Mathematics, Computational Science, Physics
-4th Year Students- Seniors
-ASU Online Barrett Honors Students (fully remote work)
-ASU Online Barrett Honors Students (fully remote work)
228
Tempe
Fully remote/Remote considered
Faculty Lead:
Jimmie Adriazola, Ph. D.
Incoming tenure-track assistant professor (August, 2026) and current National Science Foundation/Presidential Postdoctoral Fellow
School of Mathematical and Statistical Sciences
Project Description:
The central question of this project is simple yet deep: how can small, carefully designed inputs guide a dynamical system toward a desired state?
The dynamics we will wrestle with come from dispersive waves in optics, fluids, and quantum materials. These systems are visually striking and mathematically subtle since wave dynamics are known to spread, interact, and reorganize over time in complex ways. Using optimal control theory, we then seek to work *with* the natural evolution of the system, exploiting structure to achieve precise goals.
Students will learn how optimal control problems are formulated, how forward and backward equations interact through adjoint methods, and how numerical algorithms turn theory into computation. Advanced modeling techniques will be used to make large-scale systems tractable, allowing students to experiment, visualize, and test ideas efficiently, even on a standard laptop.
The project emphasizes intuition, modeling, and hands-on computation, showing how different branches of mathematics come together to address a single, well-posed challenge. It is well suited for students interested in applied mathematics, scientific computing, or mathematically driven physics, and it provides a strong foundation for more advanced topics such as optimal transport, generative modeling, and scientific machine learning.
Jimmie Adriazola, Ph. D.
Incoming tenure-track assistant professor (August, 2026) and current National Science Foundation/Presidential Postdoctoral Fellow
School of Mathematical and Statistical Sciences
Project Description:
The central question of this project is simple yet deep: how can small, carefully designed inputs guide a dynamical system toward a desired state?
The dynamics we will wrestle with come from dispersive waves in optics, fluids, and quantum materials. These systems are visually striking and mathematically subtle since wave dynamics are known to spread, interact, and reorganize over time in complex ways. Using optimal control theory, we then seek to work *with* the natural evolution of the system, exploiting structure to achieve precise goals.
Students will learn how optimal control problems are formulated, how forward and backward equations interact through adjoint methods, and how numerical algorithms turn theory into computation. Advanced modeling techniques will be used to make large-scale systems tractable, allowing students to experiment, visualize, and test ideas efficiently, even on a standard laptop.
The project emphasizes intuition, modeling, and hands-on computation, showing how different branches of mathematics come together to address a single, well-posed challenge. It is well suited for students interested in applied mathematics, scientific computing, or mathematically driven physics, and it provides a strong foundation for more advanced topics such as optimal transport, generative modeling, and scientific machine learning.
Students should be comfortable with multivariable calculus and linear algebra, including basic matrix computations. Prior exposure to differential equations is expected, at the level of an introductory ODE course.
Some programming experience is required, ideally in MATLAB or Python, though students do not need prior experience with numerical PDEs or optimization. Curiosity, persistence, and a willingness to learn mathematical ideas that connect theory and computation are more important than advanced background. Prior experience with control theory or partial differential equations is **not** required.
Some programming experience is required, ideally in MATLAB or Python, though students do not need prior experience with numerical PDEs or optimization. Curiosity, persistence, and a willingness to learn mathematical ideas that connect theory and computation are more important than advanced background. Prior experience with control theory or partial differential equations is **not** required.
Jimmie Adriazola
Tempe; Fully Remote; Flexible to remote and/or in-person