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

Bubbly flows exhibit complex multiscale dynamics, with deformable bubbles interacting through the surrounding liquid and giving rise to strongly coupled kinematic and morphological behavior. We present BubbleSH, a bubbly flows dataset consisting of transient, three-dimensional bubble-swarm dynamics obtained from high-fidelity direct numerical simulations of bubbles rising in a periodic domain. The dataset provides time-resolved bubble trajectories, velocities, and shape evolution, with bubble morphology compactly represented using spherical harmonics. Designed to be lightweight yet physically expressive, the dataset enables data-driven modeling of bubbly flow simulators where shape deformation and bubble-bubble interactions play a central role. We characterize the dataset with bubble kinematics, morphology, and interaction patterns, and introduce evaluation metrics for both trajectory and shape prediction. The sensitivity of bubble-swarm dynamics to local perturbations makes BubbleSH particularly well suited to generative models that learn distributions over possible future trajectories. We evaluate a permutationally and translationally equivariant probabilistic emulator on BubbleSH given the proposed metrics. Therefore, we establish a compact, high-fidelity dataset and a benchmark for developing and evaluating data-driven models of deformable, chaotic multiphase systems.

Compressible multiphase flows involving shocks and material interfaces arise in applications such as bubble collapse and droplet breakup, where strong nonlinear interactions produce complex interface deformation, mixing, and multiscale dynamics. Developing reliable machine learning surrogates for these flows remains challenging due to the simultaneous presence of compressibility, sharp discontinuities, and multiphase effects. In this work, we introduce the first large-scale benchmark specifically designed for shock-driven compressible multiphase flows, comprising 3 TB of high-fidelity 2D and 3D datasets featuring shock-induced bubble collapse and droplet breakup. We evaluate diverse surrogate model families on our benchmarking framework: Neptuna, including convolutional, spectral, transformer-based, and pre-trained PDE foundation models. Beyond standard MSE training, we investigate composite losses that combine MSE with Sobolev, interface-aware, and structure-aware terms, along with adaptive loss balancing using SoftAdapt and GradNorm. Evaluation includes pointwise, spectral, feature-focused, structural, and physics-informed metrics. Results show that no single model performs best across all datasets and metrics, while composite losses significantly improve interface preservation and spectral fidelity. Among adaptive weighting strategies, SoftAdapt provides the most consistent improvements with almost no overhead compared to MSE-only training. The benchmarking repository and the dataset are made available at https://tumaer.github.io/Neptuna/

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 $6\times10^4$ 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.