Theory for Inferring Interaction Kernels in Second-Order Interacting Agent Systems
Published in Sampling Theory, Signal Processing, and Data Analysis, 2020
We provide a complte learning theory for inferring second-order self organized dynamics from observation data.
Recommended citation: Miller, J. and Tang, S. and Zhong, M. and Maggioni, M. (2020). "Learning Theory for Inferring Interaction Kernels in Second-Order Interacting Agent Systems." arXiv. https://arxiv.org/abs/2010.03729
Learning Interaction Kernels for Agent Systems on Riemannian Manifolds
Published in PMLR, 2021
We extend our learning method to dynamics constrained on Riemannian manifolds.
Recommended citation: Maggioni, M. and Miller, J. and Qiu, H. and Zhong, M. (2022). "Learning Interaction Kernels for Agent Systems on Riemannian Manifolds." Proceedsings of the 38th International Conference on Machine Learning. PMLR 130: 7290 - 7300. http://proceedings.mlr.press/v139/maggioni21a.html
Machine Learning for Discovering Effective Interaction Kernels between Celestial Bodies from Ephemerides
Published in arXiv, 2021
We apply our learning theory to study Solar system with NASA JPL data.
Recommended citation: Zhong, M. and Miller, J. and Maggioni, M. (2021). "Machine Learning for Discovering Effective Interaction Kernels between Celestial Bodies from Ephemerides." arXiv. https://arxiv.org/abs/2108.11894
On the sparsity of LASSO minimizers in sparse data recovery
Published in Construtive Approximation, 2022
We provide another explanation of constrained LASSO.
Recommended citation: Foucart, S. and Tadmor, E. and Zhong, M. (2022). "On the sparsity of LASSO minimizers in sparse data recovery." Construtive Approximation. https://link.springer.com/article/10.1007/s00365-022-09594-1
Physics-Informed Neural Networks with Adaptive Localized Artificial Viscosity
Published in arXiv, 2022
We use PINN to find artificial viscosity from data to solve hyperbolic PDEs.
Recommended citation: Coutinho, E.J.R and Dall'Aqua, M. and McClenny, L. and Zhong, M. and Braga-Neto, U. and Gildin, E. (2022). "Physics-Informed Neural Networks with Adaptive Localized Artificial Viscosity." arXiv. https://arxiv.org/abs/2203.08802
Grassmanian packings: Trust region stochastic tuning for matrix incoherence
Published in Allerton Conference, 2022
We provide a new computational scheme for creating low coherence matrices.
Recommended citation: Park, J. and Saltijeral, C. and Zhong, M. (2022). "Grassmanian packings: Trust region stochastic tuning for matrix incoherence." 2022 58th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2022, pp. 1 - 6. https://ieeexplore.ieee.org/document/9929393
Learning Interaction Variables and Kernels from Observations of Agent-Based Systems
Published in MTNS, 2022
We learn both interaction functions and feature variables for self organized dynamics.
Recommended citation: Feng, J. and Maggioni, M. and Martin, P. and Zhong, M. (2022). "Learning Interaction Variables and Kernels from Observations of Agent-Based Systems." IFAC-PapersOnLine, 25th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2022), 55 (30), 162 - 167, 2022. https://www.sciencedirect.com/science/article/pii/S2405896322026799
Using Physics Informed Neural Networks for Supernova Radiative Transfer Simulation
Published in arXiv, 2022
Applying PINN to solve RTE with new Atomic Process
Recommended citation: Chen, X. and Jeffery, D. J. and Zhong, M. and McClenny, L. and Braga-Neto, U. and Wang L. (2022). "Using Physics Informed Neural Networks for Supernova Radiative Transfer Simulation." arXiv 2022. https://arxiv.org/abs/2211.05219
talks
Talk 1 on Relevant Topic in Your Field
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Conference Proceeding talk 3 on Relevant Topic in Your Field
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teaching
Introduction to Data Science
Undergraduate course, Illinois Institute of Technology, Applied Math, 2022
First course in the B.S. in Data Science major. Introducing basic data analysis skills using Python.