Transformers for modeling physical systems. (February 2022) - Geneva, Nicholas; Zabaras, Nicholas
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 provides 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. 1 Highlights: Application of self–attention transformer models for modeling physical dynamics. Use of Koopman dynamics for physics–inspired embeddings of high–dimensional systems. Discussion of the relations between self–attention with numerical time–integration. Model demonstration for high-dimensional partial differential equation problems. First work to explore transformers for surrogate modeling physical systems.