# Discretisation of regularity structures

## TL;DR

This paper develops a general framework to extend the theory of regularity structures to discretized stochastic PDEs, accommodating various discretisation methods without focusing on a specific procedure.

## Contribution

It introduces a flexible approach that applies regularity structures to discretizations using a scale parameter and a black box for sub-scale behavior, broadening applicability.

## Key findings

- Framework successfully extends regularity structures to discretized PDEs
- Applicable to various discretisation schemes without specific assumptions
- Facilitates analysis of stochastic PDEs in discrete settings

## Abstract

We introduce a general framework allowing to apply the theory of regularity structures to discretisations of stochastic PDEs. The approach pursued in this article is that we do not focus on any one specific discretisation procedure. Instead, we assume that we are given a scale $\varepsilon > 0$ and a "black box" describing the behaviour of our discretised objects at scales below $\varepsilon $.