Universal approximations of quasilinear PDEs by finite distinguishable particle systems

TL;DR

This paper demonstrates that solutions to any quasilinear PDE can be approximated by finite systems of distinguishable particles with an error decreasing as 1/ln(N), linking PDE theory with graph limit concepts.

Contribution

It introduces a novel approximation method connecting quasilinear PDE solutions with finite particle systems, expanding the understanding of PDE approximation techniques.

Findings

Approximation error decreases as 1/ln(N)

Solutions of PDEs can be represented by particle systems

Links between PDEs and graph limit theory established

Abstract

In this paper, we prove that sufficiently regular solutions of any quasilinear PDE can be approximated by solutions of systems of N distinguishable particles, to within 1/ ln(N ). This intruiguing result is related to recent developments in graph limit theory.