Nguyễn Khôi Nguyên (Alan)阮魁元
Junior Research Engineer, Boston University
nknguyen [at] bu [dot] edu
I'm a junior research engineer working on robot learning, robot perception, and machine vision systems. I'm at Boston University, advised by Wenchao Li in the Dependable Computing Lab and co-advised by Eshed Ohn-Bar in the Human-to-Everything (H2X) Lab. I'm most interested in VLMs and VLAs and how to put them to work in robotics, and in physics-informed approaches to ML and RL.
I graduated from BU in 2025 with dual degrees in Physics and Computer Science. As an undergraduate I was lucky to be advised by Lei Tian in computational imaging and Luca Dal Negro in nanophotonics. I've been an intern at Scale and Leuko, and I co-founded and led the BU AI Society.
Research
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Quantum States of Light in Cavity QED: A Computational Study of Wigner Function Dynamics and Atom–Field Entanglement in the Jaynes–Cummings Model
Preprint · Under review at the European Journal of Physics · 2026
In the Jaynes–Cummings model, the cavity field forms a nearly pure Schrödinger cat at half the revival time, just as atom and field nearly disentangle. Weak cavity loss destroys most of it.
Wigner function versus Husimi Q as the field evolves (n̄ = 10). Only the Wigner function shows the cat’s negative interference fringes; Q stays positive, with two smooth lobes. 
Coherent-state field (n̄ = 10): inversion, atomic entropy and field purity through one cycle. Entropy bottoms out at 0.14 bit as purity peaks at 0.96. @misc{nguyen2026qsol, author = {Nguyen, Nguyen Khoi}, title = {Quantum States of Light in Cavity {QED}: A Computational Study of {W}igner Function Dynamics and Atom--Field Entanglement in the {J}aynes--{C}ummings Model}, year = {2026}, note = {Preprint, under review at European Journal of Physics. Code: https://github.com/alanknguyen/QSOL\_CQED, doi:10.5281/zenodo.22806076}, url = {https://www.researchgate.net/publication/404323301_Quantum_States_of_Light_in_Cavity_QED_A_Computational_Study_of_Wigner_Function_Dynamics_and_Atom-Field_Entanglement_in_the_Jaynes-Cummings_Model} }
Projects
Coming soon.
Notes
Notes on topics from courses I’ve taken at BU, combined with other sources.
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Engineering Fourier Optics [Book]
Main source: BU ENG EC 562, Fourier Optics in Engineering
- Pages
- 268
- Draft
- Version 3 (finished)
- Also draws on
- BU ENG EC 522, Computational Optical Imaging by Lei Tian
- Textbook
- J. W. Goodman, Introduction to Fourier Optics, 4th ed. (W. H. Freeman, 2017)
Part of Elements of Fourier Optics: A Computational Approach, submitted to Springer. All text and figures are my own. The draft began as my notes on Luca Dal Negro's EC 562 Fourier Optics in Engineering lectures at Boston University (Fall 2023) and has grown well beyond them, with derivations, worked examples and extensive Python code.
Linear systems, the angular spectrum and free-space propagation, Fresnel and Fraunhofer diffraction, sampling and numerical propagation, arrays, gratings, Talbot self-imaging, zone plates and scalar diffraction theory, with extensive Python code.
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Optimal and Robust Control
Main source: BU ENG EC/ME/SE 701, Optimal and Robust Control
- Pages
- 11
- Draft
- First draft
- Textbook
- D. Liberzon, Calculus of Variations and Optimal Control Theory: A Concise Introduction, Princeton University Press, 2012
Elements of an optimal control problem. Cost functionals: Bolza, Mayer and Lagrange forms. Lyapunov feedback vs. open-loop steering. Vector spaces, inner products and norms.
- Pages
- 8
- Draft
- First draft
- Textbook
- D. Liberzon, Calculus of Variations and Optimal Control Theory: A Concise Introduction, Princeton University Press, 2012
Linearization about equilibria and nominal trajectories. Jacobians and Taylor remainder. Pendulum: hanging, inverted and time-varying. Lyapunov's indirect method.
- Pages
- 8
- Draft
- First draft
- Textbook
- D. Liberzon, Calculus of Variations and Optimal Control Theory: A Concise Introduction, Princeton University Press, 2012
State transition matrix. Peano–Baker series. Matrix exponential and similarity transforms. Cayley–Hamilton theorem. Variation of constants.
- Pages
- 7
- Draft
- First draft
- Textbook
- D. Liberzon, Calculus of Variations and Optimal Control Theory: A Concise Introduction, Princeton University Press, 2012
Accessibility and controllability. Adjoint operators. Controllability Gramian theorem. Observability Gramian and duality.
- Pages
- 6
- Draft
- First draft
- Textbook
- D. Liberzon, Calculus of Variations and Optimal Control Theory: A Concise Introduction, Princeton University Press, 2012
Kalman rank condition. Observability matrix. PBH test. Minimum-energy control vs. bang-bang.
- Pages
- 6
- Draft
- First draft
- Textbook
- D. Liberzon, Calculus of Variations and Optimal Control Theory: A Concise Introduction, Princeton University Press, 2012
LQR problem statement. A key lemma. Free end point: Riccati differential equation and optimal feedback. Double-integrator example.
- Pages
- 5
- Draft
- First draft
- Textbook
- D. Liberzon, Calculus of Variations and Optimal Control Theory: A Concise Introduction, Princeton University Press, 2012
Fixed end point, fixed end time. Reduction to the free end-point problem. Five-step procedure. Optimal cost. Worked example.
- Pages
- 8
- Draft
- First draft
- Textbook
- D. Liberzon, Calculus of Variations and Optimal Control Theory: A Concise Introduction, Princeton University Press, 2012
LTI infinite horizon and the algebraic Riccati equation. Stability margins of LQR. Observers and the separation principle. LQG. Detectability. Discrete time.
A rigorous introduction to optimal and robust control. Robust control: model reduction, H2 and H∞ control, and feedback control of uncertain systems. Optimal control: the linear quadratic regulator, the calculus of variations, the maximum principle and the Hamilton–Jacobi–Bellman equation.
- EC 710 Dynamic Programming and Reinforcement Learningcoming soon
Experience
- 2025 –Junior Research Engineer, Dependable Computing Lab, Boston University
- 2025Machine Learning Engineer Intern, Scale
- 2023Data Science Intern, Leuko
Teaching
TA at Boston University
- 09/2026: EC 545: Cyber-Physical Systems (Graduate Level)
- 01/2026: EC 575: Semiconductor Devices (Graduate Level)
- 09/2025: EC 574: Physics of Semiconductor Materials (Graduate Level)
- 01/2025: EC 575: Semiconductor Devices (Graduate Level)
Service
- 2023 – 2025Co-Founder and President, Boston University AI Society
Grew BU's largest student-run AI community, with weekly lectures, workshops and speaker events. Raised $10,000+ for compute hardware. - 2023 – 2025AI Advisor, Boston University Student Government
Served on a committee reporting directly to BU President Melissa Gilliam, and advised on the development and release of TerrierGPT, BU's AI platform. - 2023 – 2025Committee Member, Boston University Ignite Student Council
Approved funding for student clubs and built connections between CS and Engineering (CE, EE, ME, BE, MSE, SE) clubs for cross-club collaboration. - 2022