# Learning Interface Breakup: A Geometry-Conditioned Latent Surrogate for Spray Formation

arXiv: https://arxiv.org/abs/2606.16587 · HTML: https://mlsanity.com/paper/2606.16587/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 22 references that are in the map.
- First posted on arXiv 15 Jun 2026.

## Builds on (most cited first, 10 of 10)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Neural Implicit Flow: a mesh-agnostic dimensionality reduction paradigm of spatio-temporal data](https://mlsanity.com/paper/2204.03216/) (2022)
- [Dynamics of a data-driven low-dimensional model of turbulent minimal Couette flow](https://mlsanity.com/paper/2301.04638/) (2023)
- [Accelerating Simulation of Two-Phase Flows with Neural PDE Surrogates](https://mlsanity.com/paper/2405.17260/) (2024)
- [Convolutional autoencoders for the reconstruction of three-dimensional interfacial multiphase flows](https://mlsanity.com/paper/2508.04084/) (2025)

## Abstract (arXiv)

Designing spray nozzles requires predicting how geometry shapes transient two-phase breakup, but high-fidelity volume-of-fluid (VOF) simulations with adaptive mesh refinement (AMR) are too expensive for iterative design exploration. Standard surrogate models are also challenged by this setting because both the liquid--gas interface and the underlying adaptive discretization evolve across time and geometries. We introduce a geometry-conditioned latent surrogate trained on 797 two-phase nozzle simulations that addresses this by encoding the AMR cell-density field, rather than the full multi-channel flow state, as a compact proxy for where the solver concentrates resolution. From this representation, the model reconstructs transient density evolution and nozzle geometry, and a lightweight second stage recovers the remaining flow variables. On held-out simulations, the method accurately captures key interface dynamics while reducing inference time to 0.045 seconds per trajectory, corresponding to a speed-up of more than 6×104 relative to Basilisk CFD. These results suggest that AMR refinement structure can serve as a compact and learnable representation for geometry-conditioned surrogate modeling of transient two-phase flows.