Portrait of Luke Bhan

Luke Bhan

I build algorithms for controlling physical systems that combine machine learning with structure to provide provable guarantees.

Pure learning is fast but unaccountable; classical control is rigorous but requires domain expertise and lacks scalability. My research fuses their strengths, building ultra-fast controllers for robots, vehicles, and biological systems that act in real time and provide theoretic performance guarantees.

I am on the academic job market this year and excited to find the right fit. I'd love to connect, reach me at lbhan@ucsd.edu.

no predictor
neural-operator predictor
same input delay: uncompensated (left) vs. stabilized in real time by a neural-operator predictor (right)

Research

Algorithms that capitalize on the performance of machine learning, with the provable certificates needed for deployment in real-world physical systems. I tell an engineer exactly how accurately to train their controller and, from the loss it reaches, the closed-loop performance it will achieve.

Vehicle navigation

A car-like vehicle has different delays on its steering and acceleration. A separate neural-operator predictor compensates each one, so it still drives cleanly to its target.

Life Sciences

An age-structured population is steered to a target equilibrium, with the stabilizing control gains learned online from the population's birth and mortality rates.

Predictor feedback

A manipulator performs a fast task through a long actuation delay. Without compensation the delay destabilizes the loop and the task fails; a neural-operator predictor reconstructs the future state so the same task completes, with a stability guarantee.

no predictor
neural-operator predictor
PDE backstepping

Stabilizing a PDE from its boundary requires solving a kernel PDE for the control gains, recomputed for every new plant. A neural operator learns that gain-kernel map directly, preserving the stability guarantee while replacing the expensive solve, and even adapting it online when the plant's coefficients are unknown.

PDE backstepping

Check out more of my research during my Ph.D. →

About

I'm a doctoral candidate at UC San Diego in Intelligent Systems, Robotics & Control (ECE), advised by Yuanyuan Shi with mentorship from Miroslav Krstić. My PhD is supported by the DOE Computational Science Graduate Fellowship.

My goal is a single, rigorous toolkit (operator learning with formal control-theoretic guarantees) that transfers across domains rather than being rebuilt for each one. The same methods that stabilize a partial differential equation 1000× faster than classical solvers also plan robot motion that generalizes across environments, and steer biological and traffic systems in real time. I work on problems where guarantees are not optional.

Before UCSD I studied physics, applied math, and computer science at Vanderbilt University in an accelerated BS/MS program, advised by Gautam Biswas and Kálmán Varga.

More about me →

Teaching & service

In the ChatGPT era, I think the most valuable part of a classroom is the people in it, the peers and colleagues you get to think alongside. So in the lectures I help teach, I try to lean on participation and discussion rather than one-way delivery. I have mentored seven undergraduate and master's researchers. Three became publication coauthors, and three former mentees subsequently entered graduate programs at ETH Zurich, UC San Diego, and the University of Wisconsin.

Mini lecture series

A 4-lecture introduction to scientific machine learning, recorded from the live classes I help teach within Physics-Informed Machine Learning at UC San Diego.

Courses & assistantships

2025, 2026
Co-Instructor, Physics-Informed Machine Learning, UC San Diego · 5 lectures on foundation models, neural ODEs, neural operators, and PINNs; designed course homework on augmented neural ODEs, FNOs, and PINNs.
2020 – 2021
Teaching Assistant, Vanderbilt University · Numerical Analysis; Probability & Statistics; Intermediate Software Design.

Peer review

Journals
Automatica · IEEE Transactions on Automatic Control · Systems & Control Letters · Int'l Journal of Robust & Nonlinear Control · IEEE Control Systems Letters · IEEE Transactions on Control of Networked Systems.
Conferences
CDC · ACC · L4DC · AAAI · ICLR.

More on teaching →