# Probabilistic Simulation of Gas-Liquid Interfaces with Coupled Flow Matching on Spherical Harmonics

arXiv: https://arxiv.org/abs/2610.16327 · HTML: https://mlsanity.com/paper/2610.16327/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Flow matching, time series and science, one of 14 directions in Diffusion models.
- Builds on 21 of its 38 references that are in the map.
- First posted on arXiv 12 Oct 2026.

## Placed in

- Diffusion models / [Flow matching, time series and science](https://mlsanity.com/diffusion/flow-matching-time-series-and-science/)

## Builds on (most cited first, 21 of 21)

- [Diffusion Models Beat GANs on Image Synthesis](https://mlsanity.com/paper/2105.05233/) (2021)
- [Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow](https://mlsanity.com/paper/2209.03003/) (2022)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Improving and generalizing flow-based generative models with minibatch optimal transport](https://mlsanity.com/paper/2302.00482/) (2023)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [MotionDiffuser: Controllable Multi-Agent Motion Prediction using Diffusion](https://mlsanity.com/paper/2306.03083/) (2023)
- [Leapfrog Diffusion Model for Stochastic Trajectory Prediction](https://mlsanity.com/paper/2303.10895/) (2023)
- [Density-aware Chamfer Distance as a Comprehensive Metric for Point Cloud Completion](https://mlsanity.com/paper/2111.12702/) (2021)
- [Stochastic interpolants with data-dependent couplings](https://mlsanity.com/paper/2310.03725/) (2023)
- [Social Ways: Learning Multi-Modal Distributions of Pedestrian Trajectories with GANs](https://mlsanity.com/paper/1904.09507/) (2019)
- [SocialVAE: Human Trajectory Prediction using Timewise Latents](https://mlsanity.com/paper/2203.08207/) (2022)
- [FlowDAS: A Stochastic Interpolant-based Framework for Data Assimilation](https://mlsanity.com/paper/2501.16642/) (2025)
- [BubbleML: A Multi-Physics Dataset and Benchmarks for Machine Learning](https://mlsanity.com/paper/2307.14623/) (2023)
- [Geometric Trajectory Diffusion Models](https://mlsanity.com/paper/2410.13027/) (2024)
- [Efficient Trajectory Forecasting and Generation with Conditional Flow Matching](https://mlsanity.com/paper/2403.10809/) (2024)
- [STFlow: Data-Coupled Flow Matching for Geometric Trajectory Simulation](https://mlsanity.com/paper/2505.18647/) (2025)
- [LaM-SLidE: Latent Space Modeling of Spatial Dynamical Systems via Linked Entities](https://mlsanity.com/paper/2502.12128/) (2025)
- [BubbleSH: A Dataset of Rising Bubbles with Deformable Interfaces](https://mlsanity.com/paper/2607.07275/) (2026)

## Abstract (arXiv)

Bubbly flows involve strongly coupled bubble motion, deformation, and hydrodynamic interactions, making high-fidelity simulation computationally expensive. We propose a neural surrogate that jointly predicts bubble trajectories and interface deformation in a compact, shared representation, replacing costly mesh-resolved simulation with fast generative inference. Because two-phase flow dynamics is nonlinear and chaotic, we treat forecasting as a conditional generative problem rather than deterministic regression, predicting entire future windows in a single pass. We train and evaluate the surrogate on BubbleSH, a Front-Tracking dataset of rising deformable bubble swarms, assessing performance using trajectory, shape, and distributional metrics over kinematic, morphological, and interaction-based properties. The surrogate reproduces key flow statistics while running several orders of magnitude faster than the underlying DNS solver.