🤖 machine learning

BubbleSH: A Dataset of Rising Bubbles with Deformable Interfaces

This paper introduces BubbleSH, a high-fidelity dataset of transient 3D bubble-swarm dynamics with deformable interfaces derived from direct numerical simulations, which serves as a benchmark for developing and evaluating data-driven models and generative emulators for chaotic multiphase systems.

Original authors: Rachna Ramesh, Kiet Bennema ten Brinke, Douwe Orij, Ivo Roghair, Vlado Menkovski

Published 2026-07-09

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CC BY 4.0

Original authors: Rachna Ramesh, Kiet Bennema ten Brinke, Douwe Orij, Ivo Roghair, Vlado Menkovski

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a crowded dance floor where hundreds of dancers (bubbles) are trying to move upward through a thick, sticky liquid. In the real world, these dancers don't just move in straight lines; they wiggle, stretch, squash, and bump into each other, changing their shapes constantly. This chaotic movement is called a "bubbly flow," and it happens in everything from beer brewing to industrial chemical reactors.

The problem is that understanding this dance is incredibly hard. If you try to film it in a real tank, the bubbles block the camera view. If you try to simulate it on a supercomputer, the math is so complex that it takes days to simulate just a few seconds of movement.

Enter "BubbleSH": A New Way to Watch the Dance

This paper introduces a new dataset called BubbleSH. Think of it as a high-definition, perfectly organized "replay" of that bubble dance floor, created entirely by a computer simulation.

Here is how they made it and why it's special, using simple analogies:

1. The "Perfect Camera" (Front-Tracking)

Usually, computer simulations of fluids are like trying to guess the shape of a balloon by looking at a blurry, low-resolution photo. They often miss the fine details or accidentally make two bubbles merge when they shouldn't.

The researchers used a method called Front-Tracking. Imagine a camera that doesn't just take a picture of the air and water mixed together, but instead puts a tiny, invisible "net" around every single bubble. This net moves with the bubble, stretching and shrinking exactly as the bubble does. This allows them to see every wiggle and wobble without any "blur" or accidental merging.

2. The "Magic Shrink-Ray" (Spherical Harmonics)

The raw data from this "perfect camera" is huge. Every bubble is made of thousands of tiny triangles (like a very detailed 3D model). Storing all that detail for thousands of bubbles over time would fill up a hard drive instantly.

To solve this, the researchers used a mathematical trick called Spherical Harmonics.

The Analogy: Imagine you have a lumpy, wobbly potato. Instead of saving a photo of every bump and scratch, you describe the potato by saying: "It's mostly round, but it's slightly squashed on the left, and it has a small bump on top."
The Result: They turned the complex 3D shape of each bubble into a short list of numbers (coefficients). This is like compressing a 4K movie into a tiny text file. It keeps all the important information about the bubble's shape but makes the data small enough to actually use for training AI.

3. The "Chaotic Classroom" (The Dataset)

The dataset contains simulations of bubbles rising in a box where the walls disappear (if a bubble leaves the top, it reappears at the bottom). They tested different sizes of bubbles and different "crowdedness" levels (how many bubbles are in the box).

They found that as the box gets more crowded:

The bubbles move slower.
They take more twisted, "tortuous" paths (like a drunk walk).
They wiggle and change shape more violently.

4. The "Crystal Ball" Test (The AI Model)

The authors didn't just make the data; they built a "student" (an AI model) to learn from it. They asked the AI: "Here is how the bubbles moved for the last 20 milliseconds. Can you guess where they will be and what they will look like for the next 20 milliseconds?"

The Challenge: Because the bubbles interact chaotically, there isn't just one correct answer. There are many possible futures. A good AI shouldn't just memorize one path; it should understand the rules of the dance and be able to predict a range of realistic possibilities.
The Result: The AI learned to predict the bubbles' paths and shapes very well. It was 260,000 times faster than the original supercomputer simulation. While the supercomputer took days to simulate a few seconds, the AI did it in less than a second.

Why This Matters

Think of this dataset as a "textbook" for teaching computers how to understand complex, squishy, interacting objects.

Before: Engineers had to choose between slow, perfect simulations or fast, but inaccurate, guesses.
Now: With BubbleSH, they can train AI to be both fast and accurate. The AI learns the "physics" of the bubbles from the data, allowing engineers to design better reactors or processes without waiting days for a computer to finish a calculation.

In short, BubbleSH is a library of "bubble dance moves" that helps computers learn to predict how bubbles will behave, stretching, squashing, and swirling, at a speed that makes real-world engineering possible.

Technical Summary: BubbleSH Dataset and Benchmark for Deformable Bubble Swarms

Problem Statement

Bubbly flows, prevalent in chemical reactors and industrial processes, exhibit complex multiscale dynamics where deformable bubbles interact through the surrounding liquid, leading to strongly coupled kinematic and morphological behaviors. While Direct Numerical Simulations (DNS) using interface-resolving methods like Front-Tracking (FT) provide high-fidelity data on individual bubble dynamics, they are computationally prohibitive for large-scale applications. Consequently, practical engineering models (e.g., Euler–Lagrange) rely on time-averaged correlations that collapse rich information regarding bubble-to-bubble variability, transient deformation, and local interactions into effective coefficients.

A critical bottleneck in developing data-driven emulators to bridge this gap is the lack of high-quality, openly available datasets that capture transient, three-dimensional bubble dynamics at the individual bubble level within swarms. Existing datasets are primarily image-based (focused on detection/segmentation) or static reconstructions, lacking the time-resolved, physics-consistent state representations required for learning dynamical systems with deformable surfaces.

Methodology

Data Generation

The BubbleSH dataset is derived from high-fidelity DNS using a three-dimensional Front-Tracking (FT) method for incompressible two-phase flow (air-water system).

Simulation Physics: The flow is governed by the incompressible Navier–Stokes equations on a staggered Cartesian grid. The gas-liquid interface is explicitly tracked by a moving triangular surface mesh. The FT method prevents unphysical numerical coalescence, allowing the study of bubble-swarm interactions without artificial merging.
Domain: Simulations occur in a fully periodic cubic domain, representing an infinite bubble swarm without wall effects.
Parameters: The dataset covers 24 configurations varying bubble diameter ( $d \in \{4, 5, 6\}$ mm) and gas volume fraction ( $\varepsilon \in \{5\% \dots 40\%$ ). Each configuration tracks a swarm of $N=32$ bubbles.
Output: Data is recorded at temporal resolutions of 0.1 ms or 1 ms, capturing centroid positions, velocities, and full surface meshes.

Compact Representation (Spherical Harmonics)

To address the storage intensity of raw mesh data (approx. $10^4$ nodes per bubble), the dataset employs a Spherical Harmonics (SH) representation.

The bubble surface $r(\theta, \phi)$ is approximated by a truncated SH expansion:
$r(\theta, \phi) \approx \sum_{\ell=0}^{L} \sum_{m=-\ell}^{\ell} c_{\ell m} Y_{\ell}^{m}(\theta, \phi)$
Using a truncation order $L=14$ , each bubble is represented by 225 coefficients. This reduces the data footprint by a factor of $\sim 173\times$ while maintaining a Mean Absolute Percentage Error (MAPE) on surface area reconstruction below 0.1%.
This representation assumes star-shaped bubbles relative to their centroid, which is appropriate for the deformable regimes simulated.

Evaluation Metrics

The paper introduces a dual-layered evaluation framework to assess both geometric accuracy and physical consistency:

Point-Based Metrics:
- Relative Average/Final Displacement Error (R-ADE/R-FDE): Normalizes trajectory errors by the ground truth arc length to ensure dimensionless, scale-invariant comparison.
- Relative Average Chamfer Distance (R-ACD): Normalizes shape prediction errors by the total change in surface geometry over time.
Distribution-Based Metrics:
- 1-Wasserstein Distance ( $W_1$ ): Used to measure the similarity between predicted and ground-truth distributions of kinematic (velocity, rise angle), morphological (surface area, sphericity), and interaction (radial distribution, pairwise velocity angles) quantities. This is crucial for probabilistic models where multiple physically valid futures exist, preventing the conflation of diversity with error.

Key Contributions

BubbleSH Dataset: A publicly available, compact, high-fidelity dataset of rising bubble swarms. It uniquely combines time-resolved centroid trajectories with continuous SH-based shape descriptors, bridging the gap between rigid particle benchmarks and mesh-based continuum simulations.
Benchmarking Framework: The introduction of evaluation metrics that account for the stochastic nature of turbulent bubbly flows, specifically utilizing distributional comparisons (Wasserstein distance) alongside standard displacement errors.
Generative Emulator Baseline: A probabilistic generative model (based on STFlow and conditional flow matching) trained on BubbleSH. The model jointly predicts bubble trajectories and shape evolution, demonstrating that data-driven approaches can capture complex many-body interactions and deformable geometry.

Results

The authors evaluated the proposed generative model against a random-walk prior and ablation variants (conditional independence, lower SH order):

Performance: The full model ( $L=5$ ) significantly outperformed the random-walk prior across all metrics, achieving lower displacement errors and better distributional alignment (lower $W_1$ scores).
Interaction Learning: An ablation study removing spatial interaction layers showed surprisingly similar performance to the full model, suggesting the current model does not yet fully capture spatial inter-bubble interactions, or that the specific metrics used are not sensitive enough to distinguish them.
Shape Truncation: Reducing the SH order to $L=3$ lowered displacement errors but increased morphology dissimilarity, confirming that aggressive truncation limits the reproduction of accurate deformations.
Computational Efficiency: The trained emulator achieved a speedup of 260,000x to 58,000x over the original FT simulator (running 0.1s of simulation in ~0.85 seconds vs. days), while retaining per-bubble fidelity.

Significance and Claims

The paper positions BubbleSH as a foundational resource for developing data-driven emulators for deformable, chaotic multiphase systems.

Bridging the Gap: It offers a path to scalable modeling that retains individual bubble variability, which is lost in traditional averaged models but computationally expensive in DNS.
Benchmark Utility: By providing both the data and a rigorous evaluation framework (combining trajectory, shape, and distributional metrics), it enables the systematic development of geometric deep learning models that handle coupled trajectories and time-varying surface geometry.
Probabilistic Modeling: The dataset's sensitivity to local perturbations makes it particularly well-suited for generative models that learn distributions over possible future trajectories, rather than deterministic point predictions.

Limitations: The authors note that the dataset is restricted to idealized air-water systems in periodic domains (no wall effects, breakup, coalescence, or surfactants). The parameter space covers specific Reynolds (100–1000) and Eötvös (2–5) numbers, excluding nearly spherical or spherical-cap regimes. Additionally, SH truncation can introduce Gibbs-type oscillations, and the current benchmark model has limitations in long-horizon stability and rotational symmetry handling.