Research – Alan Kaptanoglu

I am looking for physics, math, and engineering graduate students to join my lab at NYU!

Please reach out at alankaptanoglu@nyu.edu if you are a graduate student at NYU and interested in working together.

Research Projects

Stellarator Optimization: Stellarators are 3D fusion devices that possess many degrees of freedom in the magnetic field. Numerical optimization must be used to design the physics and engineering properties of the devices, as well as the coils and other supporting device infrastructure. Our group works on optimization techniques and numerical methods to try innovative ideas and improve the performance of these optimization routines.

A classical stellarator, adapted from Proll [28] and courtesy of C. Brandt.

Magneto-static Optimization: Our group works on optimization techniques and numerical methods to try innovative ideas for designing magnets and coils for nuclear fusion devices. For instance, permanent magnets are a low-cost way to make stellarator magnetic fields, but they represent a challenging, high-dimensional, discrete optimization problem. We are also working on “current voxels” and superconducting tiles, and multipole methods to speed up the codes.

Z-component of the magnet solution in a hybrid continuous-discrete optimization approach.

Physics-informed machine learning: Modern sensing technology has facilitated the collection of enormous datasets of dynamical data. This data can be mined for new insights into physical explanations, low-dimensional models, and conservation laws. Our group works on sparse regression and other techniques for discovering dynamical models (differential equations) directly from data and building in constraints relating to the nonlinear stability of models identified with these methods.

A training trajectory in the (x, y) subspace with 1% added noise (black), along with a clean testing trajectory (red) for the chaotic systems in the online dysts database.