Physics-Informed Transformer operator for the prediction of three-dimensional turbulence

TL;DR

This paper introduces physics-informed Transformer operators for 3D turbulence prediction, achieving high accuracy, stability, and efficiency without labeled data, and outperforming existing neural operators in long-term turbulence simulations.

Contribution

The paper develops PITO and PIITO, novel physics-informed Transformer-based operators that learn solution operators for turbulence prediction without labeled data and with reduced computational resources.

Findings

PITO and PIITO outperform PIFNO in long-term turbulence prediction.

They require significantly less GPU memory and fewer parameters than PIFNO.

Both models are faster than traditional LES methods.

Abstract

Data-driven turbulence prediction methods often face challenges related to data dependency and lack of physical interpretability. In this paper, we propose a physics-informed Transformer operator (PITO) and its implicit variant (PIITO) for predicting three-dimensional (3D) turbulence, which are developed based on the vision Transformer (ViT) architecture with an appropriate patch size. Given the current flow field, the Transformer operator computes its prediction for the next time step. By embedding the large-eddy simulation (LES) equations into the loss function, PITO and PIITO can learn solution operators without using labeled data. Furthermore, PITO can automatically learn the subgrid scale (SGS) coefficient using a single set of flow data during training. Both PITO and PIITO exhibit excellent stability and accuracy on the predictions of various statistical properties and flow structures for the situation of long-term extrapolation exceeding 25 times the training horizon in decaying homogeneous isotropic turbulence (HIT), and outperform the physics-informed Fourier neural operator (PIFNO). Furthermore, PITO exhibits a remarkable accuracy on the predictions of forced HIT where PIFNO fails. Notably, PITO and PIITO reduce GPU memory consumption by 79.5% and 91.3% while requiring only 31.5% and 3.1% of the parameters, respectively, compared to PIFNO. Moreover, both PITO and PIITO models are much faster compared to traditional LES method.