EDUCATION

Ph.D. University of Maryland, Baltimore County, Applied Mathematics 2018

B.S. Virginia Polytechnic Institute and State University, Mathematics 2011

PUBLICATIONS

    Peer Reviewed

  1. A. Biswas and J. Hudson, Determining the viscosity of the Navier–Stokes equations from observations of finitely many modes, Inverse Problems, 39 (2023), p. 125012.
  2. J. Hudson, M. D’Elia, H. N. Najm, and K. Sargsyan, The role of stiffness in training and generalization of ResNets, Journal of Machine Learning for Modeling and Computing, 4 (2023), pp. 75–103.
  3. J. Hudson, M. D'Elia, H. N. Najm, and K. Sargsyan, Measuring stiffness in residual neural networks, in Reduction, Approximation, Machine Learning, Surrogates, Emulators and Simulators: RAMSES, G. Rozza, G. Stabile, M. Gunzburger, and M. D'Elia, eds., Springer Nature Switzerland, Cham, 2024, pp. 153--170.
  4. E. Carlson, J. Hudson, A. Larios, V. R. Martinez, E. Ng, and J. P. Whitehead, Dynamically learning the parameters of a chaotic system using partial observations, Discrete and Continuous Dynamical Systems, 42 (2022), pp. 3809– 3839.
  5. A. Biswas and J. Hudson, Space and time analyticity for inviscid equations of fluid dynamics, Pure and Applied Functional Analysis, 7 (2022), pp. 81–98.
  6. A. Biswas, J. Hudson, and J. Tian, Persistence time of solutions of the three-dimensional Navier-Stokes equations in Sobolev-Gevrey classes, Journal of Differential Equations, 277 (2021), pp. 191–233.
  7. E. Carlson, J. Hudson, and A. Larios, Parameter recovery for the 2 dimensional Navier–Stokes equations via continuous data assimilation, SIAM Journal on Scientific Computing, 42 (2020), pp. A250–A270.
  8. J. Hudson and M. Jolly, Numerical efficacy study of data assimilation for the 2D magnetohydrodynamic equations, Journal of Computational Dynamics, 6 (2019), pp. 131–145.
  9. A. Biswas, J. Hudson, A. Larios, and Y. Pei, Continuous data assimilation for the 2D magnetohydrodynamic equations using one component of the velocity and magnetic fields, Asymptotic Analysis, 108 (2018), pp. 1–43.

    10. Conference Proceedings

  10. Y. Ashenafi, S. Ayres, A. Choudhary, T. Collins, D. Drzewicki, J. Hudson, Z. Morrow, D. Pasut, Faculty Advisor: T. Witelski, Determining object characteristics from force and displacement measures: direct and inverse problem, Proceedings of the 2017 Graduate Student Mathematical Modeling Camp, Rensselaer Polytechnic Institute, Troy, NY(July 2017).

TEACHING EXPERIENCE

PRESENTATIONS

    Invited Presentations

  1. (talk) Uniquely recovering viscosity in 2D NSE from finitely many determining modes, SIAM Texas-Louisiana Section conference, Baylor University - Waco, Texas, 10 Oct. 2024.
  2. (talk) Data assimilation and inverse problems for fluid dynamics using nudging, Hunter College Mathematics Colloquium, Hunter College - City University of New York, 1 Dec. 2022, recording
  3. (talk) Data assimilation and inverse problems for fluid dynamics using nudging, Partial Differential Equations Seminar, University of Nebraska-Lincoln, 30 Nov. 2022.
  4. (Talk) Data assimilation via nudging for fluid dynamics with parameter recovery, Applied Mathematics Colloquium, University of Maryland, Baltimore County, 4 Dec. 2020.
  5. (Talk) Parameter Recovery for the NSE, 2019 SIAM Conference on Analysis of Partial Differential Equations, La Quinta California, 11 Dec. 2019.
  6. (Talk) Using data assimilation to better approximate flows and as a means to measure physical parameters, Mathematics Colloquium, Towson University, 8 Nov. 2018.
  7. (Talk) - with Andrew Rhaim - Alumni Talk, 2018 Graduate Student Orientation, University of Maryland, Baltimore County, 27 Aug. 2018.
  8. (Talk) Data assimilation for the 2D magnetohydrodynamic equations, Partial Differential Equations Seminar, University of Nebraska-Lincoln, 28 Nov. 2017.
  9. (Talk) A primer on data assimilation, with the magnetohydrodynamic equations, Research Experiences for Undergraduates in Mathematics at Indiana University, Indiana University, Bloomington, 22 June 2017.

    10. Contributed Presentations

  10. (Poster) Penalizing stiffness in ResNet flows, RAMSES: Reduced order models; Approximation theory; Machine Learning; Surrogates, Emulators and Simulators, SISSA, International School for Advanced Studies, 14 Dec. 2021.
  11. (Talk) Analysis of Neural Networks as Dynamical Systems, 2021 Sandia Machine Learning and Deep Learning Workshop, Sandia National Laboratories, 22 July 2021.
  12. (Talk) Data assimilation for the 2D magnetohydrodynamic equations, 2017 SIAM Conference on Analysis of Partial Differential Equations, Baltimore, Maryland, 12 Dec. 2017.
  13. (Talk) Determining object characteristics from force and displacement measures: direct and inverse problem, 2017 Graduate Student Mathematical Modeling Camp, Rensselaer Polytechnic Institute, 17 June 2017.
  14. (Poster) Continuous data assimilation for the MHD (in 2D under periodic boundary conditions), A Look Ahead XX (2017), University of Maryland, Baltimore County, 3 May 2017.

    15. Seminar Talks

  15. Blow-up rates for solutions of the Navier--Stokes equations in Sobolev-Gevrey classes, Analysis Seminar, University of Arkansas, 19 Oct. 2023.
  16. Eventual decay of solutions to the MHD, Graduate Student Seminar, University of Maryland, Baltimore County, 1 March 2017.
  17. Data assimilation for the 2D MHD using feedback control algorithms, Graduate Student Seminar, University of Maryland, Baltimore County, 16 Nov. 2016.
  18. Dataassimilation for the Navier–Stokes equations and the magnetohydrodynamic equations in 2D, Graduate Student Seminar, University of Maryland, Baltimore County, 6 April 2016.
  19. Global attractors, Graduate Student Seminar, University of Maryland, Baltimore County, 25 Feb. 2015.
  20. The Navier–Stokes equations (a physical derivation), Graduate Student Seminar, University of Maryland, Baltimore County, 9 April 2014.