On the Equivalence of the Newton-Raphson Algorithm and PDE of Conservation of Electric Charge

TL;DR

This paper establishes a theoretical equivalence between the Newton-Raphson algorithm and the PDE governing electric charge conservation, providing insights into their properties and potential applications in physics modeling.

Contribution

It introduces a novel theoretical link between numerical optimization and physical PDEs, and explores implications for statistical methods and physics embedding.

Findings

Proves the equivalence between Newton-Raphson and charge conservation PDEs.

Analyzes properties of Fisher-scoring method through this equivalence.

Proposes conjecture on embedding physics models into Newton's method.

Abstract

The main result characterises the equivalence of the Newton-Raphson algorithm and PDE of conservation of electric charge. Based on this equivalence we analyse the properties of the Fisher-scoring method, a variant of Newton's method commonly used in statistics. Conjecture of embedding physics models to solve Newton's method is proposed.