Projects

Differentially Private SGD with Curriculum Learning
Write-up upon request.

Towards Physically-Consistent, Chaotic Spatiotemporal Dynamics with Echo State Networks
This study explores how echo state networks (ESNs) can be used in time-series forecasting of chaotic physics. We compare the performance of a basic ESN with two physics-informed variants, tested on the canonical Lorenz attractor. We then apply the ESN to a large-scale atmospheric model and a larger real-world weather dataset to test its ability to scale to large spatiotemporal systems. We find that a traditional ESN when properly tuned can outperform our equivalent physicsinformed methods. We also find that the ESN is capable of accurately predicting the global evolution of the atmospheric primitive equations over short time frames (∼67 hrs), but struggles to accurately predict real-world data.

Investigation on 1D Area Law and XXZ Model
An area law is investigated and verified for the von Neumann entanglement entropy of ground states in XXZ model, up to 14 qubits. The Schmidt coefficients of ground states of XXZ model with up to 13 qubits appear to be distributed exponentially. Slopes are studied to predict the slope of the Schmidt coefficients distribution of 14 qubits, and discrepancies are within 0.1 for 2 ≤ $\Delta$ ≤ 80. Quasi-approximate ground state projectors $K^t$ that can map random product states to ground states are also studied and Schmidt coefficients of these states also appear to be distributed exponentially up to 10 qubits. Code