Transformers for Modeling Physical Systems

TL;DR

This paper introduces transformer models combined with Koopman embeddings to predict physical dynamical systems, achieving superior accuracy over traditional methods in scientific machine learning.

Contribution

It presents a novel approach integrating transformers with Koopman embeddings for modeling and predicting physical dynamical systems.

Findings

Transformer-based models outperform classical methods in system prediction.

Koopman embeddings effectively project dynamical systems into predictive vector spaces.

The approach demonstrates high accuracy across various physical phenomena.

Abstract

Transformers are widely used in natural language processing due to their ability to model longer-term dependencies in text. Although these models achieve state-of-the-art performance for many language related tasks, their applicability outside of the natural language processing field has been minimal. In this work, we propose the use of transformer models for the prediction of dynamical systems representative of physical phenomena. The use of Koopman based embeddings provide a unique and powerful method for projecting any dynamical system into a vector representation which can then be predicted by a transformer. The proposed model is able to accurately predict various dynamical systems and outperform classical methods that are commonly used in the scientific machine learning literature.