Theoretical Physicist | Associate Director Data Science
Technical posts about machine learning, deep learning, and research.
May 22, 2026
Methods in information retrieval from classical keyword matching to neural encoders trained with contrastive objectives, with core equations, key papers, and benchmarks on a synthetic industrial dataset.
May 16, 2026
A physics-informed machine learning pipeline rooted in the Langevin equation, training neural networks to learn probability density evolution governed by the Fokker–Planck equation, with rollout driven by analytic teacher forcing rather than simulation data.
February 15, 2026
Understanding Retrieval-Augmented Generation through the lens of Hilbert spaces, explaining why L2 normalization is essential for semantic similarity and how geometric search structures enable efficient document retrieval.
January 01, 2026
Deriving the effective equation for Active Brownian Particles using multiple scale expansion.
December 25, 2025
A rigorous mathematical derivation of the master equation for jump Markov processes, with applications spanning bacterial biofilm dynamics, antibiotic resistance strategies, and machine learning optimization.
December 23, 2025
A mathematical framework for analyzing absorbing Markov chains to predict equipment failure and optimize maintenance strategies using fundamental matrix theory.
December 22, 2025
A comprehensive comparison of three approaches to linear regression - implementing the analytic solution using least squares, numerical optimization with gradient descent, and scikit-learn’s optimized library.
December 21, 2025
A deep dive into the mathematics behind neural networks and the Adam optimizer, implemented from scratch in NumPy for digit classification.