Solving Partial Differential Equations with Equivariant Extreme Learning Machines

TL;DR

This paper introduces an innovative approach using equivariant extreme learning machines to efficiently predict PDEs, achieving high accuracy with minimal data by leveraging symmetry and windowed predictions.

Contribution

It presents a novel method combining extreme learning machines with symmetry exploitation for PDE prediction, enabling high accuracy from limited data.

Findings

High accuracy in PDE prediction with few data points

Effective use of symmetries to improve sample efficiency

Ability to predict PDE flow over long time horizons

Abstract

We utilize extreme-learning machines for the prediction of partial differential equations (PDEs). Our method splits the state space into multiple windows that are predicted individually using a single model. Despite requiring only few data points (in some cases, our method can learn from a single full-state snapshot), it still achieves high accuracy and can predict the flow of PDEs over long time horizons. Moreover, we show how additional symmetries can be exploited to increase sample efficiency and to enforce equivariance.