Jeremy Vachier

Theoretical Physicist | Associate Director Data Science

Blog

Technical posts about machine learning, deep learning, and research.


Deriving the Master Equation from Chapman-Kolmogorov

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.

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Absorbing Markov Chain Analysis for Predictive Maintenance

December 23, 2025

A mathematical framework for analyzing absorbing Markov chains to predict equipment failure and optimize maintenance strategies using fundamental matrix theory.

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Linear Regression - Analytic and Numerical Methods vs Sklearn

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.

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Building a Neural Network from Scratch - Understanding Adam Optimization

December 21, 2025

A deep dive into the mathematics behind neural networks and the Adam optimizer, implemented from scratch in NumPy for digit classification.

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