Aneesh Jonelagadda Personal Website

Projects:

Physics

• Quantum Band Structure Modeling: From 1D Chains to Graphene
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  A code-based quantum mechanical tight-binding framework designed to simulate and visualize electronic band structures. Code generalizes to any lattice given a basis as input and, for theoretical rigor, is grounded in worked-out analytical solutions for select Hamiltonians. Highlighted demonstrations include graphene's Dirac cones and emergent quantum phenomena such as massless electron behavior.

AI

• Lévy-Driven SDE Formulation of Stochastic Gradient Descent: 𝛂-Stable Jumps vs. Brownian Escape Dynamics via Radon Measure
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  A simulation analysis of the commonly used deep-learning optimizer "Stochastic Gradient Descent" (SGD) from a stochastic differential equation lens by formulating Gaussian and Lévy-𝛂-stable gradient noise and examining escape times on differently-shaped basins. Highlighted demonstrations include both theoretical and empirical escape-time dependence on gradient noise tail heaviness and basin geometry (quantified through escape-set Radon measure), and inadequacy of Brownian (𝛂=2: Gaussian) model to describe heavy-tailed gradient noise. We do the latter by numerically estimating 𝛂 from gradients sampled during training of a high-dimensional convolutional neural network.

Quantitative Finance Research

• Coming soon