I currently work in numerical linear algebra and theoretical neuroscience. I hope to transition to working at the intersection of statistical learning theory, geometry, neuroscience, and theoretical physics.
Lab for Parallel Numerical Algorithms
We are developing a Markov chain Monte Carlo algorithm to estimate contractions of closed tensor networks. This allows efficient approximation of quantities like
\[
\text{Tr}(ABCD) = \sum_{ijkl} A_{ij}B_{jk}C_{kl}D_{li}
\]
using methods from statistical physics to improve mixing.
Such contractions are trivial in small cases but become \(\#\textsf{P}\)-hard for large networks. Our approach targets use cases in quantum circuits and chemistry, where exact contraction is intractable.
We'll present this work at QSim 2025. Read more here!
Computation & Neurodynamics Lab
I work on extracting analytic Floquet decompositions of periodic dynamical systems using symbolic AI. Given a linear time-periodic system, we seek closed-form expressions for its monodromy matrix and periodic transformation \(P(t)\) so that the dynamics can be represented in a time-invariant form. This enables exact optimal control design in transformed coordinates without relying on purely numerical Floquet computations.
The systems of interest take the form \[ \dot{x}(t) = A(t) x(t), \quad A(t+T) = A(t) \] where \(T\) is the fundamental period. Floquet theory guarantees a decomposition \[ \Phi(t) = P(t) e^{R t} \] of the fundamental solution \(\Phi(t)\) into a \(T\)-periodic matrix \(P(t)\) and a constant matrix \(R\) containing the Floquet exponents. The monodromy matrix \(M = \Phi(T)\) satisfies \(M = P(0) e^{R T}\), linking periodic dynamics to their time-invariant equivalent.
We compute numerical decompositions for benchmark systems, then fit symbolic models for \(P(t)\) and \(R\) using sparse regression and periodicity constraints. The learned analytic forms are validated by reconstructing \(\Phi(t)\) and comparing to direct numerical integration. Once obtained, these symbolic decompositions allow the design of optimal controllers via periodic Riccati equations, yielding closed-form feedback laws in the transformed coordinates.
Current work focuses on defining appropriate function bases for symbolic fitting, ensuring periodicity during model discovery, and testing the framework on canonical periodic systems such as the Mathieu equation and parametrically forced oscillators.
More updates soon!