DeepONet prediction of linear instability waves in high-speed boundary layers

TL;DR

This paper demonstrates that DeepONets can efficiently predict the evolution of linear instability waves in high-speed boundary layers and perform data assimilation, significantly reducing computational costs compared to traditional methods.

Contribution

The authors develop and validate DeepONets for operator approximation of flow instability dynamics, enabling fast forward predictions and inverse problem solutions in high-speed boundary layers.

Findings

DeepONets accurately predict downstream flow disturbances.

They enable efficient data assimilation from wall measurements.

The approach reduces computational costs significantly.

Abstract

Deep operator networks (DeepONets) are trained to predict the linear amplification of instability waves in high-speed boundary layers and to perform data assimilation. In contrast to traditional networks that approximate functions, DeepONets are designed to approximate operators. Using this framework, we train a DeepONet to take as inputs an upstream disturbance and a downstream location of interest, and to provide as output the perturbation field downstream in the boundary layer. DeepONet thus approximates the linearized and parabolized Navier-Stokes operator for this flow. Once trained, the network can perform predictions of the downstream flow for a wide variety of inflow conditions, without the need to calculate the whole trajectory of the perturbations, and at a very small computational cost compared to discretization of the original equations. In addition, we show that DeepONets can solve the inverse problem, where downstream wall measurements are adopted as input and a trained network can predict the upstream disturbances that led to these observations. This capability, along with the forward predictions, allows us to perform a full data assimilation cycle: starting from wall-pressure data, we predict the upstream disturbance using the inverse DeepONet and its evolution using the forward DeepONet.