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Research Overview

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My research is in emerging fast and accurate methods for the solution of multiscale partial differential equations (PDEs) with applications in neurophysiology. I am particularly interested in utilizing traditional methods such as physical model reduction and efficient implementations of high order techniques in conjuction with modern machine learning methods, and developing software packages that are broadly usable in both research and clinical domains. My current work is in utilizing traditional discretization of PDEs and ML techniques to investigate effects of transcranial magnetic stimulation in the treatment of tremor conditions at the single cell level.

Publications

Preprints

  1. Z.M. Miksis and G. Queisser, A New Fick-Jacobs Derivation with Applications to Computational Branched Diffusion Networks, arXiv:2501.08247v2 [math.NA].

Journal

  1. Z.M. Miksis and Y.-T. Zhang, Sparse-grid implementation of fixed-point fast sweeping WENO schemes for eikonal equations, Communications on Applied Mathematics and Computation, (2022). https://doi.org/10.1007/s42967-022-00209-x. (pdf)

Conferences and Workshops

  1. Z.M. Miksis and G. Queisser, A physics-informed neural network for coupled calcium dynamics in a cable neuron, ICLR 2024 Workshop on AI4DifferentialEquations in Science, Vienna, Austria, May 2024. (pdf)

  2. Z.M. Miksis and G. Queisser, A physics-informed neural network for coupled calcium dynamics in a cable neuron, International Conference on Scientific Computing and Machine Learning 2024, Kyoto, Japan, March 2024. (pdf)

  3. S. Abraham, J. Kinnison, Z.M. Miksis, D. Poster, S. You, J. D. Hauenstein, and W. Scheirer, Efficient hyperparameter optimization for ATR using homotopy parametrization, in Automatic Target Recognition XXXIII, R. I. Hammoud, T. L. Overman, and A. Mahalanobis, eds., vol. 12521, International Society for Optics and Photonics, SPIE, 2023, p. 1252107. (pdf). [Best Student Paper Award to S. Abraham]

Theses

  1. Z.M. Miksis, Sparse-grid implementation of fixed-point fast sweeping WENO schemes for Eikonal equations, PhD dissertation, University of Notre Dame, 2022.

  2. Z.M. Miksis, An Accelerating Couette Flow in Nek5000: Applications in Oceanography and Magnetohydrodynamics, MS thesis, Illinois Institute of Technology, 2017.

Presentations

Invited Talks

  1. Advances In Efficient Computational Modeling of Transcranial Magnetic Stimulation Towards Clinical Application, Multiscale Brain Modeling and Beyond: A Focus on Biological Tissues, University of Glasgow, Glasgow, SCT, June 2025.

  2. Sparse-grid fast sweeping WENO methods for eikonal equaitons, Applied Mathematics and Scientific Computing Seminar, Temple University, Philadelphia, PA, August 2023.

  3. Numerical solutions to Hamilton-Jacobi equations on sparse grids and a Stokes problem variant with Nek5000, Virtual presentation, Sandia National Laboratory, Albuquerque, NM, June 2022.

Contributed Talks

  1. Unlocking the Brain: Exploring Transcranial Magnetic Stimulation (TMS) Through Computational Modeling, Graduate Symposium, Temple University, Philadelphia, PA, April 2025.

  2. A New Fick-Jacobs Derivation with Applications to Computational Diffusion Networks, Mid-Atlantic Numerical Analysis Day, Temple University, Philadelpia, PA, November 2024.

  3. A New Fick-Jacobs Derivation with Applications to Computational Diffusion Networks, 2nd Annual SIAM-NNP Meeting, Rochester Institute of Technology, Rochester, NY, November 2024.

  4. A New Convergent Fick-Jacobs Derivation: Applications in Computational Neurophysiology, Sayas Numerics Day, George Mason University, Arlington, VA, May 2024.

  5. A Cross-Species Computational Study of rTMS Protocol Effects on Calcium Dynamics, 1st Annual SIAM-NNP Meeting, New Jersey Institute of Technology, Newark, NJ, October 2023.

  6. Parallel implementation of a sparse grid fast sweeping WENO method for Eikonal equations, Midwest Numerical Analysis Day, University of Michigan, Ann Arbor, MI, May 2022.

  7. A sparse grid fast sweeping WENO method for Eikonal equations, Midwest Numerical Analysis Day, Missouri University of Science and Technology, Rolla, MO, October 2021.

  8. An accelerating Couette flow with MHD in Nek5000, Summer Argonne Student Symposium, Argonne National Laboratory, Lemont, IL, August 2016.

  9. MHD with Nek5000, Nek5000 Users and Developers Meeting, Massachusetts Institute of Technology, Cambridge, MA, August 2016.

  10. Verification of a Stokes problem variant, Graduate Student Colloqium, Illinois Institute of Technology, Chicago, IL, March 2016.