### Motivation: Main Research

As the observing technologies (sensors, cameras, camcorders, etc.) have matured over the years and the difficulties of data sharing have decreased, the amount of observation data has become immensely available (see this YouTube Video of swarm of starlings by National Geographic). My research is motivated by the need of making valid, useful and swift scientific discoveries from observation. For example, the story of how universal law of gravity was discovered traced back to Kepler's work on observation data of Mars' orbit.

To make a more precise statement of my research, the focus of my research is about designing and developing effective and efficient algorithms for making such discoveries. There are two major directions about my research:

- Infer dynamical structure from time-dependent obervations: Learning Dynamics
- Recover hidden variables from their noisy observations: Data Recovery

In order to make accurate, convergent, and effective algorithms, I use theories and techniques from machine learning, numerical ODE/PDE, scientific computing, approximation theory, inverse problems, probability and statistics. Oftentimes, due to the gigantic size of the data set, the algorithms have to be scalable and efficient, hence I employ various techniques which reduce computing time: multi-scale representation, iterative solver, dimension reduction, domain decomposition, parallel computing, GPU computing (check out the Code section for details), etc. My research is interdisciplinary, it requries concrete knowledge of the observation technologies and underlying system, and it has applications in physics, biology, social science, and related engineering fields.

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### Talks

In 2020:

- Data-driven Discovery of Emergent Behaviors in Collective Dynamics, the Annual Shanks Conference and Lecture, Vanderbilt University, May 2020, Nashville, TN. (Postponed)
- Data-driven Discovery of Emergent Behaviors in Collective Dynamics, SIAM Conference on Mathematics of Data Science 2020, Hilton Cincinnati Netherland Plaza, May 2020, Cincinnati, OH. (Postponed)
- Data-driven Discovery of Emergent Behaviors in Collective Dynamics, East Coast Optimization Meeting (ECOM) 2020, George Mason University, April 2020, Fairfax, VA. (Postponed)
- Data-driven Discovery of Emergent Behaviors in Collective Dynamics, AMS Spring Southeastern Sectional Meeting 2020, University of Virginia, March 2020, Charlottesville, VA. (Cancelled)

In 2019:

- Data-driven Discovery of Emergent Behaviors in Collective Dynamics, Mid-Atlantic Numerical Analysis Day 2019, Temple University, November 2019, Philadelphia, PA.
- Data-driven Discovery of Emergent Behaviors in Collective Dynamics, Young Researchers Workshop: KI-Net 2012 - 2019, Univeristy of Maryland, October 2019, Collge Park, MD.
- Recognizing Emergent States from Short-time Trajectories, CSCAMM Seminar, Univeristy of Maryland, October 2019, College Park, MD.
- Data-driven Discovery of Emergent States of Collective Dynamics, Applied Math Seminar, Univeristy of Maryland - Baltimore County, September 2019, Baltimore, MD.
- Data-driven Discovery of Emergent States of Collective Dynamics, 43rd SIAM SEAS Annual Meeting 2019, University of Tennesses - Knoxville, September 2019, Knoxville, TN.
- Data-driven Appraoches for Scientific Discoveries, Spring 2019 Conference on Applied Mathematics, George Washington University, May 2019, Washington, D.C.
- Data-driven Appraoches for Scientific Discoveries, 7th UESTC International Forum for Young Scholars, University of Electronic Science and Technology of China, April 2019, Chengdu, Sichuan, China.
- Nonparametric Inference of Interaction Laws in Systems of Agents from Trajectory Data, Seminar, George Washington University, February 2019, Washington, D.C.
- Nonparametric Inference of Interaction Laws in Systems of Agents from Trajectory Data, Seminar, Southwestern University of Finance and Economics, January 2019, Chengdu, Sichuan, China.
- Nonparametric Inference of Interaction Laws in Systems of Agents from Trajectory Data, Seminar, Sichuan University, January 2019, Chengdu, Sichuan, China.
- Nonparametric Inference of Interaction Laws in Systems of Agents from Trajectory Data, Seminar, University of Electronic Science and Technology of China, January 2019, Chengdu, Sichuan, China.

In 2018:

- Discovering governing laws of interaction in heterogeneous agents dynamics from observation, Mid-Atlantic Numerical Analysis Day 2018, Temple University, November 2018, Philadelphia, PA.
- Learning Interaction Laws from Observations, International Conference on Mathematics of Data Science (ICMDS 2018), Old Dominion University, November 2018, Norfolk, VA.
- Learning Interaction Laws from Observations, Young Researchers Workshop: Kinetic descriptions in theory and applications, University of Maryland, October 2018, CSCAMM, College Park, MD.
- Discovering Governing Laws of Interaction in Heterogeneous Agents Dynamics from Observation, Seminar, University of Maryland, October 2018, College Park, Maryland.
- Discovering Governing Laws of Interaction in Heterogeneous Agents Dynamics from Observation, Joint International Meeting of CMS and AMS, Fudan University, June 2018, Shanghai, P.R.China
- Discovering Governing Laws of Interaction in Heterogeneous Agents Dynamics from Observation, Applied Math Seminar, Southern University of Science and Technology, May 2018, Shenzhen, Guangdong, P.R.China

In 2017:

- Hierarchical Reconstruction Method for De-convolution on Discrete Helmholtz Filter, Conference on Applied Mathematics 2017, George Washington University, April 2017, Washington, DC.
- Hierarchical Reconstruction Method for Solving ill-posed Linear Inverse Problems, Applied Math Seminar, Southern University of Science and Technology, January 2017, Shenzhen, Guangdong, P.R.China

In 2015:

- Hierarchical Reconstruction of Sparse Solutions from Under-determined Linear Systems, Mid Atlantic Numerical Analysis Day 2015, Temple University, November 2015, Philadelphia, PA.

In 2012:

- Hierarchical Reconstruction of Sparse Signals, Seminar, Stone Ridge Technology, Inc., November 2012, Bel Air, MD.

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### Posters

- M. Maggioni, J. Miller, M. Zhong. Data-driven Discovery of Emergent Behaviors, 2020 ICERM Program: Algorithms for Dimension and Complexity Reduction, Providence, RI, U.S.A.
- M. Maggioni, J. Miller, M. Zhong. Data-driven Discovery of Emergent Behaviors, 2020 ICERM Program: Mathematics of Reduced Order Models, Providence, RI, U.S.A.
- F. Lu, M. Zhong, S. Tang, M. Maggioni. Learning Interaction Laws in Heterogeneous Agents Dynamics, 2019 A Nature Conference: Emergent Materials and Devices: Electronic Structures and Properties, Chengdu, Sichuan, P. R. China
- F. Lu, M. Zhong, S. Tang, M. Maggioni. Learning Interaction Laws in Heterogeneous Agents Dynamics, 2018 CISMMS Workshop, Baltimore, MD, U.S.A.
- F. Lu, M. Zhong, S. Tang, M. Maggioni. Learning Interaction Laws in Heterogeneous Agents Dynamics, 2018 IDIES Annual Symposium, Baltimore, MD, U.S.A.
- M. Maggioni, M. Zhong. Learning Dynamical Interactions on Multiple Classes of Agents, 2017 ICERM Program: Pedestrian Dynamics: Modeling, Validation and Calibration, Providence, RI, U.S.A.

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