I am Joe Germany, a second-year student at the American University of Beirut, double majoring in Mathematics and Physics.

Broadly, I am interested in the intersections of machine learning, physics, and rigorous mathematics. My "basin of attraction" is around machine learning algorithms in application to physics and PDEs. Concretely, I have worked on developing algorithms for better evolution of Hamiltonian systems (by embedding dimensional constraints and symplecticity), and also on the rigorous analysis of neural network-based solvers for partial differential equations (with strict imposition of periodicity or divergence-free properties).

My work thus far can be viewed through the lens of three groups of collaborators.

With Joseph Bakarji and Sara Najem, I have worked on developing data-driven techniques for the Hamiltonian systems that respect their underlying geometric properties (symplecticity) and explicitly impose dimensional consistency in discovering Hamiltonian expressions from data. Check out Paper [5].

With Elie Abdo and other collaborators, I work on two main frameworks:

• the analysis of nonlinear and nonlocal partial differential equations, addressing questions of well-posedness and long-time behavior of solutions, (see paper [4]), and
• the theory of (oft physics-informed) machine learning models, as demonstrated by paper [6] (and other projects in preparation!).

With Nathan Kutz and a team of collaborators, we have worked on creating a common task framework for evaluating scientific machine learning architectures, in an effort to provide a standardized way to compare the performance of these algorithms. Check out Papers [1, 2, 3].

1. J. Germany, E. Abdo, J. Bakarji. EML Trees are Universal Approximators, submitted, 2026.
2. J. Germany, J. Bakarji, S. Najem. Discovery of Symbolic Hamiltonian Expressions with Buckingham-Symplectic Networks, submitted, 2026. preprint
3. E. Abdo, J. Germany, M. K. Hamdan, K. Kontar, Long-time dynamics of the Nernst-Planck-Darcy System on ℝ³, submitted, 2026. preprint
4. A. Yermakov, Y. Zhao, M. Denolle, Y. Ni, P. M. Wyder, J. Goldfeder, S. Riva, J. Williams, D. Zoro, A. S. Rude, M. Tomasetto, J. Germany, J. Bakarji, G. Maierhofer, M. Cranmer, J. N. Kutz, The Seismic Wavefield Common Task Framework, accepted for publication as a conference paper at the International Conference on Learning Representations (ICLR) 2026. preprint
5. P. M. Wyder, J. A. Goldfeder, A. Yermakov, Y. Zhao, S. Riva, J. P. Williams, D. Zoro, A. S. Rude, M. Tomasetto, J. Germany, J. Bakarji, G. Maierhofer, M. Cranmer, J. N. Kutz, Common Task Framework For a Critical Evaluation of Scientific Machine Learning Algorithms, in The Thirty-ninth Annual Conference on Neural Information Processing Systems Datasets and Benchmarks Track, 2025. preprint; proceedings
6. P. M. Wyder, J. A. Goldfeder, A. Yermakov, Y. Zhao, S. Riva, J. P. Williams, D. Zoro, A. S. Rude, M. Tomasetto, J. Germany, J. Bakarji, G. Maierhofer, M. Cranmer, J. N. Kutz, Common Task Framework For a Critical Evaluation of Scientific Machine Learning Algorithms, Championing Open-source Development in ML Workshop @ ICML 2025. proceedings

• Math Summer Research Camp at the American University of Beirut (Summer 2026) on our paper "Long-time dynamics of the Nernst-Planck-Darcy System on $\mathbb{R}^3$", that results from work during the summer of 2025 with Elie Abdo.

• "Exactly Periodic, Divergence-Free Neural Networks and Applications to PDEs," AUB Math Seminar (May 5, 2026). abstract, recording.
• "Vector Calculus, with applications to Electromagnetism and Fluid Mechanics," presented at the American University of Beirut, as part of the Math Tutoring Center revision sessions (January 28, 2026).
• "Building Physics-Respecting Neural Networks for Hamiltonian Systems," presented at the Scientific Forum 2025 at the Lebanese University (December 16, 2025).
• LaTeX Workshop, presented at the American University of Beirut, as part of an initiative by the Math Society (October 29, 2025).

• Teaching Assistant (American University of Beirut):
  • Spring 2026:
    • EECE 798K: Data-Driven Modeling in Science and Engineering (Joseph Bakarji)
  • Fall 2025:
    • EECE 490: Introduction to Machine Learning (Joseph Bakarji)
    • Physics 222: Computational Physics (Sara Najem)
• Math Tutor at AUB’s Math Tutoring Center, helping with single- and multi-variable calculus, linear algebra, ordinary differential equations, and proof-based courses (honors linear algebra and real analysis).
  • Spring 2026
  • Fall 2025

• Currently enrolled (started Fall 2024) in a B.S in Mathematics and Physics (double major), American University of Beirut
  • Current GPA: 4.3/4.3
• International Baccalaureate Diploma, Saint Joseph School, Cornet Chehwan, Lebanon
  • Final grade: 43/45 on IB diploma with 7/7 in high-level mathematics, physics, and chemistry
  • Graduated as Valedictorian (Valedictorian Address)

• Recipient of prestigious AUB President Merit Scholarship (1 out of 10 university-wide; full tuition coverage)
• 1590/1600 SAT Score (790 Math; 800 English)
• 2022, 2023 participant in the high-school Summer Research Experience in Physics at AUB. I worked on the following projects:
  • Analytically and computationally analyzing the precession of mercury and the bending of light
  • Analyzing diffusion in networks
  • Using Faster RCNN-like technology to track Whirligig beetles and analyzing their behavior
• 2018, 2022, 2023 National Robotics Champion (1st Place) in national World Robotics Olympiad competition
• Ranked 7th overall out of 71 teams in 2022 international World Robotics Olympiad (Senior Category) in Dortmund, Germany and 3rd worldwide in impromptu 2nd day challenge
• 1st Place in 2023 AUB Math, Science, and Technology Fair, presenting a project in computational physics on analyzing the emergence of chaos in the double pendulum
• Secretary General (1st Place) in 2023 GC LAU MUN and Diplomacy award (2nd Place) in 2022 LAU MAL competition

Email: jmg15@mail.aub.edu