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

arXiv: https://arxiv.org/abs/2510.17887 · HTML: https://mlsanity.com/paper/2510.17887/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 26 references that are in the map.
- First posted on arXiv 18 Oct 2025.

## Builds on (most cited first, 3 of 3)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Fusion-DeepONet: A Data-Efficient Neural Operator for Geometry-Dependent Hypersonic and Supersonic Flows](https://mlsanity.com/paper/2501.01934/) (2025)
- [AMR-Transformer: Enabling Efficient Long-range Interaction for Complex Neural Fluid Simulation](https://mlsanity.com/paper/2503.10257/) (2025)

## Built on by (most cited first, 2 of 2)

- [Smooth Piecewise Cutting for Neural Operator to Handle Discontinuities and Sharp Transitions](https://mlsanity.com/paper/2605.19823/) (2026)
- [MeshTok: Efficient Multi-Scale Tokenization for Scalable PDE Transformers](https://mlsanity.com/paper/2606.04366/) (2026)

## Abstract (arXiv)

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.