Shock-Aware Physics-Guided Fusion-DeepONet Operator for Rarefied Micro-Nozzle Flows

TL;DR

This paper introduces a physics-aware deep learning framework combining a Fusion DeepONet architecture, shock-aligned features, and curriculum training to efficiently model complex micro-nozzle flows with shocks, validated on Burgers' equation.

Contribution

It proposes a novel integrated deep learning approach for shock-containing micro-flow modeling, emphasizing physics-guided features and curriculum strategies for improved accuracy.

Findings

Effective surrogate modeling of shock flows demonstrated.

Framework generalizes well to Burgers' equation.

Enhanced accuracy in high-gradient regions achieved.

Abstract

We present a comprehensive, physics aware deep learning framework for constructing fast and accurate surrogate models of rarefied, shock containing micro nozzle flows. The framework integrates three key components, a Fusion DeepONet operator learning architecture for capturing parameter dependencies, a physics-guided feature space that embeds a shock-aligned coordinate system, and a two-phase curriculum strategy emphasizing high-gradient regions. To demonstrate the generality and inductive bias of the proposed framework, we first validate it on the canonical viscous Burgers equation, which exhibits advective steepening and shock like gradients.